# The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being

Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens, Basile Chaix

► To cite this version:

Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens, Basile Chaix. The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being. Peer Community Journal, 2024, 4, pp.e23. 10.24072/pcjournal.388 . hal-04565549

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Submitted on 2 May 2024

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<figure><img src="image_1.png" /></figure>
# The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being

Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens, Basile Chaix

► To cite this version:

Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens, Basile Chaix. The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being. Peer Community Journal, 2024, 4, pp.e23. 10.24072/pcjournal.388. hal-04565549

HAL Id: hal-04565549

https://hal.science/hal-04565549v1

Submitted on 2 May 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
Research article

Published
2024-02-29

**Cite as**
Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens and Basile Chaix (2024) *The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being*, Peer Community Journal, 4: e23.

**Correspondence**
cedric.sueur@iphc.cnrs.fr

**Peer-review**
Peer reviewed and
recommended by
PCI Network Science,
https://doi.org/10.24072/pci-
networksci.100112

<figure><img src="image_2.png" /></figure>

This article is licensed
under the Creative Commons
Attribution 4.0 License.

# The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being

Cédric Sueur<fnref n="1" />,<fnref n="1" />, Giovanna Fancello², Alexandre Naud<fnref n="1" />, Yan Kestens³, and Basile Chaix²

Volume 4 (2024), article e23

https://doi.org/10.24072/pcjournal.388

## Abstract

Social networks play a crucial role in promoting healthy aging, yet the intricate mechanisms connecting social capital to health present a complex challenge. Additionally, the majority of social network analysis studies focusing on older adults typically concentrate on the participants' individual relationships, often overlooking the interconnections between these relationships. In this study, we went further than current ego-centered network studies by determining global social network metrics and the structure of relationships among older adult participants of the RECORD Cohort using the Veritas-Social questionnaire. The aim of this study is to identify key dimensions of social networks of older adults, and to evaluate how these dimensions relate to depressive symptoms, life satisfaction, and well-being. Using Principal Component Analyses (PCA), we identified four social network dimensions with psychological meanings. Dimension 1 (homophily) was positively linked with perceived accessibility to services in one's residential neighborhood but this same dimension was negatively linked with the level of study (i.e., Bachelor, Master, PhD, etc.). Dimension 2 (social integration) and Dimension 3 (social support) were only linked to the number of people living (being in the same residence) with ego (i.e. the interviewed participant). Dimension 4 was linked with perceived accessibility to local services. Finally, and rather surprisingly, we found that none of the four network dimensions, even the degree, were linked to the three health status metrics.

<figure><img src="image_3.png" /></figure>

<footnote n="1">¹UMR 7178, CNRS, Unistra, Institut Pluridisciplinaire Hubert Curien, Strasbourg, France, ²Sorbonne Université, INSERM, Institut Pierre Louis d'Épidémiologie et de Santé Publique, Nemesis research team, F75012, Paris, France, ³Université de Montréal/Centre de Recherche du CHUM, Pavillon S, 850 Rue St-Denis, Montréal, QC, H2X 0A9, Canada</footnote>
Research article

Published
2024-02-29

**Cite as**
Cédric Sueur, Giovanna Fancello, Alexandre Naud, Yan Kestens and Basile Chaix (2024) *The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being*, Peer Community Journal, 4: e23.

**Correspondence**
cedric.sueur@iphc.cnrs.fr

**Peer-review**
Peer reviewed and
recommended by
PCI Network Science,
https://doi.org/10.24072/pci.
networksci.100112

<figure><img src="image_2.png" /></figure>

BY

This article is licensed
under the Creative Commons
Attribution 4.0 License.

# The Complexity of Social Networks in Healthy Aging: Novel Metrics and Their Associations with Psychological Well-Being

Cédric Sueur<fnref n="1" />,<fnref n="1" />, Giovanna Fancello², Alexandre Naud<fnref n="1" />, Yan Kestens³, and Basile Chaix²

Volume 4 (2024), article e23

https://doi.org/10.24072/pcjournal.388

## Abstract

Social networks play a crucial role in promoting healthy aging, yet the intricate mechanisms connecting social capital to health present a complex challenge. Additionally, the majority of social network analysis studies focusing on older adults typically concentrate on the participants' individual relationships, often overlooking the interconnections between these relationships. In this study, we went further than current ego-centered network studies by determining global social network metrics and the structure of relationships among older adult participants of the RECORD Cohort using the Veritas-Social questionnaire. The aim of this study is to identify key dimensions of social networks of older adults, and to evaluate how these dimensions relate to depressive symptoms, life satisfaction, and well-being. Using Principal Component Analyses (PCA), we identified four social network dimensions with psychological meanings. Dimension 1 (homophily) was positively linked with perceived accessibility to services in one's residential neighborhood but this same dimension was negatively linked with the level of study (i.e., Bachelor, Master, PhD, etc.). Dimension 2 (social integration) and Dimension 3 (social support) were only linked to the number of people living (being in the same residence) with ego (i.e. the interviewed participant). Dimension 4 was linked with perceived accessibility to local services. Finally, and rather surprisingly, we found that none of the four network dimensions, even the degree, were linked to the three health status metrics.

<figure><img src="image_3.png" /></figure>

<footnote n="1">¹UMR 7178, CNRS, Unistra, Institut Pluridisciplinaire Hubert Curien, Strasbourg, France, ²Sorbonne Université, INSERM, Institut Pierre Louis d'Épidémiologie et de Santé Publique, Nemesis research team, F75012, Paris, France, ³Université de Montréal/Centre de Recherche du CHUM, Pavillon S, 850 Rue St-Denis, Montréal, QC, H2X 0A9, Canada</footnote>
Introduction

Influence of social relationships on human health has been widely studied for decades. Since the seminal work on social integration and all-cause mortality (House et al., 1988), a large body of research has shown that a lack of positive social relationships is a risk factor for all-cause mortality (Holt-Lunstad et al., 2010) with effect sizes comparable to or greater (although perhaps less consistent, meaning with more individual variations) than those of smoking and obesity (Flegal et al., 2013; Carter et al., 2015). There is also strong and multiple evidence linking social relationships to various disease-related outcomes; however, the mechanisms that explain these associations remain largely unknown and likely involve a series of complex and intertwined behavioral, psychological, and biological pathways (Berkman et al., 2014; Sueur et al., 2021).

These complex relationships between social networks and health persist in later life (Rook, 2015), suggesting that positive social relationships may be an important factor in promoting healthy aging. Nevertheless, a difficulty in gerontological research is that individuals—even those from the same population—exhibit great variability in their rate of aging. 'Aging differently' means that at the same chronological age (e.g. 81 years), we may not have the same health status and/or mortality risk (i.e., biological aging). This variability is multifactorial, with a range of causes, including the physical design and structure of cities and buildings (the built environment), sociodemographic factors, mobility, and social networks. What is more, successful aging also means 'aging in place', that is, having the resources and ability to live in one's own home and community. Aging in place is generally what older adults want—it sustains the sense of belonging to a community and favors the maintenance of social ties (Gardner, 2011; Rook, 2015), two dimensions associated with positive outcomes, including better physical and mental health, lower stress, physical activity, and survival. Social isolation and perceived loneliness can be particularly detrimental in old age. Both dimensions increase the risk of depression and contribute to cognitive decline, diminished immune function, and all-cause mortality (Barnes et al., 2004; Giles et al., 2005; Cacioppo et al., 2006; Uchino, 2006).

The mechanisms linking social network dimensions to healthy aging are complex. Social networks, participation, integration, and support are distinct concepts that interact in a complex dynamic system. Social networks encompass the aggregation and portrayal of social relationships. Social support encompasses emotional, social, physical, and financial assistance, while social engagement involves participation in various activities. Social connectedness is characterized by the sense of being cared for and experiencing a sense of belonging. Finally, social integration was considered to be related to the sense of belonging to a social network. Some social network characteristics have been linked to positive social integration and participation (Berkman et al., 2014); social network size increases the likelihood of engagement and social participation and promotes the development of a sense of community belonging (Wilkinson, 1991; Bell, 1998), which, in turn, increases the perception of social integration. Differently, social participation opens up opportunities to create new relationships and expand one's social network (Stern et al., 2011). However, network size does only seem to be positively linked to social support to a certain extent (Seeman & Berkman, 1988; Wellman, 1992). Based on a Dutch sample, Aartsen et al. (2004) found that as adults age, their networks increasingly consist of family members, and network size influences or is influenced by personal cognitive and physical decline. Recent research has emphasized the type and structure of social networks in which older adults are embedded and their implications for health. Litwin and Shiovitz-Ezra (2006), for instance, found that the association between network type and mortality was important primarily for persons aged 70 years and older; those in diverse, friend-focused, and, to a lesser extent, community-clan networks experienced a lower risk of all-cause mortality. Similarly, Cornwell (2009) examined the patterns of network bridging among older adults, hypothesizing that individuals who occupy bridge positions within their networks benefit from improved access to diverse resources and better control over the exchange of information and resources among network members. Cornwell (2009) found that older adults are more likely to serve as bridges, as measured through the betweenness coefficient if they exhibit good cognitive and functional health. While we analyzed correlations between network indices and well-being of people in France (Fernandes et al., 2021; Fancello et al., 2023) or in Canada (Kestens et al., 2016; Naud et al., 2020), we need more formal social network
Introduction

Influence of social relationships on human health has been widely studied for decades. Since the seminal work on social integration and all-cause mortality (House et al., 1988), a large body of research has shown that a lack of positive social relationships is a risk factor for all-cause mortality (Holt-Lunstad et al., 2010) with effect sizes comparable to or greater (although perhaps less consistent, meaning with more individual variations) than those of smoking and obesity (Flegal et al., 2013; Carter et al., 2015). There is also strong and multiple evidence linking social relationships to various disease-related outcomes; however, the mechanisms that explain these associations remain largely unknown and likely involve a series of complex and intertwined behavioral, psychological, and biological pathways (Berkman et al., 2014; Sueur et al., 2021).

These complex relationships between social networks and health persist in later life (Rook, 2015), suggesting that positive social relationships may be an important factor in promoting healthy aging. Nevertheless, a difficulty in gerontological research is that individuals—even those from the same population—exhibit great variability in their rate of aging. ‘Aging differently’ means that at the same chronological age (e.g. 81 years), we may not have the same health status and/or mortality risk (i.e., biological aging). This variability is multifactorial, with a range of causes, including the physical design and structure of cities and buildings (the built environment), sociodemographic factors, mobility, and social networks. What is more, successful aging also means ‘aging in place’, that is, having the resources and ability to live in one’s own home and community. Aging in place is generally what older adults want—it sustains the sense of belonging to a community and favors the maintenance of social ties (Gardner, 2011; Rook, 2015), two dimensions associated with positive outcomes, including better physical and mental health, lower stress, physical activity, and survival. Social isolation and perceived loneliness can be particularly detrimental in old age. Both dimensions increase the risk of depression and contribute to cognitive decline, diminished immune function, and all-cause mortality (Barnes et al., 2004; Giles et al., 2005; Cacioppo et al., 2006; Uchino, 2006).

The mechanisms linking social network dimensions to healthy aging are complex. Social networks, participation, integration, and support are distinct concepts that interact in a complex dynamic system. Social networks encompass the aggregation and portrayal of social relationships. Social support encompasses emotional, social, physical, and financial assistance, while social engagement involves participation in various activities. Social connectedness is characterized by the sense of being cared for and experiencing a sense of belonging. Finally, social integration was considered to be related to the sense of belonging to a social network. Some social network characteristics have been linked to positive social integration and participation (Berkman et al., 2014); social network size increases the likelihood of engagement and social participation and promotes the development of a sense of community belonging (Wilkinson, 1991; Bell, 1998), which, in turn, increases the perception of social integration. Differently, social participation opens up opportunities to create new relationships and expand one’s social network (Stern et al., 2011). However, network size does only seem to be positively linked to social support to a certain extent (Seeman & Berkman, 1988; Wellman, 1992). Based on a Dutch sample, Aartsen et al. (2004) found that as adults age, their networks increasingly consist of family members, and network size influences or is influenced by personal cognitive and physical decline. Recent research has emphasized the type and structure of social networks in which older adults are embedded and their implications for health. Litwin and Shiovitz-Ezra (2006), for instance, found that the association between network type and mortality was important primarily for persons aged 70 years and older; those in diverse, friend-focused, and, to a lesser extent, community-clan networks experienced a lower risk of all-cause mortality. Similarly, Cornwell (2009) examined the patterns of network bridging among older adults, hypothesizing that individuals who occupy bridge positions within their networks benefit from improved access to diverse resources and better control over the exchange of information and resources among network members. Cornwell (2009) found that older adults are more likely to serve as bridges, as measured through the betweenness coefficient if they exhibit good cognitive and functional health. While we analyzed correlations between network indices and well-being of people in France (Fernandes et al., 2021; Fancello et al., 2023) or in Canada (Kestens et al., 2016; Naud et al., 2020), we need more formal social network
analyses (more quantitative and less subjective) to establish the links between participant characteristics, their relationships, and their health and well-being.

This paper addresses two important methodological issues, one about the statistical interdependence of network measures, one about the dependence of these measures with healthy aging. Usually correlations are made between different network metrics and measures of wellbeing but many social network indices are dependent and this may lead to false positive results and incorrect conclusions (Sosa et al., 2020, 2021). In this paper, we adopted a new way to test data in order to avoid this data interdependence and potentially false positives and false negatives. Some studies already address this dependence of network measures. Vacca (2020) introduced an innovative method for identifying structural typologies in personal networks, highlighting the considerable impact of personal network structure — the interconnections among an individual's contacts — on social outcomes. This method was contrasted with another recent approach, revealing that while both effectively capture variations in network structures, they also show significant discrepancies and cross-classification. These findings hold promise for future research in areas such as personal communities, social support, and social capital. Bidart et al. (2018) introduced a typology of personal networks, constructed from detailed data on young French individuals in a longitudinal study, which relies on a limited set of indicators related to the structure of relationships between individuals, with the goal of creating a generalizable approach applicable to different surveys. Finally, Charbey & Prieur, (2019) applied a network science approach, drawing from methods in various disciplines, to analyze around 10,000 non-overlapping Facebook ego networks collected through a survey application, utilizing a concept called 'graphlet representativity' to classify these networks more effectively, resulting in two clusterings: one of graphlets or network motifs (paths, star-like, holes, light triangles, and dense) and one of the networks, revealing distinct structural characteristics of the Facebook ego networks, and discussing differences between results obtained using 4-node and 5-node graphlets or network motifs, with potential follow-up directions in sociology and network science. Daatland & Lowenstein (2005), based on a sample of 6,106 urban individuals aged 25 and above in five countries, explored intergenerational family solidarity across different family cultures and welfare state regimes, finding that the welfare state has not diminished family involvement in elder care, but has encouraged more independent relationships between generations. Wyngaerden et al. (2019) investigated the relationship between network cohesion and continuity of care for 380 severely mentally ill participants in Belgium, finding that cohesion indicators, such as density and egobetweenness, are relevant only for those with high-severity issues, irrespective of their living arrangements, and that optimal continuity of care is associated with fewer professionals or services in the user's network and a dense network for users with the most severe problems, suggesting the need for adaptable interventions as severity changes.

Most of social network analyses (SNA) considered only participants' relationships and not how these relationships are themselves connected independent of ego but not the connections between participants' relationships. Indeed, social integration is dependent on how participants and their relationships are connected (Brissette et al., 2000). Sense of belonging or belongingness, which can be measured through the density or transitivity (i.e. triangle of connections between three persons) of networks of relationships, has been negatively associated with depression (Hagerty & Williams, 1999). Therefore, from a public health standpoint, it is essential to identify how social network metrics are linked to each other (e.g. how transitivity influences degree) and how this interplay is correlated with social capital among older adults. This requires measuring complex and indirect relationships or what is commonly referred to as 'a friend of a friend'. In social network analysis, metrics based only on a participant's relationships are called first-order metrics, whereas those that depend on the relationships of relationships are called second-order metrics (Sosa et al., 2021). The protocol to measure first- and second-order metrics was first developed through the CURHA (Contrasted Urban settings for Healthy Aging) study using the VERITAS-Social questionnaire (Kestens et al., 2016; Naud et al., 2020). The questionnaire presents questions about in which places in the city a number of activities are conducted, to which a social network module was added. When respondents document a given destination, they are also asked to provide information on contacts from their network with whom they usually visit that destination. At the end of the questionnaire, participants are presented with all network members identified throughout the spatial questionnaire and asked to identify with whom they discuss important matters and with whom they like to socialize, and they may further add new network members at that step. Finally, they were asked to document who in their network knows whom. These questions identify relationships between network members, going a step further than current ego-
analyses (more quantitative and less subjective) to establish the links between participant characteristics, their relationships, and their health and well-being.

