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# Analysis of collaboration networks in OpenStreetMap through weighted social multigraph mining

Quy Thy Truong, Cyril de Runz, Guillaume Touya

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Quy Thy Truong, Cyril de Runz, Guillaume Touya. Analysis of collaboration networks in Open-StreetMap through weighted social multigraph mining. International Journal of Geographical Information Science, 2019, 33 (8), pp.1651-1682. 10.1080/13658816.2018.1556395. hal-01958435

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Submitted on 23 Jun 2025

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Distributed under a Creative Commons Attribution 4.0 International License
ANALYSIS OF COLLABORATION NETWORKS IN OPENSTREETMAP
THROUGH WEIGHTED SOCIAL MULTIGRAPH MINING

THIS IS THE POST-PRINT VERSION OF A PAPER PUBLISHED IN THE INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE (HTTPS://DOI.ORG/10.1080/13658816.2018.1556395).

Quy-Thy Truong

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LASTIG, Univ Gustave Eiffel, IGN, ENSG
Champs-sur-Marne, F-77420
quy-thy.truong@ign.fr

Cyril de Runz

<figure><img src="image_4.png" /></figure>

Modeco, CReSTIC, University of Reims Champagne-Ardenne
CS 30012, F-51687, Reims cedex 2, France

Guillaume Touya

<figure><img src="image_5.png" /></figure>

LASTIG, Univ Gustave Eiffel, IGN, ENSG
Champs-sur-Marne, F-77420
guillaume.touya@ign.fr

June 23, 2025

ABSTRACT

This paper aims to qualify the behaviour of contributors to OpenStreetMap (OSM), a volunteered geographic information (VGI) project, through a multigraph approach. The main purpose is to reproduce contributor's interactions in a more comprehensive way. First, we define a multigraph that combines existing spatial collaboration networks from the literature with new graphs that illustrate collaboration based on specific aspects of the VGI modes of contribution through semantics, geometry and topology. Indeed, the ways that contributors interact with one another through editing, completion, or even consumption may provide additional information on each user's operation mode and therefore, on the quality of the contributed data. Social collaborations drawn from indirect criteria – for example, comparisons between contributors' activity areas – can also be contemplated under another network. Second, the resulting multigraph is analysed using data mining approaches to characterise individuals and identify behavioural groups. The implementation of a multiplex network based on an OSM data sample and an initial analysis make it possible to identify useful behaviours for data qualification. The initial results characterise some contributors as pioneers, moderators and truthful contributors, according to their special roles in the graphs. Mapping elements that include these contributors' participation are likely to be reliable data.

**Keywords** Volunteered geographic information; data quality; collaboration; contributors' behaviour; multiplex

# 1 Introduction

The quality of geo-crowdsourced datasets has been a hot topic since the early stages of their utilisation. Similar to standardised procedures, there are two stages of quality control considerations for volunteered geographic information (VGI): proper data capture during the data acquisition stage and comparison of acquired data to a reference dataset during the quality documentation stage [1].
Quality assessment methods based on the contributions fall within the second part of the standardised procedure [2]. However, the assessment of VGI quality during the acquisition stage should focus on the identification and analysis of the contributors. Indeed, VGI data acquisition relies on the crowd, that is to say a multitude of human sensors. As everyone is welcome to participate in a VGI project, the contributing community may be composed of individuals who do not share the same knowledge on the mapped area, and who may volunteer in different ways. Obviously, the collected dataset is heterogeneous, but the main asset of this strategy is to enable each source to improve others' contributions through data interactions. Hence, collaboration in VGI plays a major role in the production and maintenance of quality up-to-date spatial information.

VGI data that have undergone successive modifications by different authors are likely to be of higher quality [3], especially if those contributors are experienced, of good-will and trustworthy. Therefore, qualifying the contributors makes it possible to conduct quality control on VGI data in the acquisition phase. Coleman et al. [4] stated that ‘the processes ultimately required to take into account not only issues of quality of the geographic information provided but also the values and rationalities of the volunteer contributors and the performance of the new social production systems’. In other words, focusing on the reliability of the contributors is crucial to qualify VGI contributions.

Crowdsourcing platforms do not necessarily provide access to contributors' personal information. The OpenStreetMap project (OSM) requires participants to create an account to contribute to the platform. In this case, the only contributor-related information available in the OSM database is a user ID, which is unique for each contributor, and a username. Therefore, getting personal information on OSM contributors is impossible, at least directly. However, analysing the interactions between contributors based on OSM contributions may provide useful information on their profiles.