This paper addresses two important methodological issues, one about the statistical interdependence of network measures, one about the dependence of these measures with healthy aging. Usually correlations are made between different network metrics and measures of wellbeing but many social network indices are dependent and this may lead to false positive results and incorrect conclusions (Sosa et al., 2020, 2021). In this paper, we adopted a new way to test data in order to avoid this data interdependence and potentially false positives and false negatives. Some studies already address this dependence of network measures. Vacca (2020) introduced an innovative method for identifying structural typologies in personal networks, highlighting the considerable impact of personal network structure — the interconnections among an individual's contacts — on social outcomes. This method was contrasted with another recent approach, revealing that while both effectively capture variations in network structures, they also show significant discrepancies and cross-classification. These findings hold promise for future research in areas such as personal communities, social support, and social capital. Bidart et al. (2018) introduced a typology of personal networks, constructed from detailed data on young French individuals in a longitudinal study, which relies on a limited set of indicators related to the structure of relationships between individuals, with the goal of creating a generalizable approach applicable to different surveys. Finally, Charbey & Prieur, (2019) applied a network science approach, drawing from methods in various disciplines, to analyze around 10,000 non-overlapping Facebook ego networks collected through a survey application, utilizing a concept called 'graphlet representativity' to classify these networks more effectively, resulting in two clusterings: one of graphlets or network motifs (paths, star-like, holes, light triangles, and dense) and one of the networks, revealing distinct structural characteristics of the Facebook ego networks, and discussing differences between results obtained using 4-node and 5-node graphlets or network motifs, with potential follow-up directions in sociology and network science. Daatland & Lowenstein (2005), based on a sample of 6,106 urban individuals aged 25 and above in five countries, explored intergenerational family solidarity across different family cultures and welfare state regimes, finding that the welfare state has not diminished family involvement in elder care, but has encouraged more independent relationships between generations. Wyngaerden et al. (2019) investigated the relationship between network cohesion and continuity of care for 380 severely mentally ill participants in Belgium, finding that cohesion indicators, such as density and egobetweenness, are relevant only for those with high-severity issues, irrespective of their living arrangements, and that optimal continuity of care is associated with fewer professionals or services in the user's network and a dense network for users with the most severe problems, suggesting the need for adaptable interventions as severity changes.

Most of social network analyses (SNA) considered only participants' relationships and not how these relationships are themselves connected independent of ego but not the connections between participants' relationships. Indeed, social integration is dependent on how participants and their relationships are connected (Brissette et al., 2000). Sense of belonging or belongingness, which can be measured through the density or transitivity (i.e. triangle of connections between three persons) of networks of relationships, has been negatively associated with depression (Hagerty & Williams, 1999). Therefore, from a public health standpoint, it is essential to identify how social network metrics are linked to each other (e.g. how transitivity influences degree) and how this interplay is correlated with social capital among older adults. This requires measuring complex and indirect relationships or what is commonly referred to as 'a friend of a friend'. In social network analysis, metrics based only on a participant's relationships are called first-order metrics, whereas those that depend on the relationships of relationships are called second-order metrics (Sosa et al., 2021). The protocol to measure first- and second-order metrics was first developed through the CURHA (Contrasted Urban settings for Healthy Aging) study using the VERITAS-Social questionnaire (Kestens et al., 2016; Naud et al., 2020). The questionnaire presents questions about in which places in the city a number of activities are conducted, to which a social network module was added. When respondents document a given destination, they are also asked to provide information on contacts from their network with whom they usually visit that destination. At the end of the questionnaire, participants are presented with all network members identified throughout the spatial questionnaire and asked to identify with whom they discuss important matters and with whom they like to socialize, and they may further add new network members at that step. Finally, they were asked to document who in their network knows whom. These questions identify relationships between network members, going a step further than current ego-
centered network classic studies, and allowing global social network metrics and the structure of relationships among participants' first order contacts (Naud et al., 2020).

In this paper, we present various social network metrics that this SNA data enables, and how metrics are correlated together. In our study, we employed a range of network indices to investigate the complex dynamics of social networks among older adults, with each index serving a distinct purpose. Simmelian brokerage, as one of our chosen measures, provided unique insights into the role of participants (egos) as brokers in the network, shedding light on the potential fragmentation of network components when egos are removed (Krackhardt, 1999; Krackhardt & Kilduff, 2002). This index, while less commonly employed in sociology, was selected due to its ability to combine elements of both betweenness and the clustering coefficients, offering a more comprehensive view of network structure. Additionally, our study incorporated other well-established indices, such as degree centrality, which measured the number of connections participants had with other network members, and network density, assessing the overall interconnectedness of the network (Borgatti et al., 2009; Newman, 2010a; Scott, 2000; Sosa et al., 2021; Wasserman & Faust, 1994). The global clustering coefficient was used to gauge the extent to which cohesive structures formed within the network. Furthermore, the diversity index allowed us to examine the diversity of connections across different categories of people (Newman, 2006). Together, these indices provided a multifaceted approach to comprehensively explore the structure, diversity, and dynamics of social networks among older adults, offering a more nuanced understanding of the factors influencing their social interactions and potential impacts on well-being. Roucolle et al. (2020) stipulated that there are difficulties of capturing the network complexity in a simple manner. While Simmelian brokerage may not have enjoyed the same recognition as some traditional measures, our study aimed to broaden the scope of methodologies in the field, opening avenues for future research to delve deeper into these intricate network dynamics. Statistically speaking, it is not logical to separately test the effects of two independent variables on one different dependent variable in distinct tests, as we cannot determine whether these two dependent variables exhibit collinearity, which may result in false positives. Similarly, it is inadvisable to test the effects of two collinear independent variables on a dependent variable in a same model, as this could lead to false negatives by nullifying the genuine impact of one factor. This is why in this paper we initially examined variable correlations and employed a principal component analysis (PCA) to identify which dependent variables contribute to the dimensions revealed by PCA and to elucidate their implications. In addition, and more importantly, we ascertain how these different social network metrics can relate to measures of depression and general well-being. The aim of this study is to assess how social network metrics are intertwined thanks to Principal Component Analyses (PCA) (Roucolle et al., 2020), to identify key dimensions of social networks of older adults, and to evaluate how these dimensions relate to depressive symptoms, life satisfaction, and well-being but also how socio-demographic factors (participants socioeconomic profiles and characteristics of residential neighborhood) may influence the social network of participants.

## Methods

### Study population

We employed data from a survey conducted between September 2019 and March 2020 that was administered to 73 older adults (aged 60 and over) residing in the Paris region (Île-de-France). We initially had a larger sample size, but our study was impacted by the COVID-19 pandemic, so we chose to focus solely on a pre-COVID-19 period for this study. This event and this choice explain our low sample size. These participants were recruited from the RECORD Cohort (Chaix, Kestens, Bean, et al., 2012). Using the framework of the Healthy Aging and Networks in Cities (HANC) and Promoting Mental Well-Being and Healthy Aging in Cities (MINDMAP) projects, this survey provides information on participants' socioeconomic profiles, their residential neighborhoods, and their regular social visited locations (Kestens et al., 2016; Fernandes et al., 2021). VERITAS is an interactive map-based questionnaire that allows participants to draw the limits of their perceived neighborhood and locate their regular activities (Chaix, Kestens, Perchoux, et al., 2012). Moreover, a social network component allows participants to describe each member of their social network (sociodemographic profile and their residence place) and how they are connected. It further collects data about the level of inter-knowledge of social network members and asks to specify places visited together (see Kestens et al., 2016) for a detailed explanation of the
centered network classic studies, and allowing global social network metrics and the structure of relationships among participants' first order contacts (Naud et al., 2020).

In this paper, we present various social network metrics that this SNA data enables, and how metrics are correlated together. In our study, we employed a range of network indices to investigate the complex dynamics of social networks among older adults, with each index serving a distinct purpose. Simmelian brokerage, as one of our chosen measures, provided unique insights into the role of participants (egos) as brokers in the network, shedding light on the potential fragmentation of network components when egos are removed (Krackhardt, 1999; Krackhardt & Kilduff, 2002). This index, while less commonly employed in sociology, was selected due to its ability to combine elements of both betweenness and the clustering coefficients, offering a more comprehensive view of network structure. Additionally, our study incorporated other well-established indices, such as degree centrality, which measured the number of connections participants had with other network members, and network density, assessing the overall interconnectedness of the network (Borgatti et al., 2009; Newman, 2010a; Scott, 2000; Sosa et al., 2021; Wasserman & Faust, 1994). The global clustering coefficient was used to gauge the extent to which cohesive structures formed within the network. Furthermore, the diversity index allowed us to examine the diversity of connections across different categories of people (Newman, 2006). Together, these indices provided a multifaceted approach to comprehensively explore the structure, diversity, and dynamics of social networks among older adults, offering a more nuanced understanding of the factors influencing their social interactions and potential impacts on well-being. Roucolle et al. (2020) stipulated that there are difficulties of capturing the network complexity in a simple manner. While Simmelian brokerage may not have enjoyed the same recognition as some traditional measures, our study aimed to broaden the scope of methodologies in the field, opening avenues for future research to delve deeper into these intricate network dynamics. Statistically speaking, it is not logical to separately test the effects of two independent variables on one different dependent variable in distinct tests, as we cannot determine whether these two dependent variables exhibit collinearity, which may result in false positives. Similarly, it is inadvisable to test the effects of two collinear independent variables on a dependent variable in a same model, as this could lead to false negatives by nullifying the genuine impact of one factor. This is why in this paper we initially examined variable correlations and employed a principal component analysis (PCA) to identify which dependent variables contribute to the dimensions revealed by PCA and to elucidate their implications. In addition, and more importantly, we ascertain how these different social network metrics can relate to measures of depression and general well-being. The aim of this study is to assess how social network metrics are intertwined thanks to Principal Component Analyses (PCA) (Roucolle et al., 2020), to identify key dimensions of social networks of older adults, and to evaluate how these dimensions relate to depressive symptoms, life satisfaction, and well-being but also how socio-demographic factors (participants socioeconomic profiles and characteristics of residential neighborhood) may influence the social network of participants.

## Methods

### Study population

We employed data from a survey conducted between September 2019 and March 2020 that was administered to 73 older adults (aged 60 and over) residing in the Paris region (Île-de-France). We initially had a larger sample size, but our study was impacted by the COVID-19 pandemic, so we chose to focus solely on a pre-COVID-19 period for this study. This event and this choice explain our low sample size. These participants were recruited from the RECORD Cohort (Chaix, Kestens, Bean, et al., 2012). Using the framework of the Healthy Aging and Networks in Cities (HANC) and Promoting Mental Well-Being and Healthy Aging in Cities (MINDMAP) projects, this survey provides information on participants' socioeconomic profiles, their residential neighborhoods, and their regular social visited locations (Kestens et al., 2016; Fernandes et al., 2021). VERITAS is an interactive map-based questionnaire that allows participants to draw the limits of their perceived neighborhood and locate their regular activities (Chaix, Kestens, Perchoux, et al., 2012). Moreover, a social network component allows participants to describe each member of their social network (sociodemographic profile and their residence place) and how they are connected. It further collects data about the level of inter-knowledge of social network members and asks to specify places visited together (see Kestens et al., 2016) for a detailed explanation of the
questionnaire). Finally, data from the National Institute of Statistics Economic Studies and the National Institute of Geography were used to derive socioeconomic, demographic and built environment characteristics and perceived neighborhoods.

## Measures

These data allowed us to analyze a set of indicators regarding social network structural characteristics, sociodemographic and residential factors, and health status.

Participants' socioeconomic profiles were defined through the following variables: age, gender, household income per capita (seven categories: <500, 500-1,000, 1,000-1,500, 1,000-2,000, 2,000-3,000, 3,000-4,000, and >4000); educational attainment (four categories: no education, primary education, secondary education, higher education); marital status (single or a couple); household type (number of people living with the interviewed person); and employment status. A summary of the data is provided in Table 1.

Characteristics of residential neighborhoods were defined from a combination of objective and subjective variables. Objective variables include location (Paris, close suburb, far suburb), neighborhood demographic and socioeconomic condition (average income, aging index, and population density), and urban walkability variables (density and diversity of services and street intersection density). Additionally, we investigated the following subjective variables obtained from self-report: urban quality (see Table 2), pedestrian accessibility, social support, and neighborhood safety. These indicators represent environmental opportunities (i.e. resources) in participants' neighborhoods and unveil the motivations that lead people to select a specific environment (internal or external to their residential neighborhood) for social activities. A summary of the data is provided in Table 2.

<table><caption>Table 1 - Socioeconomic and demographic variables</caption><thead><tr><th></th><th>Women %</th><th>Men %</th><th>Sum %</th></tr></thead><tbody><tr><td><strong>Sex</strong></td><td>36%</td><td>64%</td><td></td></tr><tr><td><strong>Age</strong></td><td></td><td></td><td></td></tr><tr><td>&gt;60 years</td><td>13.3%</td><td>24%</td><td>37.3%</td></tr><tr><td>&gt;70 years</td><td>21.3%</td><td>32%</td><td>53.3%</td></tr><tr><td>&gt;80 years</td><td>1.3%</td><td>8%</td><td>9.3%</td></tr><tr><td><strong>Income per capita (in €)</strong></td><td></td><td></td><td></td></tr><tr><td>500</td><td>0%</td><td>1.4%</td><td>1.4%</td></tr><tr><td>500-1,000</td><td>0%</td><td>2.7%</td><td>2.7%</td></tr><tr><td>1,000-1,500</td><td>6.8%</td><td>6.8%</td><td>13.6%</td></tr><tr><td>1,500-2,000</td><td>5.4%</td><td>10.8%</td><td>16.2%</td></tr><tr><td>2,000-3,000</td><td>16.2%</td><td>24.3%</td><td>40.5%</td></tr><tr><td>3,000-4,000</td><td>4.1%</td><td>14.9%</td><td>19%</td></tr><tr><td>&gt;4,000</td><td>4.1%</td><td>2.8%</td><td>6.9%</td></tr><tr><td><strong>Employment status</strong></td><td></td><td></td><td></td></tr><tr><td>Stage</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Worker</td><td>0%</td><td>9.3%</td><td>9.3%</td></tr><tr><td>Unemployed</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Retired</td><td>34.7%</td><td>53.3%</td><td>88%</td></tr><tr><td>Home Caretaker</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Other</td><td>1.3%</td><td>1.3%</td><td>2.6%</td></tr><tr><td><strong>Level of education</strong></td><td></td><td></td><td></td></tr><tr><td>No education</td><td>1.3%</td><td>2.7%</td><td>4%</td></tr><tr><td>Primary education</td><td>4%</td><td>1.3%</td><td>5.3%</td></tr><tr><td>Secondary education</td><td>13.3%</td><td>10.7%</td><td>24%</td></tr><tr><td>Higher education</td><td>17.3%</td><td>49.3%</td><td>66.6%</td></tr><tr><td><strong>Household size (n. individuals living with)</strong></td><td></td><td></td><td></td></tr><tr><td>Single</td><td>18.7%</td><td>16.0%</td><td>34.7%</td></tr><tr><td>Couple</td><td>16.0%</td><td>36.0%</td><td>52.0%</td></tr><tr><td>Family</td><td>1.3%</td><td>12.0%</td><td>13.3%</td></tr><tr><td><strong>Depression status - CES D20 Index</strong></td><td></td><td></td><td></td></tr><tr><td>Not depressed (0-15)</td><td>28.0%</td><td>60%</td><td>88%</td></tr><tr><td>Depressed (&gt;16)</td><td>8%</td><td>4%</td><td>12%</td></tr><tr><td><strong>Anxiety - Stai Y B Index</strong></td><td></td><td></td><td></td></tr><tr><td>Not anxious</td><td>33.2%</td><td>49%</td><td>82.2%</td></tr><tr><td>Anxious (men&gt;39; women &gt;47)</td><td>2.8%</td><td>15%</td><td>17.8%</td></tr></tbody></table>
questionnaire). Finally, data from the National Institute of Statistics Economic Studies and the National Institute of Geography were used to derive socioeconomic, demographic and built environment characteristics and perceived neighborhoods.

## Measures

These data allowed us to analyze a set of indicators regarding social network structural characteristics, sociodemographic and residential factors, and health status.

Participants' socioeconomic profiles were defined through the following variables: age, gender, household income per capita (seven categories: <500, 500-1,000, 1,000-1,500, 1,000-2,000, 2,000-3,000, 3,000-4,000, and >4000); educational attainment (four categories: no education, primary education, secondary education, higher education); marital status (single or a couple); household type (number of people living with the interviewed person); and employment status. A summary of the data is provided in Table 1.

Characteristics of residential neighborhoods were defined from a combination of objective and subjective variables. Objective variables include location (Paris, close suburb, far suburb), neighborhood demographic and socioeconomic condition (average income, aging index, and population density), and urban walkability variables (density and diversity of services and street intersection density). Additionally, we investigated the following subjective variables obtained from self-report: urban quality (see Table 2), pedestrian accessibility, social support, and neighborhood safety. These indicators represent environmental opportunities (i.e. resources) in participants' neighborhoods and unveil the motivations that lead people to select a specific environment (internal or external to their residential neighborhood) for social activities. A summary of the data is provided in Table 2.

<table><caption>Table 1 - Socioeconomic and demographic variables</caption><thead><tr><th></th><th>Women %</th><th>Men %</th><th>Sum %</th></tr></thead><tbody><tr><td><strong>Sex</strong></td><td>36%</td><td>64%</td><td></td></tr><tr><td><strong>Age</strong></td><td></td><td></td><td></td></tr><tr><td>&gt;60 years</td><td>13.3%</td><td>24%</td><td>37.3%</td></tr><tr><td>&gt;70 years</td><td>21.3%</td><td>32%</td><td>53.3%</td></tr><tr><td>&gt;80 years</td><td>1.3%</td><td>8%</td><td>9.3%</td></tr><tr><td><strong>Income per capita (in €)</strong></td><td></td><td></td><td></td></tr><tr><td>500</td><td>0%</td><td>1.4%</td><td>1.4%</td></tr><tr><td>500-1,000</td><td>0%</td><td>2.7%</td><td>2.7%</td></tr><tr><td>1,000-1,500</td><td>6.8%</td><td>6.8%</td><td>13.6%</td></tr><tr><td>1,500-2,000</td><td>5.4%</td><td>10.8%</td><td>16.2%</td></tr><tr><td>2,000-3,000</td><td>16.2%</td><td>24.3%</td><td>40.5%</td></tr><tr><td>3,000-4,000</td><td>4.1%</td><td>14.9%</td><td>19%</td></tr><tr><td>&gt;4,000</td><td>4.1%</td><td>2.8%</td><td>6.9%</td></tr><tr><td><strong>Employment status</strong></td><td></td><td></td><td></td></tr><tr><td>Stage</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Worker</td><td>0%</td><td>9.3%</td><td>9.3%</td></tr><tr><td>Unemployed</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Retired</td><td>34.7%</td><td>53.3%</td><td>88%</td></tr><tr><td>Home Caretaker</td><td>0%</td><td>0%</td><td>0%</td></tr><tr><td>Other</td><td>1.3%</td><td>1.3%</td><td>2.6%</td></tr><tr><td><strong>Level of education</strong></td><td></td><td></td><td></td></tr><tr><td>No education</td><td>1.3%</td><td>2.7%</td><td>4%</td></tr><tr><td>Primary education</td><td>4%</td><td>1.3%</td><td>5.3%</td></tr><tr><td>Secondary education</td><td>13.3%</td><td>10.7%</td><td>24%</td></tr><tr><td>Higher education</td><td>17.3%</td><td>49.3%</td><td>66.6%</td></tr><tr><td><strong>Household size (n. individuals living with)</strong></td><td></td><td></td><td></td></tr><tr><td>Single</td><td>18.7%</td><td>16.0%</td><td>34.7%</td></tr><tr><td>Couple</td><td>16.0%</td><td>36.0%</td><td>52.0%</td></tr><tr><td>Family</td><td>1.3%</td><td>12.0%</td><td>13.3%</td></tr><tr><td><strong>Depression status - CES D20 Index</strong></td><td></td><td></td><td></td></tr><tr><td>Not depressed (0-15)</td><td>28.0%</td><td>60%</td><td>88%</td></tr><tr><td>Depressed (&gt;16)</td><td>8%</td><td>4%</td><td>12%</td></tr><tr><td><strong>Anxiety - Stai Y B Index</strong></td><td></td><td></td><td></td></tr><tr><td>Not anxious</td><td>33.2%</td><td>49%</td><td>82.2%</td></tr><tr><td>Anxious (men&gt;39; women &gt;47)</td><td>2.8%</td><td>15%</td><td>17.8%</td></tr></tbody></table>
We examined whether neighborhood measures showed high correlations, but this was not the case (Fig. S1). The highest correlation (R²) was 0.63, while collinearity is typically considered to be present when correlations are approximately 0.9 or higher (Franke, 2010).

Structure of social networks. We are working on networks composed of a focal node (the ego) and its connected social members (alters). Among the social network measures, we are interested in evaluating the characteristics that we postulate can be related to older adults' well-being:

a) the number of social network members (i.e. the network degree);

b) the strength of contact with social network members—1.) by face-to-face contact only or 2.) by all contacts (mail, phone call, face-to-face)—approximated through the number of contacts per week;

c) the level of connection between the social members (i.e. the network density): we calculated this density with and without the presence of ego in the network to avoid correlation with other network measures;

d) the centrality of the participant with respect to his/her social network (i.e. Simmelian brokerage);

e) the presence of closed cohesive structures among social network members (i.e. clustering coefficient);

f) the diversity of people in a social network (the Evenness Index and Assortativity Index for age, sex, occupation, and level of study).

We provide a summary of these data and definitions in Table 3.

Health status. Participants provided answers to the following tests (see Table 4 for definitions): the CES-20 item test (Center for Epidemiological Studies Depression Scale (Radloff, 1977)), the CASP-12 scale test (Quality of life, Hyde et al., 2003), and the STAI Y-B test (Spielberger et al., 1983). We calculated the corresponding health status indices (see Table 4).

## Statistical analyses

We first performed a correlation analysis using the R package PerformanceAnalytics (Carl et al., 2010; Peterson et al., 2018) (to check whether some variables were highly correlated (variables with r > 0.9)) (first, socioeconomic ones and second network ones, in two different PCA). Concerning network variables, because of the high correlations between network density and Simmelian brokerage and the clustering coefficient, we also decided to correct the Simmelian brokerage and the clustering coefficient by performing a linear regression with these two metrics as the response variable and network density as an explanatory factor. We took the residuals from this linear regression of the two metrics, which correspond to the variance of each point not explained by the network density, and created two new variables: res(simbrok) and res(clustcoeff). The correlations of these new variables with other network metrics are given in Fig. S2.

The next steps only concerned the network variables. We conducted a Principal Component Analysis (PCA) with Varimax rotation using the Psych R package (Revelle, 2011; Revelle & Revelle, 2015). PCA is a statistical technique employed to reduce the number of variables into more biologically, psychologically, or socially interpretable dimensions. Prior to analysis, the variables were automatically adjusted by centering them around their means for comparability in terms of mean and range. Four dimensions were retained based on eigenvalues exceeding the threshold of 1, a commonly accepted practice (Budaev, 2010; Holland, 2008; Smith, 2002). The application of Varimax rotation aimed to simplify the representation of a specific subspace using only a select set of key items. Essentially, Varimax rotation maximizes the explained variance by adjusting the variables' positions on the dimensions. We then assessed the loading of each variable on each dimension, which represented the coefficients of the linear combination from which the principal components were derived. These loadings were obtained by dividing the coordinates of the variables by the square root of the eigenvalue linked to the respective component. Variables with loadings below 0.6, indicating a limited contribution to each dimension and the overall explained variance, were subsequently eliminated. The resulting four new dimensions were employed as variables in our subsequent analyses. We used linear regression model selection and multi-model inference (Burnham & Anderson, 2004) to test the links of sociodemographic variables with network metrics and we used Poisson models to test the effect of network metrics on health status. We used the four network dimension values to better understand the interplay between participants' social environments, their networks, and their well-being, and we used the Poisson distribution with health status scores as the outcomes. We used the Gaussian
We examined whether neighborhood measures showed high correlations, but this was not the case (Fig. S1). The highest correlation (R²) was 0.63, while collinearity is typically considered to be present when correlations are approximately 0.9 or higher (Franke, 2010).

Structure of social networks. We are working on networks composed of a focal node (the ego) and its connected social members (alters). Among the social network measures, we are interested in evaluating the characteristics that we postulate can be related to older adults' well-being:

a) the number of social network members (i.e. the network degree);

b) the strength of contact with social network members—1.) by face-to-face contact only or 2.) by all contacts (mail, phone call, face-to-face)—approximated through the number of contacts per week;

c) the level of connection between the social members (i.e. the network density): we calculated this density with and without the presence of ego in the network to avoid correlation with other network measures;

d) the centrality of the participant with respect to his/her social network (i.e. Simmelian brokerage);

e) the presence of closed cohesive structures among social network members (i.e. clustering coefficient);

f) the diversity of people in a social network (the Evenness Index and Assortativity Index for age, sex, occupation, and level of study).

We provide a summary of these data and definitions in Table 3.

Health status. Participants provided answers to the following tests (see Table 4 for definitions): the CES-20 item test (Center for Epidemiological Studies Depression Scale (Radloff, 1977)), the CASP-12 scale test (Quality of life, Hyde et al., 2003), and the STAI Y-B test (Spielberger et al., 1983). We calculated the corresponding health status indices (see Table 4).

## Statistical analyses

We first performed a correlation analysis using the R package PerformanceAnalytics (Carl et al., 2010; Peterson et al., 2018) (to check whether some variables were highly correlated (variables with r > 0.9)) (first, socioeconomic ones and second network ones, in two different PCA). Concerning network variables, because of the high correlations between network density and Simmelian brokerage and the clustering coefficient, we also decided to correct the Simmelian brokerage and the clustering coefficient by performing a linear regression with these two metrics as the response variable and network density as an explanatory factor. We took the residuals from this linear regression of the two metrics, which correspond to the variance of each point not explained by the network density, and created two new variables: res(simbrok) and res(clustcoeff). The correlations of these new variables with other network metrics are given in Fig. S2.

The next steps only concerned the network variables. We conducted a Principal Component Analysis (PCA) with Varimax rotation using the Psych R package (Revelle, 2011; Revelle & Revelle, 2015). PCA is a statistical technique employed to reduce the number of variables into more biologically, psychologically, or socially interpretable dimensions. Prior to analysis, the variables were automatically adjusted by centering them around their means for comparability in terms of mean and range. Four dimensions were retained based on eigenvalues exceeding the threshold of 1, a commonly accepted practice (Budaev, 2010; Holland, 2008; Smith, 2002). The application of Varimax rotation aimed to simplify the representation of a specific subspace using only a select set of key items. Essentially, Varimax rotation maximizes the explained variance by adjusting the variables' positions on the dimensions. We then assessed the loading of each variable on each dimension, which represented the coefficients of the linear combination from which the principal components were derived. These loadings were obtained by dividing the coordinates of the variables by the square root of the eigenvalue linked to the respective component. Variables with loadings below 0.6, indicating a limited contribution to each dimension and the overall explained variance, were subsequently eliminated. The resulting four new dimensions were employed as variables in our subsequent analyses. We used linear regression model selection and multi-model inference (Burnham & Anderson, 2004) to test the links of sociodemographic variables with network metrics and we used Poisson models to test the effect of network metrics on health status. We used the four network dimension values to better understand the interplay between participants' social environments, their networks, and their well-being, and we used the Poisson distribution with health status scores as the outcomes. We used the Gaussian
distribution with the four network dimensions as the outcomes as they were normalized and scaled owing to the PCA.

<table><caption>Table 2 - Residential neighborhood indicators</caption><caption>Residential Neighborhood Indicators (the neighborhood area defined by the interviewed) (* Descriptive Variables; **Analytical Variables)</caption><thead><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Resources</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>Location of the residence**</td><td>Proportion of the residential neighborhood within a specific class of municipality (based on population size): Paris center, medium suburbs, small suburbs, and rural communities.</td><td>Geographical location of the residential neighborhood with reference to the class of the municipality.</td><td>(Vallée et al., 2015)</td><td>INSEE</td><td>Paris center 37.33% Medium suburbs 30.67% Small suburbs 32.00%</td></tr><tr><td>Income**</td><td>Resident population's income per capita.</td><td>The wealth of the resident people living in the neighborhood.</td><td></td><td>INSEE</td><td>31,376 €</td></tr><tr><td>Aging index**</td><td>Number of resident older adults (&gt;65 years old) per 100 persons younger than 17 years old.</td><td>Represents the proportion of elderly population in the space chosen by individuals to meet their social members.</td><td></td><td>INSEE</td><td>77.71</td></tr><tr><td>Population density*</td><td>Geographic Information System processing: the resident population density.</td><td>The urban quality and the walkability of social places visited: density and diversity of services, density of population and density of intersections are related to a conducive walking environment.</td><td>(Cervero &amp; Kockelman, 1997; Yue et al., 2017; Zandieh et al., 2017)</td><td>INSEE</td><td>17,344 ppl/km²</td></tr><tr><td>Density of services*</td><td>Geographic Information System processing: the number of places/km².</td><td>The density of services represents one of the variables of the urban quality and walkability of social places visited.</td><td></td><td>INSEE/BPE</td><td>23.3 places/km²</td></tr><tr><td>Diversity of services*</td><td>Geographic Information System processing: the Shannon Index normalized (Evenness Index).</td><td>The diversity index represents one of the variables of the urban quality and walkability of social places visited. It provides information about the urban composition by accounting for both abundance and evenness of the services present in space.</td><td></td><td>INSEE/BPE</td><td>0.41</td></tr><tr><td>Street intersection density*</td><td>Geographic Information System processing: the ratio of intersections that are three or more ways per kilometer.</td><td>It is one of the most used walkability variables in the literature representing the street design and connectivity, block size, and the vitality of a place. Ewing and Cervero (2010) find that a 10% increase in intersections is linked to a 3.9% increase in walking.</td><td></td><td></td><td>196.89 km²</td></tr><tr><td>Urban quality **</td><td>Subjective urban quality: a total of 18 questions on a 4-point Likert scale. The higher the points, the greater the problems: the range is from 0 to 1.</td><td>The perceived urban quality of the residential area. It can be useful to better understand people's choice to engage in social activities in other parts of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.54</td></tr><tr><td>Perceived pedestrian accessibility **</td><td>The ratio of the number of types of services accessible by foot and the maximum number of types of services (12).</td><td>The perceived pedestrian accessibility of the neighborhood can be useful to understand people's choice to engage in social activities in other parts of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.94</td></tr><tr><td>Social support *</td><td>A total of six questions on a 4-point Likert scale: in my neighborhood, outside my neighborhood, no. Higher scores indicate higher degrees of social isolation, with scores ranging from 0 to 1.</td><td>The perceived social support in the neighborhood can be meaningful regarding people's choice to find social support in other areas of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.17</td></tr><tr><td>Neighborhood safety **</td><td>Perceived safety measured on a 3-point scale: high, medium, low.</td><td>Perceived safety can be a proxy for urban quality.</td><td></td><td>VERITAS-CAPI</td><td>0.46</td></tr></tbody></table>
distribution with the four network dimensions as the outcomes as they were normalized and scaled owing to the PCA.