This study aims to understand what collaboration says about contributors and thus about the quality of the contributions themselves. To that end, collaboration needs to be modelled from the VGI contributions. The goals are to qualify the contributors' behaviour based on their interactions on a VGI platform and to infer their influence on data quality. We will focus primarily on the OSM project as it is currently one of the most developed VGI platforms. The analysis of the collaboration between OSM contributors should provide answers to the following questions:

* Do collaboration groups exist among the OSM community of contributors?

* What kinds of behaviours can be identified from collaboration?

* What do these behaviours indicate about the contributors and their contributions?

Our approach does not question nor underestimate the importance of data-centric quality assessment methods. However, we intend to demonstrate the benefits of contributor analysis for the purpose of data quality control.

The remainder of this paper is structured as follows: Section 2 provides an overview of related works that address collaboration and contributor behaviour in VGI and in crowdsourcing projects more generally. Section 3 introduces a multiplex model of collaboration network, which is a multigraph that collects various types of collaborative operations performed by OSM contributors. Section 4 describes an experimental use of the proposed model on real OSM datasets. Section 5 discusses the results obtained from the case study. Section 6 concludes the study.

# 2 Collaboration and behaviours: related works

## 2.1 Mapping operations in OpenStreetMap

This study provides an analysis on collaboration between OSM contributors to qualify their behaviours, starting from their own contributions. Therefore, our research includes both user-centric and data-centric approaches. The analysis of behaviours requires a list of the different kinds of actions allowed on OpenStreetMap. There are four different ways to contribute in VGI [5]:

* Contributing geographic information

* Building community structures

* Working on norms and rules

* Working on community tools

Among these activities, the paper will only focus on mapping activity (i.e. contributing geographic information) because our approach consists in qualifying data based on their contributor's trustworthiness. Here, a contribution is to be understood as a given version of a geographic object. Therefore, only one contributor, known as the last author of the mapping element, is associated with a contribution. Rehrl et al. [5] broke down mapping tasks into four atomic
operations: Create, Read, Update and Delete, also known as the CRUD paradigm. As we only take into account
operations that make changes into the dataset, the Read operation is set aside.

The Create operation consists of contributing the first version of an object. Regarding OSM basic data elements (node, way and relation), creating a node does not require any interaction between contributors. Admittedly, ways and relations can also be built from scratch; a contributor can map a new way by reusing existing nodes. Likewise, they can map a new relation based on existing ways and nodes. This operation is typically a collaboration between contributors, for the resulting object is the product of a collective effort. Besides, creating a new map feature based on contributions authored by other people means that those contributions are quite reliable.

The Update operation is necessarily performed on an existing element. This operation consists in creating a new version of an existing feature. Except for the case when a contributor updates his/her own contributions, updating someone else's contribution is another type of collaboration. Moreover, the meaning of this operation depends on the type of performed update. The Update operation can be split into two sub-operations: correction and completion [6]. The former implies that the initial version of the mapping object was not correct, for instance, correcting a node's geographic coordinates or a tag value. In this case, correction consists in erasing part of the existing piece of information and possibly replacing it with new information. The latter implies that the existing information is correct but can be expanded upon. Completion leaves the content of the previous version untouched and adds new information to the object. This information can either be a spatial element (e.g. adding a node in a way) or a semantic element (e.g. adding a new tag to the object).

On this, Rehrl et al. [5] subdivided the Update operation into the Add, Remove and Modify operations. Thus, a completion corresponds to an Add operation, whereas a correction includes both Remove and Modify operations. In terms of contributor interactions, a correction implies that, in the corrector's opinion, the author of the object's initial version might be wrong. However, a completion means that the last author supports the object's previous version. A Delete operation consists in eliminating a mapping object from the dataset. In OSM, a mapping object is not definitively erased from the database when it has been deleted, but the element's 'visible' attribute is set to 'false'. A contributor who deletes someone else's contribution implicitly indicates that they consider the latter's contribution to be irrelevant if not incorrect.

Therefore, OSM mapping activity is composed of the following operations:

1. Creating a new object from scratch

2. Reusing contribution (e.g. using someone else's node to build a way)

3. Correcting contribution, which can be either a spatial or a textual correction

4. Completing contribution

5. Deleting contribution

Once two contributors are involved in an operation, one may see it as collaboration or interaction in the context of mapping activity (see Figure 1).