<table><caption>Table 2 - Residential neighborhood indicators</caption><caption>Residential Neighborhood Indicators (the neighborhood area defined by the interviewed) (* Descriptive Variables; **Analytical Variables)</caption><thead><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Resources</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>Location of the residence**</td><td>Proportion of the residential neighborhood within a specific class of municipality (based on population size): Paris center, medium suburbs, small suburbs, and rural communities.</td><td>Geographical location of the residential neighborhood with reference to the class of the municipality.</td><td>(Vallée et al., 2015)</td><td>INSEE</td><td>Paris center 37.33% Medium suburbs 30.67% Small suburbs 32.00%</td></tr><tr><td>Income**</td><td>Resident population's income per capita.</td><td>The wealth of the resident people living in the neighborhood.</td><td></td><td>INSEE</td><td>31,376 €</td></tr><tr><td>Aging index**</td><td>Number of resident older adults (&gt;65 years old) per 100 persons younger than 17 years old.</td><td>Represents the proportion of elderly population in the in the space chosen by individuals to meet their social members.</td><td></td><td>INSEE</td><td>77.71</td></tr><tr><td>Population density*</td><td>Geographic Information System processing: the resident population density.</td><td>The urban quality and the walkability of social places visited: density and diversity of services, density of population and density of intersections are related to a conducive walking environment.</td><td>(Cervero &amp; Kockelman, 1997; Yue et al., 2017; Zandieh et al., 2017)</td><td>INSEE</td><td>17,344 ppl/km²</td></tr><tr><td>Density of services*</td><td>Geographic Information System processing: the number of places/km².</td><td>The density of services represents one of the variables of the urban quality and walkability of social places visited.</td><td></td><td>INSEE/BPE</td><td>23.3 places/km²</td></tr><tr><td>Diversity of services*</td><td>Geographic Information System processing: the Shannon Index normalized (Evenness Index).</td><td>The diversity index represents one of the variables of the urban quality and walkability of social places visited. It provides information about the urban composition by accounting for both abundance and evenness of the services present in space.</td><td></td><td>INSEE/BPE</td><td>0.41</td></tr><tr><td>Street intersection density*</td><td>Geographic Information System processing: the ratio of intersections that are three or more ways per kilometer.</td><td>It is one of the most used walkability variables in the literature representing the street design and connectivity, block size, and the vitality of a place. Ewing and Cervero (2010) find that a 10% increase in intersections is linked to a 3.9% increase in walking.</td><td></td><td></td><td>196.89 km²</td></tr><tr><td>Urban quality **</td><td>Subjective urban quality: a total of 18 questions on a 4-point Likert scale. The higher the points, the greater the problems: the range is from 0 to 1.</td><td>The perceived urban quality of the residential area. It can be useful to better understand people' choice to engage in social activities in other parts of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.54</td></tr><tr><td>Perceived pedestrian accessibility **</td><td>The ratio of the number of types of services accessible by foot and the maximum number of types of services (12).</td><td>The perceived pedestrian accessibility of the neighborhood can be useful to understand people's choice to engage in social activities in other parts of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.94</td></tr><tr><td>Social support *</td><td>A total of six questions on a 4-point Likert scale: in my neighborhood, outside my neighborhood, no. Higher scores indicate higher degrees of social isolation, with scores ranging from 0 to 1.</td><td>The perceived social support in the neighborhood can be meaningful regarding people's choice to find social support in other areas of the city.</td><td></td><td>VERITAS-CAPI</td><td>0.17</td></tr><tr><td>Neighborhood safety **</td><td>Perceived safety measured on a 3-point scale: high, medium, low.</td><td>Perceived safety can be a proxy for urban quality.</td><td></td><td>VERITAS-CAPI</td><td>0.46</td></tr></tbody></table>
<table><caption>Table 3: Social network indicators</caption><thead><tr><th colspan="6">Social Network Indicators (* Descriptive Variables; **Analytical Variables)</th></tr><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Resource</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>Degree centrality**</td><td>The number of connections from ego to alter.</td><td>The number of social network members with whom the participant usually performs social activities. Individuals with a high degree of centrality have more influence and engage in more social activities.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>5.66</td></tr><tr><td>Connectivity/network Density**</td><td>The ratio of the numbers of edges and the maximum possible numbers of edges in the network.</td><td>The percentage of possible connections vs. the effective connections among all social members.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>0.79</td></tr><tr><td>Simmelian brokerage**</td><td>The role of the ego as a broker in the graph.</td><td>The extent to which the social network components are disconnected from each other when removing the participant from the network.</td><td>(Latora et al., 2013)</td><td>VERITAS</td><td>2.44</td></tr><tr><td>Global Clustering coefficient*</td><td>The ratio of the triangles and the connected triples in the graph.</td><td>The extent to which the social network components are embedded in a closed cohesive structure.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>0.79</td></tr><tr><td>Diversity Index**</td><td>The Evenness Index for types of alters (husband/wife, child, other family members, friends, co-workers, acquaintances): the average number of friendships that the ego has with agents who are of the same type, and the average number of friendships that the ego forms with agents of different types.</td><td>The extent to which aged people are connected with different categories of people.</td><td>(Putnam, 1993)</td><td>VERITAS</td><td>0.49</td></tr><tr><td>Homophily Index</td><td>The probability of having relationships with similar people for age, sex, education, and occupation.</td><td>The extent to which people with similar personal or social traits are connected.</td><td></td><td>VERITAS</td><td>Age - 0.26<br>Sex - 0.25<br>Education - 0.26<br>Occupation - 0.23</td></tr></tbody></table>

<table><caption>Table 4 - Mental health indicator</caption><thead><tr><th colspan="6">Mental Health Indicators (*Descriptive Variables; **Analytical Variables)</th></tr><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Reference</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>CES-D20**</td><td>A total of 20 questions on a 4-point Likert scale: Rarely or none of the time (less than 1 day); Some or a little of the time (1-2 days); Occasionally or a moderate amount of time (3-4 days); Most or all of the time (5-7 days). Range: 0-60. Individuals scoring >16 are considered to be depressed.</td><td>Depression status of the interviewed.</td><td>(Radloff, 1977)</td><td>VERITAS-CAPI</td><td>8.88</td></tr><tr><td>CASP-12**</td><td>A total of 12 questions on a 4-point Likert scale ('often', 'sometimes', 'rarely', 'never'). Range: 12-48, with higher scores representing higher quality of life.</td><td>Perceived quality of life of the interviewed.</td><td>(Hyde et al., 2003)</td><td>VERITAS-CAPI</td><td>25.49</td></tr><tr><td>STAI Y-B**</td><td>A total of 20 questions on a 4-point Likert scale.</td><td>Anxiety of the interviewed.</td><td>(Spielberger et al., 1983)</td><td>VERITAS-CAPI</td><td>34.77</td></tr></tbody></table>

We checked statistically several model assumptions (normality and homogeneity of residuals, variance inflation factors) and no obvious violations or influential cases were detected. We ran multi-model inferences to compare and rank candidate models according to (i) their respective Akaike information criteria after correction for small sample sizes (AICc) and (ii) normalized Akaike weights (AICw) (Burnham & Anderson, 2004). ΔAICc is the difference in AICc between a given model and the model with the lowest
<table><caption>Table 3: Social network indicators</caption><caption>Social Network Indicators (*Descriptive Variables; **Analytical Variables)</caption><thead><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Resource</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>Degree centrality**</td><td>The number of connections from ego to alter.</td><td>The number of social network members with whom the participant usually performs social activities. Individuals with a high degree of centrality have more influence and engage in more social activities.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>5.66</td></tr><tr><td>Connectivity/network Density**</td><td>The ratio of the numbers of edges and the maximum possible numbers of edges in the network.</td><td>The percentage of possible connections vs. the effective connections among all social members.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>0.79</td></tr><tr><td>Simmelian brokerage**</td><td>The role of the ego as a broker in the graph.</td><td>The extent to which the social network components are disconnected from each other when removing the participant from the network.</td><td>(Latora et al., 2013)</td><td>VERITAS</td><td>2.44</td></tr><tr><td>Global Clustering coefficient*</td><td>The ratio of the triangles and the connected triples in the graph.</td><td>The extent to which the social network components are embedded in a closed cohesive structure.</td><td>(Newman, 2010a)</td><td>VERITAS</td><td>0.79</td></tr><tr><td>Diversity Index**</td><td>The Evenness Index for types of alters (husband/wife, child, other family members, friends, co-workers, acquaintances): the average number of friendships that the ego has with agents who are of the same type, and the average number of friendships that the ego forms with agents of different types.</td><td>The extent to which aged people are connected with different categories of people.</td><td>(Putnam, 1993)</td><td>VERITAS</td><td>0.49</td></tr><tr><td>Homophily Index</td><td>The probability of having relationships with similar people for age, sex, education, and occupation.</td><td>The extent to which people with similar personal or social traits are connected.</td><td></td><td>VERITAS</td><td>Age - 0.26<br>Sex - 0.25<br>Education - 0.26<br>Occupation - 0.23</td></tr></tbody></table>

<table><caption>Table 4 - Mental health indicator</caption><caption>Mental Health Indicators (*Descriptive Variables; **Analytical Variables)</caption><thead><tr><th>Name</th><th>Indicator</th><th>Meaning</th><th>Reference</th><th>Source data</th><th>Mean</th></tr></thead><tbody><tr><td>CES-D20**</td><td>A total of 20 questions on a 4-point Likert scale: Rarely or none of the time (less than 1 day); Some or a little of the time (1–2 days); Occasionally or a moderate amount of time (3–4 days); Most or all of the time (5–7 days). Range: 0–60. Individuals scoring >16 are considered to be depressed.</td><td>Depression status of the interviewed.</td><td>(Radloff, 1977)</td><td>VERITAS-CAPI</td><td>8.88</td></tr><tr><td>CASP-12**</td><td>A total of 12 questions on a 4-point Likert scale (‘often’, ‘sometimes’, ‘rarely’, ‘never’). Range: 12–48, with higher scores representing higher quality of life.</td><td>Perceived quality of life of the interviewed.</td><td>(Hyde et al., 2003)</td><td>VERITAS-CAPI</td><td>25.49</td></tr><tr><td>STAI Y-B**</td><td>A total of 20 questions on a 4-point Likert scale.</td><td>Anxiety of the interviewed.</td><td>(Spielberger et al., 1983)</td><td>VERITAS-CAPI</td><td>34.77</td></tr></tbody></table>

We checked statistically several model assumptions (normality and homogeneity of residuals, variance inflation factors) and no obvious violations or influential cases were detected. We ran multi-model inferences to compare and rank candidate models according to (i) their respective Akaike information criteria after correction for small sample sizes (AICc) and (ii) normalized Akaike weights (AICw) (Burnham & Anderson, 2004). ΔAICc is the difference in AICc between a given model and the model with the lowest
AIC value. The AIC weight indicates the probability that a given model is the best among candidate models. Models with a ΔAICc<4 were considered equally possible candidates and their statistics were averaged. The null model was also included as a possible candidate but was never among the models with the lowest AICc. The averaged model coefficients were obtained for models with ΔAICc<4. Model inference and averaging were performed using the R package MuMln (Barton, 2013; Barton & Barton, 2013). This method allows us to find the independent variables that affect the response variable, even if they are covariant.

All analyses were performed using RStudio 1.4.1103 (Allaire, 2012; Racine, 2012). The significance threshold was set at $\alpha = 0.05$. Supplemental material, dataset and scripts are available on Zenodo: https://doi.org/10.5281/zenodo.7763430 (Sueur et al., 2023).

# Results

## Analyses of network indices

The strength of face-to-face contact was 9.9±5.9 contacts per week, whereas the strength of all contacts was 14.7±9.5 contacts per week. The degree of participants was 5.7±3.3 (i.e. relationships). Only one participant had a network with a degree of one, and the maximum degree was 19. The network density with ego was 0.79±0.23 and remained high without ego (0.68±0.34). The clustering coefficient of participants was 0.78±0.27 and the Simmelian brokerage was 2.4±2.29. The Everness Index equalled 0.51±0.20, and the assortativity, whatever the sociodemographic factor considered, was approximately -0.21±0.20.

The correlation chart (Fig. 1) shows two correlations with $r > (-0.9):$ between network density with ego and network density without ego ($r=0.90$), between network density without ego and the clustering coefficient ($r=-0.94$). Network density with ego and Simmelian brokerage were also significantly correlated ($r=-0.84$). These high correlations were due to the high connectivity between alters. Among the 73 participants, 34 (45%) had a network density (without ego) of 1. For the remaining participants, the difference in network density with and without ego was 0.18±0.11. Naturally, this difference in density with and without the presence of ego is directly due to the degree of participants: the higher the degree, the lower the probability of seeing all alters connected, and the lower the density ($R^2=0.36, p<0.001$). Removing ego from the network also increased the correlation between the network density and the clustering coefficient (from 0.74 to 0.94) as the density of networks in which alters were only connected to ego fell to 0, as their clustering coefficient after the removal. This occurred for five participants (see details in Fig. S3a). Removing these five individuals significantly increased the correlation between the latter variables (see Fig. S3b), indicating dependencies between these network metrics. Next, analyses were performed by removing the density without ego and by analyzing the residuals of the clustering coefficient and the Simmelian brokerage according to the density to test the part of the variance that is independent of network density.

We performed a PCA on all the network metrics that provided four dimensions ($eigenvalue > 1$ which is commonly accepted as significantly explaining the variance (Smith, 2002; Holland, 2008; Budaev, 2010)). The total explained variance was 78.4%. Some variables did not have any loadings superior to 0.6 in any of the four dimensions, and we decided to remove these—not only because of their low contribution but also because they bring noise to explanations of dimensions. These variables were degree (loading between 0.44 and 0.49), Everness Index (loading between 0.28 and 0.52), and assortativity according to education (loading between 0.11 and 0.38). We repeated the PCA and obtained a better explained variance of 85.8% (dimension 1 = 26.2%, dimension 2= 24.4%, dimension 3 = 18.1%, dimension 4 = 17.1%). Each remaining variable had a loading higher for one dimension compared to the other, which allowed us to group variables in each of the four dimensions (see Table 5). Dimension 1 is mainly weighted by all the assortativities and residuals of the clustering coefficient. Dimension 2 includes the network density, clustering coefficient, and Simmelian brokerage and corresponds to ego centrality. Dimension 3 has the two variables of strength of contact. Finally, Dimension 4 includes only the residuals of Simmelian brokerage.
AIC value. The AIC weight indicates the probability that a given model is the best among candidate models. Models with a ΔAICc<4 were considered equally possible candidates and their statistics were averaged. The null model was also included as a possible candidate but was never among the models with the lowest AICc. The averaged model coefficients were obtained for models with ΔAICc<4. Model inference and averaging were performed using the R package MuMln (Barton, 2013; Barton & Barton, 2013). This method allows us to find the independent variables that affect the response variable, even if they are covariant.

All analyses were performed using RStudio 1.4.1103 (Allaire, 2012; Racine, 2012). The significance threshold was set at $\alpha = 0.05$. Supplemental material, dataset and scripts are available on Zenodo: https://doi.org/10.5281/zenodo.7763430 (Sueur et al., 2023).

# Results

## Analyses of network indices

The strength of face-to-face contact was 9.9±5.9 contacts per week, whereas the strength of all contacts was 14.7±9.5 contacts per week. The degree of participants was 5.7±3.3 (i.e. relationships). Only one participant had a network with a degree of one, and the maximum degree was 19. The network density with ego was 0.79±0.23 and remained high without ego (0.68±0.34). The clustering coefficient of participants was 0.78±0.27 and the Simmelian brokerage was 2.4±2.29. The Everness Index equalled 0.51±0.20, and the assortativity, whatever the sociodemographic factor considered, was approximately -0.21±0.20.

The correlation chart (Fig. 1) shows two correlations with $r > (-0.9)$: between network density with ego and network density without ego ($r=0.90$), between network density without ego and the clustering coefficient ($r=-0.94$). Network density with ego and Simmelian brokerage were also significantly correlated ($r=-0.84$). These high correlations were due to the high connectivity between alters. Among the 73 participants, 34 (45%) had a network density (without ego) of 1. For the remaining participants, the difference in network density with and without ego was 0.18±0.11. Naturally, this difference in density with and without the presence of ego is directly due to the degree of participants: the higher the degree, the lower the probability of seeing all alters connected, and the lower the density ($R^2=0.36, p<0.001$). Removing ego from the network also increased the correlation between the network density and the clustering coefficient (from 0.74 to 0.94) as the density of networks in which alters were only connected to ego fell to 0, as their clustering coefficient after the removal. This occurred for five participants (see details in Fig. S3a). Removing these five individuals significantly increased the correlation between the latter variables (see Fig. S3b), indicating dependencies between these network metrics. Next, analyses were performed by removing the density without ego and by analyzing the residuals of the clustering coefficient and the Simmelian brokerage according to the density to test the part of the variance that is independent of network density.

We performed a PCA on all the network metrics that provided four dimensions ($eigenvalue > 1$ which is commonly accepted as significantly explaining the variance (Smith, 2002; Holland, 2008; Budaev, 2010)). The total explained variance was 78.4%. Some variables did not have any loadings superior to 0.6 in any of the four dimensions, and we decided to remove these—not only because of their low contribution but also because they bring noise to explanations of dimensions. These variables were degree (loading between 0.44 and 0.49), Everness Index (loading between 0.28 and 0.52), and assortativity according to education (loading between 0.11 and 0.38). We repeated the PCA and obtained a better explained variance of 85.8% (dimension 1 = 26.2%, dimension 2= 24.4%, dimension 3 = 18.1%, dimension 4 = 17.1%). Each remaining variable had a loading higher for one dimension compared to the other, which allowed us to group variables in each of the four dimensions (see Table 5). Dimension 1 is mainly weighted by all the assortativities and residuals of the clustering coefficient. Dimension 2 includes the network density, clustering coefficient, and Simmelian brokerage and corresponds to ego centrality. Dimension 3 has the two variables of strength of contact. Finally, Dimension 4 includes only the residuals of Simmelian brokerage.
<table><caption>Table 5 - Loadings for each variable in each dimension of the PCA</caption><thead><tr><th></th><th>RC1</th><th>RC2</th><th>RC3</th><th>RC4</th></tr></thead><tbody><tr><td>strength_direct</td><td></td><td></td><td>0.934</td><td></td></tr><tr><td>strength_all</td><td>0.182</td><td></td><td>0.9</td><td>0.122</td></tr><tr><td>network_density</td><td>-0.217</td><td>0.953</td><td></td><td></td></tr><tr><td>Clustering coefficient</td><td>0.309</td><td>0.878</td><td></td><td>0.343</td></tr><tr><td>Simmelian brokerage</td><td>0.193</td><td>-0.814</td><td>0.112</td><td>0.531</td></tr><tr><td>assortativity sex</td><td>0.676</td><td></td><td>0.184</td><td>0.331</td></tr><tr><td>assortativity_occupation</td><td>0.896</td><td>-0.127</td><td>-0.111</td><td></td></tr><tr><td>assortativity_class_age</td><td>0.81</td><td></td><td>0.129</td><td>-0.12</td></tr><tr><td>res(simbrok)</td><td></td><td></td><td>0.131</td><td>0.932</td></tr><tr><td>res(clustcoeff)</td><td>0.702</td><td>0.254</td><td>0.169</td><td>0.543</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Figure 1 - Correlation chart for the network metrics</figcaption></figure>

## Relation between sociodemographic variables and network dimensions and metrics

Dimension 1 (assortativity) was positively linked to perceived accessibility to services (z=2.96, p=0.0003) but negatively linked with the level of study (z=2.01, p=0.045) (see Table s1). Dimensions 2 (ego centrality) and 3 (strengths of connections) were positively linked with the number of people living with ego (z=3.04, p=0.002; see Tables s2 and s3). Dimension 4 (residuals of Simmelian brokerage) was linked with the perceived accessibility to services (z=2.06, p=0.04; Table s4). Finally, the degree was positively linked with the age of the participants (z=2.34, p=0.02) and negatively linked with the level of education (z=2.85, p=0.004), population density (z=2.2, p=0.027), and gender (men compared to women, z=2.43, p=0.015) (see Table s5).

## Links between network dimensions, metrics and well-being

No associations were found between the social network dimensions, even the degree (removed from the PCA analysis), and our health measures (see Table 6). Moreover, only the two variables of the strength
<table><caption>Table 5 - Loadings for each variable in each dimension of the PCA</caption><thead><tr><th></th><th>RC1</th><th>RC2</th><th>RC3</th><th>RC4</th></tr></thead><tbody><tr><td>strength_direct</td><td></td><td></td><td>0.934</td><td></td></tr><tr><td>strength_all</td><td>0.182</td><td></td><td>0.9</td><td>0.122</td></tr><tr><td>network_density</td><td>-0.217</td><td>0.953</td><td></td><td></td></tr><tr><td>Clustering coefficient</td><td>0.309</td><td>0.878</td><td></td><td>0.343</td></tr><tr><td>Simmelian brokerage</td><td>0.193</td><td>-0.814</td><td>0.112</td><td>0.531</td></tr><tr><td>assortativity sex</td><td>0.676</td><td></td><td>0.184</td><td>0.331</td></tr><tr><td>assortativity_occupation</td><td>0.896</td><td>-0.127</td><td>-0.111</td><td></td></tr><tr><td>assortativity_class_age</td><td>0.81</td><td></td><td>0.129</td><td>-0.12</td></tr><tr><td>res(simbrok)</td><td></td><td></td><td>0.131</td><td>0.932</td></tr><tr><td>res(clustcoeff)</td><td>0.702</td><td>0.254</td><td>0.169</td><td>0.543</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Figure 1 - Correlation chart for the network metrics</figcaption></figure>

## Relation between sociodemographic variables and network dimensions and metrics

Dimension 1 (assortativity) was positively linked to perceived accessibility to services (z=2.96, p=0.0003) but negatively linked with the level of study (z=2.01, p=0.045) (see Table s1). Dimensions 2 (ego centrality) and 3 (strengths of connections) were positively linked with the number of people living with ego (z=3.04, p=0.002; see Tables s2 and s3). Dimension 4 (residuals of Simmelian brokerage) was linked with the perceived accessibility to services (z=2.06, p=0.04; Table s4). Finally, the degree was positively linked with the age of the participants (z=2.34, p=0.02) and negatively linked with the level of education (z=2.85, p=0.004), population density (z=2.2, p=0.027), and gender (men compared to women, z=2.43, p=0.015) (see Table s5).

## Links between network dimensions, metrics and well-being

No associations were found between the social network dimensions, even the degree (removed from the PCA analysis), and our health measures (see Table 6). Moreover, only the two variables of the strength
of contact are linked with the Depression Scale (CES-20). The other metrics are not linked with any of the three health status metrics (see Table S6). The strength of all contacts (direct and indirect) is positively linked with the depression scale (Z=3.22, p=0.001), whereas the strength of direct contact (only face-to-face, z=2.45, p=0.014) is negatively linked with the depression scale. Other network metrics taken individually are not linked with the three health status metrics. We also conducted a qualitative assessment, indicating depressed participants with a 1 and non-depressed participants with a 0, to examine the effects of network dimensions and indices on the depression scale. However, we did not observe any significant effects (|z| < 1.5, p > 0.129).

<table><caption>**Table 6** - Averaged statistical values following the model selection for the three health status as response variables and the four dimensions, plus the degree as independent variables</caption><thead><tr><th rowspan="2"></th><th colspan="3">CES-20 (Depression)</th><th colspan="3">CASP-12 (Quality of life)</th><th colspan="3">Stay Y-B test (Anxiety)</th></tr><tr><th>Estimate</th><th>Z-value</th><th>P-value</th><th>Estimate</th><th>Z-value</th><th>P-value</th><th>Estimate</th><th>Z-value</th><th>P-value</th></tr></thead><tbody><tr><td>Dim 1</td><td>0.15±0.36</td><td>0.42</td><td>0.670</td><td>-0.08±0.26</td><td>0.51</td><td>0.604</td><td>0.23±0.41</td><td>0.56</td><td>0.577</td></tr><tr><td>Dim 2</td><td>-0.30±0.35</td><td>0.86</td><td>0.389</td><td>-0.07±0.15</td><td>0.46</td><td>0.647</td><td>-0.66±0.45</td><td>1.44</td><td>0.150</td></tr><tr><td>Dim 3</td><td>0.78±0.46</td><td>1.66</td><td>0.096</td><td>-0.16±0.21</td><td>0.77</td><td>0.438</td><td>0.36±0.58</td><td>0.53</td><td>0.536</td></tr><tr><td>Dim 4</td><td>0.42±0.54</td><td>0.76</td><td>0.443</td><td>0.11±0.23</td><td>0.47</td><td>0.603</td><td>0.37±0.61</td><td>0.55</td><td>0.548</td></tr><tr><td>Degree</td><td>0.06±0.26</td><td>0.77</td><td>0.810</td><td>-0.08±0.11</td><td>0.72</td><td>0.469</td><td>-0.22±0.36</td><td>0.60</td><td>0.547</td></tr></tbody></table>

Discussion

This study aimed to examine the structure of the social network, its drivers, and the consequences of this structure on health using new methodologies that can be summarized in three points:

Knowing how the participants (ego) and their alters are connected thanks to VeritasSocial (Kestens et al., 2016; Naud et al., 2020). This new questionnaire allows for the measurement of new network metrics. Indeed, social integration is dependent on not only how participants are connected but also how their relationships are connected with each other independently of ego (Brissette et al., 2000), which is also negatively linked to depression (Hagerty & Williams, 1999).

The importance of some network metrics can be measured by removing the influence of others as network density using as in this study linear regression. This parameter is linked to most other metrics as adding one connection in a network increases density as it increases indirect metrics (i.e., metrics that measure for ego how an individual's alters are connected). In our study, these indirect metrics were the clustering coefficient and the Simmelian brokerage. We then decided to extract the effect of density using residuals of the linear regression with indirect measures as response variables and density as a factor. This process seems scientifically viable as these residuals were important variables in the subsequent analyses.

PCA was performed on all network dimensions to find dimensions with psychological or sociological meanings by gathering the different metrics measured. PCA is used to reduce the number of estimators in one or several dimensions while retaining as much of the information as possible; the new resultant variable(s) are constructed as a linear combination of the original variables and allow the synthesis of all metrics (Zass & Shashua, 2007; Berni et al., 2011). PCA also allows us to understand the different dimensions of a system and participants' social network and extract psychological or sociological meaning from these dimensions. To our knowledge, PCA associated to SNA in order to highlight such dimensions was never done in health or gerontology research. In our study, we identified four network dimensions, which we explain in detail below.

Dimension 1 includes all the assortativities and residuals of the clustering coefficient. This corresponds simply to assortativity, the preference that participants attach to similar characteristics in other people (here, individuals of the same age, sex, and occupation). Dimension 2 includes the network density, clustering coefficient, and Simmelian brokerage and corresponds to ego centrality. Here, centrality concerns not only the direct and indirect connections—how ego is strongly connected—but also how one's alters are connected. Dimension 2 fits the concept of social integration and is linked to social participation. Indeed, network density increases social participation (Wang et al., 2002) and promotes the development of a sense of community belonging (reflected in the clustering coefficient (Wilkinson, 1991; Bell, 1998)) and opens up new opportunities to create new relationships and expand one's social network (i.e., the Simmelian brokerage (Stern et al., 2011)). Therefore, given that they mutually influence each other, it is
of contact are linked with the Depression Scale (CES-20). The other metrics are not linked with any of the three health status metrics (see Table S6). The strength of all contacts (direct and indirect) is positively linked with the depression scale (z=3.22, p=0.001), whereas the strength of direct contact (only face-to-face, z=2.45, p=0.014) is negatively linked with the depression scale. Other network metrics taken individually are not linked with the three health status metrics. We also conducted a qualitative assessment, indicating depressed participants with a 1 and non-depressed participants with a 0, to examine the effects of network dimensions and indices on the depression scale. However, we did not observe any significant effects (|z| < 1.5, p > 0.129).

<table><caption>**Table 6** - Averaged statistical values following the model selection for the three health status as response variables and the four dimensions, plus the degree as independent variables</caption><thead><tr><th rowspan="2"></th><th colspan="3">CES-20 (Depression)</th><th colspan="3">CASP-12 (Quality of life)</th><th colspan="3">Stay Y-B test (Anxiety)</th></tr><tr><th>Estimate</th><th>Z-value</th><th>P-value</th><th>Estimate</th><th>Z-value</th><th>P-value</th><th>Estimate</th><th>Z-value</th><th>P-value</th></tr></thead><tbody><tr><td>Dim 1</td><td>0.15±0.36</td><td>0.42</td><td>0.670</td><td>-0.08±0.26</td><td>0.51</td><td>0.604</td><td>0.23±0.41</td><td>0.56</td><td>0.577</td></tr><tr><td>Dim 2</td><td>-0.30±0.35</td><td>0.86</td><td>0.389</td><td>-0.07±0.15</td><td>0.46</td><td>0.647</td><td>-0.66±0.45</td><td>1.44</td><td>0.150</td></tr><tr><td>Dim 3</td><td>0.78±0.46</td><td>1.66</td><td>0.096</td><td>-0.16±0.21</td><td>0.77</td><td>0.438</td><td>0.36±0.58</td><td>0.53</td><td>0.536</td></tr><tr><td>Dim 4</td><td>0.42±0.54</td><td>0.76</td><td>0.443</td><td>0.11±0.23</td><td>0.47</td><td>0.603</td><td>0.37±0.61</td><td>0.55</td><td>0.548</td></tr><tr><td>Degree</td><td>0.06±0.26</td><td>0.77</td><td>0.810</td><td>-0.08±0.11</td><td>0.72</td><td>0.469</td><td>-0.22±0.36</td><td>0.60</td><td>0.547</td></tr></tbody></table>

Discussion

This study aimed to examine the structure of the social network, its drivers, and the consequences of this structure on health using new methodologies that can be summarized in three points:

Knowing how the participants (ego) and their alters are connected thanks to VeritasSocial (Kestens et al., 2016; Naud et al., 2020). This new questionnaire allows for the measurement of new network metrics. Indeed, social integration is dependent on not only how participants are connected but also how their relationships are connected with each other independently of ego (Brissette et al., 2000), which is also negatively linked to depression (Hagerty & Williams, 1999).

The importance of some network metrics can be measured by removing the influence of others as network density using as in this study linear regression. This parameter is linked to most other metrics as adding one connection in a network increases density as it increases indirect metrics (i.e., metrics that measure for ego how an individual's alters are connected). In our study, these indirect metrics were the clustering coefficient and the Simmelian brokerage. We then decided to extract the effect of density using residuals of the linear regression with indirect measures as response variables and density as a factor. This process seems scientifically viable as these residuals were important variables in the subsequent analyses.

PCA was performed on all network dimensions to find dimensions with psychological or sociological meanings by gathering the different metrics measured. PCA is used to reduce the number of estimators in one or several dimensions while retaining as much of the information as possible; the new resultant variable(s) are constructed as a linear combination of the original variables and allow the synthesis of all metrics (Zass & Shashua, 2007; Berni et al., 2011). PCA also allows us to understand the different dimensions of a system and participants' social network and extract psychological or sociological meaning from these dimensions. To our knowledge, PCA associated to SNA in order to highlight such dimensions was never done in health or gerontology research. In our study, we identified four network dimensions, which we explain in detail below.

Dimension 1 includes all the assortativities and residuals of the clustering coefficient. This corresponds simply to assortativity, the preference that participants attach to similar characteristics in other people (here, individuals of the same age, sex, and occupation). Dimension 2 includes the network density, clustering coefficient, and Simmelian brokerage and corresponds to ego centrality. Here, centrality concerns not only the direct and indirect connections—how ego is strongly connected—but also how one's alters are connected. Dimension 2 fits the concept of social integration and is linked to social participation. Indeed, network density increases social participation (Wang et al., 2002) and promotes the development of a sense of community belonging (reflected in the clustering coefficient (Wilkinson, 1991; Bell, 1998)) and opens up new opportunities to create new relationships and expand one's social network (i.e., the Simmelian brokerage (Stern et al., 2011)). Therefore, given that they mutually influence each other, it is
logical that these metrics are gathered into one dimension. Dimension 3 includes the two strength of contact variables, meaning the strengths concerning all contacts (face-to-face and indirect) and the one for face-to-face contact only. It is interesting to see that these metrics are well separated from the other metrics, which implies that they do not reflect the same concept. Indeed, the strength or frequency of contact, whether direct or indirect, is the basis of social support (House et al., 1988; Wellman, 1992). Finally, Dimension 4 includes only the residuals of the Simmelian brokerage. Assessing what remains after removing the effect of network density from the Simmelian brokerage is not intuitive. The Simmelian brokerage is based on a complex value measure of Simmelian tie strength. Notably, while the basic ties are known as strong or weak and focus on the strength of the analyzed relationship, Simmelian ties are concerned with more than just the strength of the relationship; they examine the number of strong ties within a group. For a Simmelian tie to exist, there must be three (or more) reciprocal strong ties in a group (Krackhardt, 1999; Krackhardt & Kilduff, 2002). To understand this dimension more deeply, it is important to recognize that the Simmelian brokerage metric is a complex value measure that assesses the strength of Simmelian ties. These ties extend beyond the simple strength of a relationship, taking into account the number of strong reciprocal ties within a group. In other words, Simmelian ties signify that there must be at least three or more mutual strong ties within a specific network group for them to exist. When considering the residuals of the Simmelian brokerage, we are essentially examining what remains after removing the influence of network density. Since these residuals form a distinct dimension, separate from assortativity (Dimension 1) and ego centrality (Dimension 2), it implies that they capture a specific aspect of connectivity or relationship dynamics that is not fully explained by either network density, the clustering coefficient, or Simmelian brokerage. While the exact interpretation of Dimension 4 may require further investigation and analysis, it suggests that it represents a unique feature of participants' social networks, potentially related to their social integration or network structure. Further research could help uncover the specific nature of this dimension and its implications for participants' well-being and social interactions.