The distinction between semantic and geometric information is not necessary for the Create and Delete operations, because these operations apply on the object as a whole. However, Update operations (Add, Remove, Modify) can either impact the semantic or the geometric part of the object. Additionally, geometric Update operations cannot be performed on every OSM feature type. Indeed, spatially updating a way through the Modify operation requires relocating its nodes. Yet, relocating the nodes that compose an OSM way does not create a new version of this way or of associated OSM relations. Therefore, a geometric Modify operation is only traceable for OSM nodes. Moreover, from a geometric perspective, Add and Remove operations only work on complex objects, that is OSM ways and relations. Therefore, these operations cannot be performed on OSM nodes.

## 2.2 Interaction and collaboration

Collaboration within a VGI community is crucial to ensure data quality. In this context, our work is related to the crowdsourcing and social approaches introduced by Goodchild and Li [1]. The crowdsourcing approach can be defined as the community's ability to correct individual contributions. The social approach refers to the existence of contributors who behave like moderators. In that respect, collaboration is essential for the maintenance of high-quality information.

Literature on collaboration in OSM is quite recent [1, 5, 8, 10]. These works deal with interaction through OSM editing history, and all conduct their analyses using graph theory. Indeed, as collaboration in VGI communities is comparable to relationships in a social network, building collaboration networks is a relevant way to address this research question.
<figure><img src="image_6.png" /><figcaption>Figure 1: Example of interactions between three OSM contributors.</figcaption></figure>

Mooney and Corcoran [7, 8] focused on co-editing, where contributors' interactions are captured in direct edits only, whereas Stein et al. [10] favoured indirect editing based on interlocking communication [11]. Interactions based on direct editing only connect the contributors who authored version *v* and version *v* − 1 of an OSM object. In contrast, interlocking communication connects the author of version *v* of an OSM object to all the authors of the previous versions until *v* − *k* if *v* − *k* − 1 was authored by the author of version *v*. Otherwise, the author of version *v* is connected to every previous contributor, including the one who created the object. Collaboration intensity is measured according to a concept of depth and breadth; collaboration depth consists of the maximum number of responding edits between two contributors to a given object, while collaboration breadth counts the number of unique objects that were successively edited by two authors (see Figure 2). Ma et al. [9] also address collaboration by connecting contributors who contributed to the same object. Contrary to the previous suggested networks, the co-contribution network is unweighted and undirected.

These networks seem quite similar and are likely to render some interactions in common. Nevertheless, each graph captures a type of interaction that another graph may not take into account. For instance, say that contributor A purposely corrects every single contribution from one specific contributor B. This behaviour will be more noticeable in the co-edit network, while in the collaboration breadth network, they will not only be connected to contributor B, but also to all contributors who were corrected by B. The collaboration breadth network is also important because it quantifies the variety of objects that were edited by two users, whereas this aspect is not taken into account in the co-edit network. The collaboration depth network counts the maximum number of interactions between two contributors that happened on a unique object. Therefore, this network is interesting because it may reveal arguments between the authors
<figure><img src="image_7.png" /><figcaption>Figure 2: Examples of a co-edit graph [7], a collaboration breadth graph and a collaboration depth graph [10].</figcaption></figure>

of heavily edited objects. The co-contribution network can be associated to an unweighted and undirected version of the spatial collaboration graphs (collaboration depth and collaboration breadth graphs). This graph may reveal groups of contributors who work on a specific type of geographic element, for instance, buildings, roads or vegetation.

The collaboration graphs that are described in the research literature are interesting because they connect contributors on the edited objects that they hold in common. However, they do not differentiate the Add, Remove and Modify operations described in the previous subsection. Yet, representing these operations may reveal ‘same-direction collaborations’, as well as conflicts between OSM contributors. Accordingly, discovering interaction patterns in the context of VGI collaboration is a first step in determining whether a contributor belongs to a group that meets the description of the crowdsourcing approach, or whether they act like a moderator towards their peers.