PCA leads to the opportunity to have dimensions that give quantitative and objective measures to aspects as social support or social integration. On the basis of our better understanding of participants' social network structure, we may now understand the drivers and consequences of these social networks. These analyses were conducted with results confirmed by the existing literature, which also yielded some contradictory results as we did not find some correlations between our dimensions and usual sociodemographic variables. First, Dimension 1 (assortativity or homophily) was positively linked with perceived accessibility to services in one's residential neighborhood but negatively linked with the level of study. The higher the number of activities people who can perform near their residence, the more relationships they share with people who are similar to them in terms of age, education, or occupation. Because they can easily walk and join different services, they can meet their local counterparts who are more likely to be similar to them. However, the higher the level of education, the lower the homophily. This means that educated people show a greater diversity of relationships with people of different ages, education levels, or occupations. Dimension 2 (ego centrality or social integration) and Dimension 3 (strengths of contacts or social support) were only linked to the number of people living with ego. This last result is logical and has been found in many studies (Seeman & Berkman, 1988; Zainuddin et al., 2020; Katayama et al., 2021; Lowndes et al., 2021; Hsieh & Zhang, 2021), but we expected to observe other influences, such as those from income, population density, urban quality, and accessibility (Sharmeen et al., 2014; Kim et al., 2018). Wood et al. (2010) for example, studied the association between sense of community, walking, and neighborhood design characteristics and found that the sense of community was enhanced by living in areas that encourage leisurely walking. However, a limited number of living areas are walkable, densely populated, and have a multiple choice of service contexts.⁴⁸ Carrasco et al. (2008) analyzed the spatial distribution of home locations of socialized social network members and found that a wider social network, frequent interactions, and greater distances are associated with people with high income. However, what we found by analyzing the degree of participants, was that older people, people with lower education, those living in lower population density areas, and females had higher degree networks. With age, while older adults show social selectivity (Sueur et al., 2021), they are less dependent on time constraints and may see their families or other people at home more often (Kjær & Siren, 2020; Dupraz et al., 2020; Galof & Balantič, 2021). Dimension 4, which is linked to participants' social integration, was only linked with perceived accessibility to local services. The same explanations than for Dimension 1 apply. The higher the perceived pedestrian accessibility, the higher the number of participants who may
logical that these metrics are gathered into one dimension. Dimension 3 includes the two strength of contact variables, meaning the strengths concerning all contacts (face-to-face and indirect) and the one for face-to-face contact only. It is interesting to see that these metrics are well separated from the other metrics, which implies that they do not reflect the same concept. Indeed, the strength or frequency of contact, whether direct or indirect, is the basis of social support (House et al., 1988; Wellman, 1992). Finally, Dimension 4 includes only the residuals of the Simmelian brokerage. Assessing what remains after removing the effect of network density from the Simmelian brokerage is not intuitive. The Simmelian brokerage is based on a complex value measure of Simmelian tie strength. Notably, while the basic ties are known as strong or weak and focus on the strength of the analyzed relationship, Simmelian ties are concerned with more than just the strength of the relationship; they examine the number of strong ties within a group. For a Simmelian tie to exist, there must be three (or more) reciprocal strong ties in a group (Krackhardt, 1999; Krackhardt & Kilduff, 2002). To understand this dimension more deeply, it is important to recognize that the Simmelian brokerage metric is a complex value measure that assesses the strength of Simmelian ties. These ties extend beyond the simple strength of a relationship, taking into account the number of strong reciprocal ties within a group. In other words, Simmelian ties signify that there must be at least three or more mutual strong ties within a specific network group for them to exist. When considering the residuals of the Simmelian brokerage, we are essentially examining what remains after removing the influence of network density. Since these residuals form a distinct dimension, separate from assortativity (Dimension 1) and ego centrality (Dimension 2), it implies that they capture a specific aspect of connectivity or relationship dynamics that is not fully explained by either network density, the clustering coefficient, or Simmelian brokerage. While the exact interpretation of Dimension 4 may require further investigation and analysis, it suggests that it represents a unique feature of participants' social networks, potentially related to their social integration or network structure. Further research could help uncover the specific nature of this dimension and its implications for participants' well-being and social interactions.

PCA leads to the opportunity to have dimensions that give quantitative and objective measures to aspects as social support or social integration. On the basis of our better understanding of participants' social network structure, we may now understand the drivers and consequences of these social networks. These analyses were conducted with results confirmed by the existing literature, which also yielded some contradictory results as we did not find some correlations between our dimensions and usual sociodemographic variables. First, Dimension 1 (assortativity or homophily) was positively linked with perceived accessibility to services in one's residential neighborhood but negatively linked with the level of study. The higher the number of activities people who can perform near their residence, the more relationships they share with people who are similar to them in terms of age, education, or occupation. Because they can easily walk and join different services, they can meet their local counterparts who are more likely to be similar to them. However, the higher the level of education, the lower the homophily. This means that educated people show a greater diversity of relationships with people of different ages, education levels, or occupations. Dimension 2 (ego centrality or social integration) and Dimension 3 (strengths of contacts or social support) were only linked to the number of people living with ego. This last result is logical and has been found in many studies (Seeman & Berkman, 1988; Zainuddin et al., 2020; Katayama et al., 2021; Lowndes et al., 2021; Hsieh & Zhang, 2021), but we expected to observe other influences, such as those from income, population density, urban quality, and accessibility (Sharmeen et al., 2014; Kim et al., 2018). Wood et al. (2010) for example, studied the association between sense of community, walking, and neighborhood design characteristics and found that the sense of community was enhanced by living in areas that encourage leisurely walking. However, a limited number of living areas are walkable, densely populated, and have a multiple choice of service contexts.⁴⁸ Carrasco et al. (2008) analyzed the spatial distribution of home locations of socialized social network members and found that a wider social network, frequent interactions, and greater distances are associated with people with high income. However, what we found by analyzing the degree of participants, was that older people, people with lower education, those living in lower population density areas, and females had higher degree networks. With age, while older adults show social selectivity (Sueur et al., 2021), they are less dependent on time constraints and may see their families or other people at home more often (Kjær & Siren, 2020; Dupraz et al., 2020; Galof & Balantič, 2021). Dimension 4, which is linked to participants' social integration, was only linked with perceived accessibility to local services. The same explanations than for Dimension 1 apply. The higher the perceived pedestrian accessibility, the higher the number of participants who may
go outside, may engage in different activities, and may be connected with different people. Similar results were reported by Buffel et al. (2014), who examined the relationship between subjective neighborhood perceptions and social participation among older adults living in medium-sized cities in Flanders, Belgium. They found that older adults reporting greater access to a larger number of services and amenities also reported higher levels of social participation.

Finally, and rather surprisingly, we found that none of the four aggregated network dimensions, even the degree, were linked to the three health status metrics. Only the strength of all contacts (direct and indirect) and the strength of direct contact were associated with the Depression Scale. However, the relationship was positive for all contacts and negative for face-to-face contact. This does not mean that direct contact leads to depression, but rather that it is likely that depressed participants often asked for face-to-face contacts with their family or friends to talk about their problems. However, indirect contact using social media or social technologies is increasingly important for older adults and is negatively linked with a sense of loneliness (Silva et al., 2020; Schlomann et al., 2020; Bonsaksen et al., 2021; Casanova et al., 2021). We found a link between health status and the strengths of contacts but not with degree or other network metrics. This is astonishing as several studies have shown a link between social capital (social network, social support, etc.) and different measures of physical and mental health. Our results may be due to our PCA to decrease the variance of explanatory variables and mask potentially existing associations. However, we also did not find relationships when network metrics were analyzed separately. Our sample size of 73 might also have been a limiting factor. This sample set is somewhat biased due to the setting of Paris, where the cost of living is quite high, which could decrease the variance of variables and, in turn, the possible effects of explanatory variables. Paris presents a unique setting for epidemiological research due to its densely populated urban environment, socioeconomic and cultural diversity, and access to healthcare services. The city's multicultural population and varying socioeconomic statuses introduce complexities in studying social networks and their associations with health. Factors like lifestyle, access to resources, and the cost of living in Paris can impact social network dynamics and health outcomes. Additionally, the city's public health initiatives and environmental factors, such as air quality and traffic congestion, play a role in the health of its residents. Researchers must consider these specific characteristics of Paris when conducting epidemiological studies to provide meaningful insights into the relationships between social networks and health.

We acknowledge the limitation of a small sample size, which can impact the generalizability and statistical power of the findings. A small sample size can lead to limited representativeness of the broader population, making it challenging to draw definitive conclusions that apply to a larger group of people. It can also affect the ability to detect statistically significant relationships or associations between variables. One other possible criticism is that the relationship between mental health and network features may not follow a linear pattern. Threshold effects could be at play, where certain network characteristics have a significant impact only once they cross a specific threshold. For example, complete social isolation may indeed have a detrimental effect on mental health, but having at least one friend could provide a protective effect against loneliness. The study's small sample size might not have been sufficient to detect such threshold effects. We checked however for sigmoid functions indicating a threshold effect and did not find such nonlinear data. Further investigation into extreme cases or subgroup analysis could shed light on these nuances. By doing so, researchers could examine whether specific network characteristics have a more pronounced impact on those who are already experiencing higher levels of depression, potentially identifying critical thresholds or nonlinear relationships that might not be evident in the overall analysis. This approach could provide a deeper understanding of how social networks influence mental health and may help uncover patterns that were not apparent in the primary analysis due to the limitations of the small sample size. In this context, we recognize that the findings may not fully capture the complexity and nuances of social network dynamics and their impact on health, and that the results should be interpreted with caution. We emphasize the need for further research with larger and more diverse datasets to validate and extend their methodology, allowing for a more comprehensive understanding of social network structures, their determinants, and their consequences for various population groups. However we need to be careful about comparisons between studies. The purpose and methodologies of our study differ significantly from studies like Charbey & Prieur (2019) Vacca (2020), primarily because these studies also incorporate online and social media friends. This discrepancy is particularly relevant to the issue of defining social support, a concept we highlighted. In our research, we concentrated on tangible, physical, and
go outside, may engage in different activities, and may be connected with different people. Similar results were reported by Buffel et al. (2014), who examined the relationship between subjective neighborhood perceptions and social participation among older adults living in medium-sized cities in Flanders, Belgium. They found that older adults reporting greater access to a larger number of services and amenities also reported higher levels of social participation.

Finally, and rather surprisingly, we found that none of the four aggregated network dimensions, even the degree, were linked to the three health status metrics. Only the strength of all contacts (direct and indirect) and the strength of direct contact were associated with the Depression Scale. However, the relationship was positive for all contacts and negative for face-to-face contact. This does not mean that direct contact leads to depression, but rather that it is likely that depressed participants often asked for face-to-face contacts with their family or friends to talk about their problems. However, indirect contact using social media or social technologies is increasingly important for older adults and is negatively linked with a sense of loneliness (Silva et al., 2020; Schlomann et al., 2020; Bonsaksen et al., 2021; Casanova et al., 2021). We found a link between health status and the strengths of contacts but not with degree or other network metrics. This is astonishing as several studies have shown a link between social capital (social network, social support, etc.) and different measures of physical and mental health. Our results may be due to our PCA to decrease the variance of explanatory variables and mask potentially existing associations. However, we also did not find relationships when network metrics were analyzed separately. Our sample size of 73 might also have been a limiting factor. This sample set is somewhat biased due to the setting of Paris, where the cost of living is quite high, which could decrease the variance of variables and, in turn, the possible effects of explanatory variables. Paris presents a unique setting for epidemiological research due to its densely populated urban environment, socioeconomic and cultural diversity, and access to healthcare services. The city's multicultural population and varying socioeconomic statuses introduce complexities in studying social networks and their associations with health. Factors like lifestyle, access to resources, and the cost of living in Paris can impact social network dynamics and health outcomes. Additionally, the city's public health initiatives and environmental factors, such as air quality and traffic congestion, play a role in the health of its residents. Researchers must consider these specific characteristics of Paris when conducting epidemiological studies to provide meaningful insights into the relationships between social networks and health.

We acknowledge the limitation of a small sample size, which can impact the generalizability and statistical power of the findings. A small sample size can lead to limited representativeness of the broader population, making it challenging to draw definitive conclusions that apply to a larger group of people. It can also affect the ability to detect statistically significant relationships or associations between variables. One other possible criticism is that the relationship between mental health and network features may not follow a linear pattern. Threshold effects could be at play, where certain network characteristics have a significant impact only once they cross a specific threshold. For example, complete social isolation may indeed have a detrimental effect on mental health, but having at least one friend could provide a protective effect against loneliness. The study's small sample size might not have been sufficient to detect such threshold effects. We checked however for sigmoid functions indicating a threshold effect and did not find such nonlinear data. Further investigation into extreme cases or subgroup analysis could shed light on these nuances. By doing so, researchers could examine whether specific network characteristics have a more pronounced impact on those who are already experiencing higher levels of depression, potentially identifying critical thresholds or nonlinear relationships that might not be evident in the overall analysis. This approach could provide a deeper understanding of how social networks influence mental health and may help uncover patterns that were not apparent in the primary analysis due to the limitations of the small sample size. In this context, we recognize that the findings may not fully capture the complexity and nuances of social network dynamics and their impact on health, and that the results should be interpreted with caution. We emphasize the need for further research with larger and more diverse datasets to validate and extend their methodology, allowing for a more comprehensive understanding of social network structures, their determinants, and their consequences for various population groups. However we need to be careful about comparisons between studies. The purpose and methodologies of our study differ significantly from studies like Charbey & Prieur (2019) Vacca (2020), primarily because these studies also incorporate online and social media friends. This discrepancy is particularly relevant to the issue of defining social support, a concept we highlighted. In our research, we concentrated on tangible, physical, and
psychological support, which naturally leads to a smaller number of network connections, or 'alters'. While studies with larger network sizes often offer greater applicability and generalizability, it is important to recognize that smaller networks can still yield valuable insights into specific social dynamics and phenomena. Researchers should be diligent in designing their studies and carefully consider the network size that best aligns with their research objectives and constraints.

While our findings are limited, our study illustrates a new method to analyze social network metrics and better identify the different concepts of social capital (e.g. social support, social integration, Sueur et al., 2021a). Our methodology should be extended to other datasets to better understand the structure, drivers, and consequences of social networks of older adults and of people in general.

## Conflicts of Interest

YK holds shares in Polygon Research Inc., the company that markets the VERITAS application. All other authors declare that they have no competing interests. The authors declare they comply with the PCI rule of having no financial conflicts of interest.

## Funding

MINDMAP is funded by the European Commission HORIZON 2020 research and innovation action 667661. HANC is funded by a grant from the French National Research Agency (ANR-15-CE36-0005).

## Acknowledgements

The team would like to thank all participants of the study. Preprint version 3 of this article has been peer-reviewed and recommended by Peer Community In Network Science (https://doi.org/10.24072/pci.networksci.100112; Lawford, 2024).

## Data script and code availability

Data, script and codes are available at https://doi.org/10.5281/zenodo.7763430 (Sueur et al., 2023).

## References

* Aartsen MJ, van Tilburg T, Smits CHM, Knipscheer KCPM (2004) A Longitudinal Study of the Impact of Physical and Cognitive Decline on the Personal Network in Old Age. Journal of Social and Personal Relationships, 21, 249-266. https://doi.org/10.1177/0265407504041386

* Allaire J (2012) RStudio: integrated development environment for R. Boston, MA, 770, 394.

* Barnes LL, De Leon CM, Wilson RS, Bienias JL, Evans DA (2004) Social resources and cognitive decline in a population of older African Americans and whites. Neurology, 63, 2322-2326. https://doi.org/10.1212/01.WNL.0000147473.04043.B3

* Bartoń K (2013) MuMln: multi-model inference. R package version, 1. https://cran.r-project.org/package=MuMln

* Bell MM (1998) The dialogue of solidarities, or why the lion spared Androcles. Sociological Focus, 31, 181-199. https://doi.org/10.1080/00380237.1998.10571100

* Berkman LF, Kawachi I, Glymour MM (2014) Social epidemiology. Oxford University Press. https://doi.org/10.1093/med/9780195377903.001.0001

* Berni A, Giuliani A, Tartaglia F, Tromba L, Sgueglia M, Blasi S, Russo G (2011a) Effect of vascular risk factors on increase in carotid and femoral intima-media thickness. Identification of a risk scale. Atherosclerosis, 216, 109-114. https://doi.org/10.1016/j.atherosclerosis.2011.01.034

* Bidart C, Degenne A, Grossetti M (2018) Personal networks typologies: A structural approach. Social Networks, 54, 1-11. https://doi.org/10.1016/j.socnet.2017.11.003
psychological support, which naturally leads to a smaller number of network connections, or 'alters'. While studies with larger network sizes often offer greater applicability and generalizability, it is important to recognize that smaller networks can still yield valuable insights into specific social dynamics and phenomena. Researchers should be diligent in designing their studies and carefully consider the network size that best aligns with their research objectives and constraints.

While our findings are limited, our study illustrates a new method to analyze social network metrics and better identify the different concepts of social capital (e.g. social support, social integration, Sueur et al., 2021a). Our methodology should be extended to other datasets to better understand the structure, drivers, and consequences of social networks of older adults and of people in general.

## Conflicts of Interest

YK holds shares in Polygon Research Inc., the company that markets the VERITAS application. All other authors declare that they have no competing interests. The authors declare they comply with the PCI rule of having no financial conflicts of interest.

## Funding

MINDMAP is funded by the European Commission HORIZON 2020 research and innovation action 667661. HANC is funded by a grant from the French National Research Agency (ANR-15-CE36-0005).

## Acknowledgements

The team would like to thank all participants of the study. Preprint version 3 of this article has been peer-reviewed and recommended by Peer Community In Network Science (https://doi.org/10.24072/pci.networksci.100112; Lawford, 2024).

## Data script and code availability

Data, script and codes are available at https://doi.org/10.5281/zenodo.7763430 (Sueur et al., 2023).

## References

Aartsen MJ, van Tilburg T, Smits CHM, Knipscheer KCPM (2004) A Longitudinal Study of the Impact of Physical and Cognitive Decline on the Personal Network in Old Age. Journal of Social and Personal Relationships, 21, 249-266. https://doi.org/10.1177/0265407504041386

Allaire J (2012) RStudio: integrated development environment for R. Boston, MA, 770, 394.

Barnes LL, De Leon CM, Wilson RS, Bienias JL, Evans DA (2004) Social resources and cognitive decline in a population of older African Americans and whites. Neurology, 63, 2322-2326. https://doi.org/10.1212/01.WNL.0000147473.04043.B3

Bartoń K (2013) MuMln: multi-model inference. R package version, 1. https://cran.r-project.org/package=MuMln

Bell MM (1998) The dialogue of solidarities, or why the lion spared Androcles. Sociological Focus, 31, 181-199. https://doi.org/10.1080/00380237.1998.10571100

Berkman LF, Kawachi I, Glymour MM (2014) Social epidemiology. Oxford University Press. https://doi.org/10.1093/med/9780195377903.001.0001

Berni A, Giuliani A, Tartaglia F, Tromba L, Sgueglia M, Blasi S, Russo G (2011a) Effect of vascular risk factors on increase in carotid and femoral intima-media thickness. Identification of a risk scale. Atherosclerosis, 216, 109-114. https://doi.org/10.1016/j.atherosclerosis.2011.01.034

Bidart C, Degenne A, Grossetti M (2018) Personal networks typologies: A structural approach. Social Networks, 54, 1-11. https://doi.org/10.1016/j.socnet.2017.11.003
Bonsaksen T, Thygesen H, Leung J, Ruffolo M, Schoultz M, Price D, Østertun Geirdal A (2021) Video-Based Communication and Its Association with Loneliness, Mental Health and Quality of Life among Older People during the COVID-19 Outbreak. International Journal of Environmental Research and Public Health, 18, 6284. https://doi.org/10.3390/ijerph18126284

Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network Analysis in the Social Sciences. Science, 323, 892-895. https://doi.org/10.1126/science.1165821

Brissette I, Cohen S, Seeman TE (2000) Measuring social integration and social networks. in Sheldon Cohen, Lynn G. Underwood, and Benjamin H. Gottlieb (eds), Social Support Measurement and Intervention: A Guide for Health and Social Scientists. Oxford University Press https://doi.org/10.1093/med:psych/9780195126709.003.0003

Budaev SV (2010) Using principal components and factor analysis in animal behaviour research: caveats and guidelines. Ethology, 116, 472-480. https://doi.org/10.1111/j.1439-0310.2010.01758.x

Buffel T, De Donder L, Phillipson C, Dury S, De Witte N, Verté D (2014) Social participation among older adults living in medium-sized cities in Belgium: the role of neighbourhood perceptions. Health Promotion International, 29, 655-668. https://doi.org/10.1093/heapro/dat009

Burnham KP, Anderson DR (2004) Multimodel inference understanding AIC and BIC in model selection. Sociological methods & research, 33, 261-304. https://doi.org/10.1177/0049124104268644

Cacioppo JT, Hughes ME, Waite LJ, Hawkley LC, Thisted RA (2006) Loneliness as a specific risk factor for depressive symptoms: cross-sectional and longitudinal analyses. Psychology and aging, 21, 140. https://doi.org/10.1037/0882-7974.21.1.140

Carl P, Peterson BG, Peterson MBG (2010) Package 'PerformanceAnalytics.' https://cran.r-project.org/package=PerformanceAnalytics

Carrasco JA, Miller EJ, Wellman B (2008) How far and with whom do people socialize?: Empirical evidence about distance between social network members. Transportation Research Record, 114-122. https://doi.org/10.3141/2076-13

Carter BD, Abnet CC, Feskanich D, Freedman ND, Hartge P, Lewis CE, Ockene JK, Prentice RL, Speizer FE, Thun MJ (2015) Smoking and mortality-beyond established causes. New England journal of medicine, 372, 631-640. https://doi.org/10.1056/NEJMsa1407211

Casanova G, Zaccaria D, Rolandi E, Guaita A (2021) The Effect of Information and Communication Technology and Social Networking Site Use on Older People's Well-Being in Relation to Loneliness: Review of Experimental Studies. Journal of Medical Internet Research, 23, e23588. https://doi.org/10.2196/23588

Cervero R, Kockelman K (1997) Travel demand and the 3Ds: Density, diversity, and design. Transportation Research Part D: Transport and Environment, 2, 199-219. https://doi.org/10.1016/S1361-9209(97)00009-6

Chaix B, Kestens Y, Bean K, Leal C, Karusisi N, Meghiref K, Burban J, Fon Sing M, Perchoux C, Thomas F, Merlo J, Pannier B (2012) Cohort Profile: Residential and non-residential environments, individual activity spaces and cardiovascular risk factors and diseases-The RECORD Cohort Study. International Journal of Epidemiology, 41, 1283-1292. https://doi.org/10.1093/ije/dyr107

Chaix B, Kestens Y, Perchoux C, Karusisi N, Merlo J, Labadi K (2012) An Interactive Mapping Tool to Assess Individual Mobility Patterns in Neighborhood Studies. American Journal of Preventive Medicine, 43, 440-450. https://doi.org/10.1016/j.amepre.2012.06.026

Charbey R, Prieur C (2019) Stars, holes, or paths across your Facebook friends: A graphlet-based characterization of many networks. Network Science, 7, 476-497. https://doi.org/10.1017/nws.2019.20

Cornwell B (2009) Network Bridging Potential in Later Life: Life-Course Experiences and Social Network Position. Journal of Aging and Health, 21, 129-154. https://doi.org/10.1177/0898264308328649

Daatland SO, Lowenstein A (2005) Intergenerational solidarity and the family-welfare state balance. European Journal of Ageing, 2, 174-182. https://doi.org/10.1007/s10433-005-0001-1

Dupraz J, Henchoz Y, Santos-Eggimann B (2020) Formal home care use by older adults: trajectories and determinants in the Lc65+ cohort. BMC Health Services Research, 20, 22. https://doi.org/10.1186/s12913-019-4867-6

Ewing R, Cervero R (2010) Travel and the built environment. Journal of the American Planning Association. https://doi.org/10.1080/01944361003766766
Bonsaksen T, Thygesen H, Leung J, Ruffolo M, Schoultz M, Price D, Østertun Geirdal A (2021) Video-Based Communication and Its Association with Loneliness, Mental Health and Quality of Life among Older People during the COVID-19 Outbreak. International Journal of Environmental Research and Public Health, 18, 6284. https://doi.org/10.3390/ijerph18126284

Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network Analysis in the Social Sciences. Science, 323, 892-895. https://doi.org/10.1126/science.1165821

Brissette I, Cohen S, Seeman TE (2000) Measuring social integration and social networks. in Sheldon Cohen, Lynn G. Underwood, and Benjamin H. Gottlieb (eds), Social Support Measurement and Intervention: A Guide for Health and Social Scientists. Oxford University Press https://doi.org/10.1093/med:psych/9780195126709.003.0003

Budaev SV (2010) Using principal components and factor analysis in animal behaviour research: caveats and guidelines. Ethology, 116, 472-480. https://doi.org/10.1111/j.1439-0310.2010.01758.x

Buffel T, De Donder L, Phillipson C, Dury S, De Witte N, Verté D (2014) Social participation among older adults living in medium-sized cities in Belgium: the role of neighbourhood perceptions. Health Promotion International, 29, 655-668. https://doi.org/10.1093/heapro/dat009

Burnham KP, Anderson DR (2004) Multimodel inference understanding AIC and BIC in model selection. Sociological methods & research, 33, 261-304. https://doi.org/10.1177/0049124104268644

Cacioppo JT, Hughes ME, Waite LJ, Hawkley LC, Thisted RA (2006) Loneliness as a specific risk factor for depressive symptoms: cross-sectional and longitudinal analyses. Psychology and aging, 21, 140. https://doi.org/10.1037/0882-7974.21.1.140

Carl P, Peterson BG, Peterson MBG (2010) Package 'PerformanceAnalytics.' https://cran.r-project.org/package=PerformanceAnalytics

Carrasco JA, Miller EJ, Wellman B (2008) How far and with whom do people socialize?: Empirical evidence about distance between social network members. Transportation Research Record, 114-122. https://doi.org/10.3141/2076-13

Carter BD, Abnet CC, Feskanich D, Freedman ND, Hartge P, Lewis CE, Ockene JK, Prentice RL, Speizer FE, Thun MJ (2015) Smoking and mortality-beyond established causes. New England journal of medicine, 372, 631-640. https://doi.org/10.1056/NEJMsa1407211

Casanova G, Zaccaria D, Rolandi E, Guaita A (2021) The Effect of Information and Communication Technology and Social Networking Site Use on Older People's Well-Being in Relation to Loneliness: Review of Experimental Studies. Journal of Medical Internet Research, 23, e23588. https://doi.org/10.2196/23588

Cervero R, Kockelman K (1997) Travel demand and the 3Ds: Density, diversity, and design. Transportation Research Part D: Transport and Environment, 2, 199-219. https://doi.org/10.1016/S1361-9209(97)00009-6

Chaix B, Kestens Y, Bean K, Leal C, Karusisi N, Meghiref K, Burban J, Fon Sing M, Perchoux C, Thomas F, Merlo J, Pannier B (2012) Cohort Profile: Residential and non-residential environments, individual activity spaces and cardiovascular risk factors and diseases-The RECORD Cohort Study. International Journal of Epidemiology, 41, 1283-1292. https://doi.org/10.1093/ije/dyr107

Chaix B, Kestens Y, Perchoux C, Karusisi N, Merlo J, Labadi K (2012) An Interactive Mapping Tool to Assess Individual Mobility Patterns in Neighborhood Studies. American Journal of Preventive Medicine, 43, 440-450. https://doi.org/10.1016/j.amepre.2012.06.026

Charbey R, Prieur C (2019) Stars, holes, or paths across your Facebook friends: A graphlet-based characterization of many networks. Network Science, 7, 476-497. https://doi.org/10.1017/nws.2019.20

Cornwell B (2009) Network Bridging Potential in Later Life: Life-Course Experiences and Social Network Position. Journal of Aging and Health, 21, 129-154. https://doi.org/10.1177/0898264308328649

Daatland SO, Lowenstein A (2005) Intergenerational solidarity and the family-welfare state balance. European Journal of Ageing, 2, 174-182. https://doi.org/10.1007/s10433-005-0001-1

Dupraz J, Henchoz Y, Santos-Eggimann B (2020) Formal home care use by older adults: trajectories and determinants in the Lc65+ cohort. BMC Health Services Research, 20, 22. https://doi.org/10.1186/s12913-019-4867-6

Ewing R, Cervero R (2010) Travel and the built environment. Journal of the American Planning Association. https://doi.org/10.1080/01944361003766766
Fancello G, Vallée J, Sueur C, van Lenthe FJ, Kestens Y, Montanari A, Chaix B (2023) Micro urban spaces and mental well-being: Measuring the exposure to urban landscapes along daily mobility paths and their effects on momentary depressive symptomatology among older population. Environment International, 178, 108095. https://doi.org/10.1016/j.envint.2023.108095

Fernandes A, Van Lenthe FJ, Vallée J, Sueur C, Chaix B (2021) Linking physical and social environments with mental health in old age: a multisensor approach for continuous real-life ecological and emotional assessment. Journal of Epidemiology and Community Health, 75, 477-483. https://doi.org/10.1136/jech-2020-214274

Flegal KM, Kit BK, Orpana H, Graubard BI (2013) Association of all-cause mortality with overweight and obesity using standard body mass index categories: a systematic review and meta-analysis. Jama, 309, 71-82. https://doi.org/10.1001/jama.2012.113905

Franke GR (2010) Multicollinearity. Wiley international encyclopedia of marketing. https://doi.org/10.1002/9781444316568.wiem02066

Galof K, Balantič Z (2021) Making the Decision to Stay at Home: Developing a Community-Based Care Process Model for Aging in Place. International Journal of Environmental Research and Public Health, 18, 5987. https://doi.org/10.3390/ijerph18115987

Gardner PJ (2011) Natural neighborhood networks-Important social networks in the lives of older adults aging in place. Journal of aging studies, 25, 263-271. https://doi.org/10.1016/j.jaging.2011.03.007

Giles LC, Glonek GF, Luszcz MA, Andrews GR (2005) Effect of social networks on 10 year survival in very old Australians: the Australian longitudinal study of aging. Journal of Epidemiology & Community Health, 59, 574-579. https://doi.org/10.1136/jech.2004.025429

Hagerty BM, Williams A (1999) The effects of sense of belonging, social support, conflict, and loneliness on depression. Nursing research, 48, 215-219. https://doi.org/10.1097/00006199-199907000-00004

Holland SM (2008) Principal component analysis (PCA): A tutorial in the R-Studio environment. Department of Geology, University of Georgia, Athens, GA 30602-2501: 10pp.

Holt-Lunstad J, Smith TB, Layton JB (2010) Social relationships and mortality risk: a meta-analytic review. PLoS medicine, 7, e1000316. https://doi.org/10.1371/journal.pmed.1000316

House JS, Umberson D, Landis KR (1988) Structures and processes of social support. Annual review of sociology, 14, 293-318. https://doi.org/10.1146/annurev.so.14.080188.001453

Hsieh N, Zhang Z (2021) Childlessness and Social Support in Old Age in China. Journal of Cross-Cultural Gerontology, 36, 121-137. https://doi.org/10.1007/s10823-021-09427-x

Hyde M, Wiggins RD, Higgs P, Blane DB (2003) A measure of quality of life in early old age: The theory, development and properties of a needs satisfaction model (CASP-19). Aging and Mental Health. https://doi.org/10.1080/1360786031000101157

Katayama O, Lee S, Bae S, Makino K, Chiba I, Harada K, Shinkai Y, Shimada H (2021) Participation in Social Activities and Relationship between Walking Habits and Disability Incidence. Journal of Clinical Medicine, 10, 1895. https://doi.org/10.3390/jcm10091895

Kestens Y, Chaix B, Gerber P, Desprès M, Gauvin L, Klein O, Klein S, Köppen B, Lord S, Naud A, Patte M, Payette H, Richard L, Rondier P, Shareck M, Sueur C, Thierry B, Vallée J, Wasfi R (2016) Understanding the role of contrasting urban contexts in healthy aging: an international cohort study using wearable sensor devices (the CURHA study protocol). BMC Geriatrics, 16, 96. https://doi.org/10.1186/s12877-016-0273-7

Kim J, Rasouli S, Timmermans HJP (2018) Social networks, social influence and activity-travel behaviour: a review of models and empirical evidence. Transport Reviews, 38, 499-523. https://doi.org/10.1080/01441647.2017.1351500

Kjær AA, Siren A (2020) Formal and informal care: trajectories of home care use among Danish older adults. Ageing and Society, 40, 2495-2518. https://doi.org/10.1017/S0144686X19000771

Krackhardt D (1999) The ties that torture: Simmelian tie analysis in organizations. In: SB Andrews, D. Knoke, eds. Networks In and Around Organizations. Research in the Sociology of Organizations, Vol. 16.

Krackhardt D, Kilduff M (2002) Structure, culture and Simmelian ties in entrepreneurial firms. Social networks, 24, 279-290. https://doi.org/10.1016/S0378-8733(02)00008-4

Latora V, Nicosia V, Panzarasa P (2013) Social Cohesion, Structural Holes, and a Tale of Two Measures. Journal of Statistical Physics, 151, 745-764. https://doi.org/10.1007/s10955-013-0722-z
Fancello G, Vallée J, Sueur C, van Lenthe FJ, Kestens Y, Montanari A, Chaix B (2023) Micro urban spaces and mental well-being: Measuring the exposure to urban landscapes along daily mobility paths and their effects on momentary depressive symptomatology among older population. Environment International, 178, 108095. https://doi.org/10.1016/j.envint.2023.108095

Fernandes A, Van Lenthe FJ, Vallée J, Sueur C, Chaix B (2021) Linking physical and social environments with mental health in old age: a multisensor approach for continuous real-life ecological and emotional assessment. Journal of Epidemiology and Community Health, 75, 477-483. https://doi.org/10.1136/jech-2020-214274

Flegal KM, Kit BK, Orpana H, Graubard BI (2013) Association of all-cause mortality with overweight and obesity using standard body mass index categories: a systematic review and meta-analysis. Jama, 309, 71-82. https://doi.org/10.1001/jama.2012.113905

Franke GR (2010) Multicollinearity. Wiley international encyclopedia of marketing. https://doi.org/10.1002/9781444316568.wiem02066

Galof K, Balantič Z (2021) Making the Decision to Stay at Home: Developing a Community-Based Care Process Model for Aging in Place. International Journal of Environmental Research and Public Health, 18, 5987. https://doi.org/10.3390/ijerph18115987

Gardner PJ (2011) Natural neighborhood networks-Important social networks in the lives of older adults aging in place. Journal of aging studies, 25, 263-271. https://doi.org/10.1016/j.jaging.2011.03.007

Giles LC, Glonek GF, Luszcz MA, Andrews GR (2005) Effect of social networks on 10 year survival in very old Australians: the Australian longitudinal study of aging. Journal of Epidemiology & Community Health, 59, 574-579. https://doi.org/10.1136/jech.2004.025429

Hagerty BM, Williams A (1999) The effects of sense of belonging, social support, conflict, and loneliness on depression. Nursing research, 48, 215-219. https://doi.org/10.1097/00006199-199907000-00004

Holland SM (2008) Principal component analysis (PCA): A tutorial in the R-Studio environment. Department of Geology, University of Georgia, Athens, GA 30602-2501: 10pp.