## 2.3 Contributors' behaviours

VGI research is quite prolific from a user-centric perspective. Many research projects have proposed to highlight contribution patterns in OSM to address the issue of crowd heterogeneity. Indeed, grouping contributors into distinct categories helps to qualify the underlying contributions. According to the overview drawn by Neis and Zielstra [12], recent research distinguishes contributor analyses through various criteria such as their participation, the mapping activity area and their motivation (see Figure 3).

By analysing a contributor's number of contributions and their spatio-temporal level of activity, Neis and Zipf [13] came up with a typology of contributors that would aid in understanding the quality of OSM contributions. This typology – consisting of four categories: senior mappers, junior mappers, non-recurring mappers and no edit users – implies that quality data come from contributors with greater participation. Similarly, Bégin et al. [14] proposed a typology of contributors based on temporal patterns of contributions.

Contributors may also be characterised according to their mapping habits, such as their preference for a specific type of mapping operation [7] – for example, object creation, geometry editing only, tag editing only or both – or for a certain type of map feature [15]. In the latter case, contributor characterisation consists in assessing data completeness depending on the mapping preferences of the contributor. For instance, an area that is mapped by a contributor who mainly edits road objects will be more complete regarding roads than regarding other types of objects such as buildings and points of interest, especially if no one else has contributed to the same area. Besides, Neis and Zipf [13], Zielstra et al. [16] proposed several methods to compute contributors' mapping areas.

As a contributor's expertise greatly influences the quality of data, Coleman et al. [4] drew a spectrum of contributors, which is composed of five overlapping classes: neophyte, interested amateur, expert amateur, expert professional and expert authority. However, the authors did not provide a methodology for classifying VGI contributors according to this
<figure><img src="image_8.png" /><figcaption>Figure 3: Literature’s typologies of contributors.</figcaption></figure>

typology. From the same perspective, Comber et al. [17] compared data collected by Geo-Wiki contributors from both personal and professional backgrounds. These pieces of information are directly provided by the contributors in this case. Yang et al. [18] proposed a methodology for determining whether OSM major contributors are professionals, based on indicators of practice, skill and motivation. In addition, the analysis of collaboration by Stein et al. [10] resulted in identifying local mappers who the authors considered as experts. Finally, analyses of contributors’ gender, age and professional training are conducted in [19, 20].

Certainly, each typology proposed in the literature is defensible and relies on relevant criteria. Nevertheless, these works focus on only one criterion at a time (co-editing, duration of participation, contributed feature type, etc.), leading to biased typologies that only depict a small part of the complexity of VGI contributors’ behaviour. Our goal is not to deny the relevance of the existing analyses related to VGI behaviours, but to combine them to yield a better grasp of the subject.

Across all of the behaviours focused on in the aforementioned research, each typology includes a notion of trust that can be linked to VGI quality assessment. As stated in [21], data trust is a consequence of interpersonal trust. In that respect, previous research on VGI has addressed this issue in combination with the notion of reputation. Trust and reputation can be viewed from both data-centric [3] and user-centric points of view [22, 6]. Indeed, data trust can be measured to evaluate data quality [3]. However, there appears to be a double connection between data trustworthiness and user reputation, as on the one hand, data trustworthiness is considered a component of user reputation [22, 23] and on the other hand, the level of trust for a contribution depends on its contributor’s reputation [21]. In brief, Figure 4 summarises various literature approaches to VGI quality assessment that are based on the calculation of reputation and trustworthiness. This paper aims to qualify contributors’ behaviour to address VGI trustworthiness and therefore, VGI quality. Our approach can be related to that of Neis et al. [24] when it comes to detecting vandalism. Indeed, the proposed system takes into account user reputation in order to determine whether a contribution is a fraud. Similarly, our approach aims to take into account contributors’ behaviour in the process of data qualification, regardless of the case study. Thus, we intend to qualify VGI contributions using a behavioural analysis as a first step.

## 2.4 Related fields

As VGI is a specific example of crowdsourcing, we will focus here on how related works on crowdsourcing address collaboration, interaction and contributors’ behaviour. In general, crowdsourcing projects rely on collaboration to succeed. Therefore, Ikeda et al. [25] distinguished three modes of collaboration: sequential, simultaneous and hybrid.
<figure><img src="image_9.png" /><figcaption>Figure 4: Literature's approaches for data quality assessment based on proxy measures.</figcaption></figure>

Sequential collaboration allows contributors to improve one another's contributions, as in OpenIDEO<fnref n="1" /> or Climate CoLab<fnref n="2" /> where participants are expected to generate solutions to world challenges by sharing their ideas. Simultaneous collaboration is a mode of contribution where users take part in a project by independently generating their own content, as it is the case in Ushahidi<fnref n="3" />, SafeCity<fnref n="4" /> and some projects from the Zooniverse platform<fnref n="5" />. A hybrid collaboration mode combines both sequential and simultaneous modes, as is precisely the case for OpenStreetMap and Wikipedia. Consequently, in order to be complete and up-to-date, OSM requires both types of contributors: those who generate new content and those who improve existing data.