Holt-Lunstad J, Smith TB, Layton JB (2010) Social relationships and mortality risk: a meta-analytic review. PLoS medicine, 7, e1000316. https://doi.org/10.1371/journal.pmed.1000316

House JS, Umberson D, Landis KR (1988) Structures and processes of social support. Annual review of sociology, 14, 293-318. https://doi.org/10.1146/annurev.so.14.080188.001453

Hsieh N, Zhang Z (2021) Childlessness and Social Support in Old Age in China. Journal of Cross-Cultural Gerontology, 36, 121-137. https://doi.org/10.1007/s10823-021-09427-x

Hyde M, Wiggins RD, Higgs P, Blane DB (2003) A measure of quality of life in early old age: The theory, development and properties of a needs satisfaction model (CASP-19). Aging and Mental Health. https://doi.org/10.1080/1360786031000101157

Katayama O, Lee S, Bae S, Makino K, Chiba I, Harada K, Shinkai Y, Shimada H (2021) Participation in Social Activities and Relationship between Walking Habits and Disability Incidence. Journal of Clinical Medicine, 10, 1895. https://doi.org/10.3390/jcm10091895

Kestens Y, Chaix B, Gerber P, Desprès M, Gauvin L, Klein O, Klein S, Köppen B, Lord S, Naud A, Patte M, Payette H, Richard L, Rondier P, Shareck M, Sueur C, Thierry B, Vallée J, Wasfi R (2016) Understanding the role of contrasting urban contexts in healthy aging: an international cohort study using wearable sensor devices (the CURHA study protocol). BMC Geriatrics, 16, 96. https://doi.org/10.1186/s12877-016-0273-7

Kim J, Rasouli S, Timmermans HJP (2018) Social networks, social influence and activity-travel behaviour: a review of models and empirical evidence. Transport Reviews, 38, 499-523. https://doi.org/10.1080/01441647.2017.1351500

Kjær AA, Siren A (2020) Formal and informal care: trajectories of home care use among Danish older adults. Ageing and Society, 40, 2495-2518. https://doi.org/10.1017/S0144686X19000771

Krackhardt D (1999) The ties that torture: Simmelian tie analysis in organizations. In: SB Andrews, D. Knoke, eds. Networks In and Around Organizations. Research in the Sociology of Organizations, Vol. 16.

Krackhardt D, Kilduff M (2002) Structure, culture and Simmelian ties in entrepreneurial firms. Social networks, 24, 279-290. https://doi.org/10.1016/S0378-8733(02)00008-4

Latora V, Nicosia V, Panzarasa P (2013) Social Cohesion, Structural Holes, and a Tale of Two Measures. Journal of Statistical Physics, 151, 745-764. https://doi.org/10.1007/s10955-013-0722-z
Lawford, S. (2024) An application of PCA to social networks and healthy ageing. Peer Community in Network Science, 100112. https://doi.org/10.24072/pci.networksci.100112

Litwin H, Shiovitz-Ezra S (2006) The association between activity and wellbeing in later life: what really matters? Ageing & Society, 26, 225-242. https://doi.org/10.1017/S0144686X05004538

Lowndes R, Struthers J, Ågotnes G (2021) Social Participation in Long-term Residential Care: Case Studies from Canada, Norway, and Germany. Canadian Journal on Aging / La Revue canadienne du vieillissement, 40, 138-155. https://doi.org/10.1017/S0714980820000318

Naud A, Sueur C, Chaix B, Kestens Y (2020) Combining social network and activity space data for health research: tools and methods. Health & Place, 66, 102454. https://doi.org/10.1016/j.healthplace.2020.102454

Newman MEJ (2006) Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103, 8577-8582. https://doi.org/10.1073/pnas.0601602103

Newman M (2010) Networks: An Introduction. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199206650.001.0001

Peterson BG, Carl P, Boudt K, Bennett R, Ulrich J, Zivot E, Cornilly D, Hung E, Lestel M, Balkissoon K (2018) Package 'performanceanalytics.' https://cran.r-project.org/package=PerformanceAnalytics

Putnam R (1993) The Prosperous Community: Social Capital and Public Life. The American Prospect, 4, 35-42.

Racine JS (2012) RStudio: a platform-independent IDE for R and Sweave. Journal of Applied Econometrics https://doi.org/10.1002/jae.1278

Radloff LS (1977) The CES-D Scale: A Self-Report Depression Scale for Research in the General Population. Applied Psychological Measurement. https://doi.org/10.1177/014662167700100306

Rook KS (2015) Social Networks in Later Life: Weighing Positive and Negative Effects on Health and Well-Being. Current directions in psychological science, 24, 45-51. https://doi.org/10.1177/0963721414551364

Roucolle C, Seregina T, Urdanoz M (2020) Measuring the development of airline networks: Comprehensive indicators. Transportation Research Part A: Policy and Practice, 133, 303-324. https://doi.org/10.1016/j.tra.2019.12.010

Schlomann A, Seifert A, Zank S, Woopen C, Rietz C (2020) Use of Information and Communication Technology (ICT) Devices Among the Oldest-Old: Loneliness, Anomie, and Autonomy. Innovation in Aging, 4, igz050. https://doi.org/10.1093/geroni/igz050

Scott J (2000) Social network analysis: a handbook. SAGE.

Seeman TE, Berkman LF (1988) Structural characteristics of social networks and their relationship with social support in the elderly: who provides support. Social science & medicine, 26, 737-749. https://doi.org/10.1016/0277-9536(88)90065-2

Sharmeen F, Arentze T, Timmermans H (2014) Dynamics of face-to-face social interaction frequency: role of accessibility, urbanization, changes in geographical distance and path dependence. Journal of Transport Geography, 34, 211-220. https://doi.org/10.1016/j.jtrangeo.2013.12.011

Silva BCS, Ávila AA de, Rocha G da S, Nunes DP, Lucia FD, Brito TRP de (2020) The impact of the use of FacebookTM on social support networks and symptoms of depression reported by the elderly. International Psychogeriatrics, 32, 407-408. https://doi.org/10.1017/S1041610219000735

Smith LI (2002) A tutorial on principal components analysis. (Computer Science Technical Report No. OUCS-2002-12). http://hdl.handle.net/10523/7534

Sosa S, Puga-Gonzalez I, Hu F, Pansanel J, Xie X, Sueur C (2020) A multilevel statistical toolkit to study animal social networks: The Animal Network Toolkit Software (ANTs) R package. Scientific reports, 10, 1-8. https://doi.org/10.1038/s41598-020-69265-8

Sosa S, Sueur C, Puga-Gonzalez I (2021) Network measures in animal social network analysis: Their strengths, limits, interpretations and uses. Methods in Ecology and Evolution, 12, 10-21. https://doi.org/10.1111/2041-210X.13366

Spielberger CD, Gorsuch RL, Lushene R, Vagg PR, Jacobs GA (1983) Manual for the State-Trait Anxiety Inventory. Consulting Psychologists Press, Palo Alto, CA.

Stern MJ, Adams AE, Boase J (2011) Rural community participation, social networks, and broadband use: Examples from localized and national survey data. Agricultural and Resource Economics Review, 40, 158-171. https://doi.org/10.1017/S106828050000798X
Lawford, S. (2024) An application of PCA to social networks and healthy ageing. Peer Community in Network Science, 100112. https://doi.org/10.24072/pci.networksci.100112

Litwin H, Shiovitz-Ezra S (2006) The association between activity and wellbeing in later life: what really matters? Ageing & Society, 26, 225-242. https://doi.org/10.1017/S0144686X05004538

Lowndes R, Struthers J, Ågotnes G (2021) Social Participation in Long-term Residential Care: Case Studies from Canada, Norway, and Germany. Canadian Journal on Aging / La Revue canadienne du vieillissement, 40, 138-155. https://doi.org/10.1017/S0714980820000318

Naud A, Sueur C, Chaix B, Kestens Y (2020) Combining social network and activity space data for health research: tools and methods. Health & Place, 66, 102454. https://doi.org/10.1016/j.healthplace.2020.102454

Newman MEJ (2006) Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103, 8577-8582. https://doi.org/10.1073/pnas.0601602103

Newman M (2010) Networks: An Introduction. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199206650.001.0001

Peterson BG, Carl P, Boudt K, Bennett R, Ulrich J, Zivot E, Cornilly D, Hung E, Lestel M, Balkissoon K (2018) Package 'performanceanalytics.' https://cran.r-project.org/package=PerformanceAnalytics

Putnam R (1993) The Prosperous Community: Social Capital and Public Life. The American Prospect, 4, 35-42.

Racine JS (2012) RStudio: a platform-independent IDE for R and Sweave. Journal of Applied Econometrics https://doi.org/10.1002/jae.1278

Radloff LS (1977) The CES-D Scale: A Self-Report Depression Scale for Research in the General Population. Applied Psychological Measurement. https://doi.org/10.1177/014662167700100306

Rook KS (2015) Social Networks in Later Life: Weighing Positive and Negative Effects on Health and Well-Being. Current directions in psychological science, 24, 45-51. https://doi.org/10.1177/0963721414551364

Roucolle C, Seregina T, Urdanoz M (2020) Measuring the development of airline networks: Comprehensive indicators. Transportation Research Part A: Policy and Practice, 133, 303-324. https://doi.org/10.1016/j.tra.2019.12.010

Schlomann A, Seifert A, Zank S, Woopen C, Rietz C (2020) Use of Information and Communication Technology (ICT) Devices Among the Oldest-Old: Loneliness, Anomie, and Autonomy. Innovation in Aging, 4, igz050. https://doi.org/10.1093/geroni/igz050

Scott J (2000) Social network analysis: a handbook. SAGE.

Seeman TE, Berkman LF (1988) Structural characteristics of social networks and their relationship with social support in the elderly: who provides support. Social science & medicine, 26, 737-749. https://doi.org/10.1016/0277-9536(88)90065-2

Sharmeen F, Arentze T, Timmermans H (2014) Dynamics of face-to-face social interaction frequency: role of accessibility, urbanization, changes in geographical distance and path dependence. Journal of Transport Geography, 34, 211-220. https://doi.org/10.1016/j.jtrangeo.2013.12.011

Silva BCS, Ávila AA de, Rocha G da S, Nunes DP, Lucia FD, Brito TRP de (2020) The impact of the use of FacebookTM on social support networks and symptoms of depression reported by the elderly. International Psychogeriatrics, 32, 407-408. https://doi.org/10.1017/S1041610219000735

Smith LI (2002) A tutorial on principal components analysis. (Computer Science Technical Report No. OUCS-2002-12). http://hdl.handle.net/10523/7534

Sosa S, Puga-Gonzalez I, Hu F, Pansanel J, Xie X, Sueur C (2020) A multilevel statistical toolkit to study animal social networks: The Animal Network Toolkit Software (ANTs) R package. Scientific reports, 10, 1-8. https://doi.org/10.1038/s41598-020-69265-8

Sosa S, Sueur C, Puga-Gonzalez I (2021) Network measures in animal social network analysis: Their strengths, limits, interpretations and uses. Methods in Ecology and Evolution, 12, 10-21. https://doi.org/10.1111/2041-210X.13366

Spielberger CD, Gorsuch RL, Lushene R, Vagg PR, Jacobs GA (1983) Manual for the State-Trait Anxiety Inventory. Consulting Psychologists Press, Palo Alto, CA.

Stern MJ, Adams AE, Boase J (2011) Rural community participation, social networks, and broadband use: Examples from localized and national survey data. Agricultural and Resource Economics Review, 40, 158-171. https://doi.org/10.1017/S106828050000798X
Sueur C, Quque M, Naud A, Bergouignan A, Criscuolo F (2021) Social capital: an independent dimension of healthy ageing. Peer Community Journal, 1. https://doi.org/10.24072/pcjournal.33

Sueur, C., Fancello, G., Naud, A., Kestens, Y., & Chaix, B. (2023). Data for "Structure and drivers of social networks and their links with health in older adults" [Data set]. Zenodo. https://doi.org/10.5281/zenodo.7763430

Uchino BN (2006) Social support and health: a review of physiological processes potentially underlying links to disease outcomes. Journal of behavioral medicine, 29, 377-387. https://doi.org/10.1007/s10865-006-9056-5

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Vallée J, Le Roux G, Chaix B, Kestens Y, Chauvin P (2015) The 'constant size neighbourhood trap' in accessibility and health studies. Urban Studies, 52, 338-357. https://doi.org/10.1177/0042098014528393

Wang H-X, Karp A, Winblad B, Fratiglioni L (2002) Late-life engagement in social and leisure activities is associated with a decreased risk of dementia: a longitudinal study from the Kungsholmen project. American journal of epidemiology, 155, 1081-1087. https://doi.org/10.1093/aje/155.12.1081

Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511815478

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Wyngaerden F, Nicaise P, Dubois V, Lorant V (2019) Social support network and continuity of care: an ego-network study of psychiatric service users. Social Psychiatry and Psychiatric Epidemiology, 54, 725-735. https://doi.org/10.1007/s00127-019-01660-7

Yue Y, Zhuang Y, Yeh AGO, Xie JY, Ma CL, Li QQ (2017) Measurements of POI-based mixed use and their relationships with neighbourhood vibrancy. International Journal of Geographical Information Science, 31, 658-675. https://doi.org/10.1080/13658816.2016.1220561

Zainuddin FHB, Hamidi MB, Wahab HBA (2020) The Barriers of Financial Support Towards Successful Aging Among the Participants of Activity Center for the Older Persons in Malaysia. Global Social Welfare, 7, 367-381. https://doi.org/10.1007/s40609-020-00182-4

Zandieh R, Flacke J, Martinez J, Jones P, van Maarseveen M (2017) Do Inequalities in Neighborhood Walkability Drive Disparities in Older Adults' Outdoor Walking? International journal of environmental research and public health, 14, 740. https://doi.org/10.3390/ijerph14070740

Zass R, Shashua A (2007) Nonnegative sparse PCA. In: Advances in neural information processing systems, pp. 1561-1568. https://doi.org/10.7551/mitpress/7503.003.0200
Sueur C, Quque M, Naud A, Bergouignan A, Criscuolo F (2021) Social capital: an independent dimension of healthy ageing. Peer Community Journal, 1. https://doi.org/10.24072/pcjournal.33

Sueur, C., Fancello, G., Naud, A., Kestens, Y., & Chaix, B. (2023). Data for "Structure and drivers of social networks and their links with health in older adults" [Data set]. Zenodo. https://doi.org/10.5281/zenodo.7763430

Uchino BN (2006) Social support and health: a review of physiological processes potentially underlying links to disease outcomes. Journal of behavioral medicine, 29, 377-387. https://doi.org/10.1007/s10865-006-9056-5

Vacca R (2020) Structure in personal networks: Constructing and comparing typologies. Network Science, 8, 142-167. https://doi.org/10.1017/nws.2019.29

Vallée J, Le Roux G, Chaix B, Kestens Y, Chauvin P (2015) The 'constant size neighbourhood trap' in accessibility and health studies. Urban Studies, 52, 338-357. https://doi.org/10.1177/0042098014528393

Wang H-X, Karp A, Winblad B, Fratiglioni L (2002) Late-life engagement in social and leisure activities is associated with a decreased risk of dementia: a longitudinal study from the Kungsholmen project. American journal of epidemiology, 155, 1081-1087. https://doi.org/10.1093/aje/155.12.1081

Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511815478

Wellman B (1992) Which types of ties and networks provide what kinds of social support. Advances in group processes, 9, 207-235.

Wilkinson KP (1991) The community in rural America. Greenwood Publishing Group, New York, 141 p.

Wood L, Frank LD, Giles-Corti B (2010) Sense of community and its relationship with walking and neighborhood design. Social Science and Medicine, 70, 1381-1390. https://doi.org/10.1016/j.socscimed.2010.01.021

Wyngaerden F, Nicaise P, Dubois V, Lorant V (2019) Social support network and continuity of care: an ego-network study of psychiatric service users. Social Psychiatry and Psychiatric Epidemiology, 54, 725-735. https://doi.org/10.1007/s00127-019-01660-7

Yue Y, Zhuang Y, Yeh AGO, Xie JY, Ma CL, Li QQ (2017) Measurements of POI-based mixed use and their relationships with neighbourhood vibrancy. International Journal of Geographical Information Science, 31, 658-675. https://doi.org/10.1080/13658816.2016.1220561

Zainuddin FHB, Hamidi MB, Wahab HBA (2020) The Barriers of Financial Support Towards Successful Aging Among the Participants of Activity Center for the Older Persons in Malaysia. Global Social Welfare, 7, 367-381. https://doi.org/10.1007/s40609-020-00182-4

Zandieh R, Flacke J, Martinez J, Jones P, van Maarseveen M (2017) Do Inequalities in Neighborhood Walkability Drive Disparities in Older Adults' Outdoor Walking? International journal of environmental research and public health, 14, 740. https://doi.org/10.3390/ijerph14070740

Zass R, Shashua A (2007) Nonnegative sparse PCA. In: Advances in neural information processing systems, pp. 1561-1568. https://doi.org/10.7551/mitpress/7503.003.0200