Research on Wikipedia quality assessment through contributor analysis is extensive. Wikipedia vandalism is a much-studied topic where the contributor's behaviour is taken into account [26]. Besides, analysis of contributor behaviour is exploited to assess the knowledge community [27] and to infer characteristics about the crowdsourcing platform, for instance the evolution of its norm network [28]. These works particularly focus on the collaboration mode aspect to qualify the Wikipedia platform. Again, we note here the existence of a bridge between contributor analysis and data quality assessment.

## 3 Our Model

Many papers have reported studying user behaviours through the modelling and the analysis of a social network [7, 8, 10, 28]. As with many of these previous works, our OSM collaboration analysis method is also based on graph theory. However, the model should be a multigraph that captures the various forms of collaboration between OSM contributors. Indeed, as collaboration between contributors can be depicted through various operations, a multigraph would gather as many edges linking two vertices as there are collaboration-type actions between the corresponding contributors. In the field of social network analysis, scientists have exploited the concept of the multiplex network [29], also called multidimensional network [30], to model the various dimensions in which the same individuals are connected by different relationships (see Figure 5). Modelling a multiplex network for OSM collaboration makes it possible to bring together as many interaction types as possible and thus, to retrace users' behaviour in a more realistic way.

<footnote n="1">¹https://openideo.com/</footnote>

<footnote n="2">²https://climatecolab.org/</footnote>

<footnote n="3">³https://www.ushahidi.com/</footnote>

<footnote n="4">⁴http://www.safecity.in</footnote>

<footnote n="5">⁵https://www.zooniverse.org/</footnote>
<figure><img src="image_10.png" /><figcaption>Figure 5: Example of a social multiplex network depicting different relationships between the same individuals in different environments.</figcaption></figure>

## 3.1 Definitions

In this section, we define $G$ as a multiplex network according to the formalism proposed in [29]. A multiplex network is defined as the following set of $\alpha$ graphs:

$$G = \{(V_k, E_k)\} \quad \text{for } k \text{ in } [1, \alpha] \quad (1)$$

where $V_k$ is the set of vertices representing OSM contributors of the $k^t h$ graph (layer) such as:

$$V_k = V_l = V \quad \forall k, l = 1..\alpha \quad (2)$$

and

$$E_k = \{(i, j, w)\} \quad \forall i, j \in V_k \quad w \in \mathbf{R} \quad (3)$$

where $w$ is the weight of edge $(i, j)$. If $\alpha = 1$, the network is called a monoplex network [29].

Each graph is described by an adjacency matrix. This matrix identifies the neighbours of each vertex of a graph. Thus, we define $A^{[k]} = (a_{i,j}^{[k]})$ as the adjacency matrix of graph $G_k$, where each cell of the matrix encodes whether two vertices are connected:

$$a_{i,j}^{[k]} = \begin{cases} 1 & \text{if } (i, j) \in E_k \\ 0 & \text{otherwise} \end{cases} \quad (4)$$

Therefore, as proposed in [31], the whole multiplex network is described by the vector of each layer's adjacency matrix:

$$A = (A^{[1]}, \dots, A^{[\alpha]}) \quad (5)$$

## 3.2 Multiplex collaboration network model

Our multiplex network is composed of layers (or graphs) representing the various forms of collaboration in OSM mapping activity. Hence, in this subsection, we examine literature that addresses user interactions and collaboration in VGI and related fields in order to integrate existing graphs into our multiplex network model or to take inspiration from current research to build new graphs.
### 3.2.1 Spatio-temporal layers

Unlike social networks, the OSM platform does not make it possible to indicate the social relationships that bind mapping contributors in real life (acquaintance, friend, family, etc.). Such a relationship information is useful when it comes to studying contributor behaviours, for instance, assessing trust behaviours. In actuality, we do not know whether contributors know one another or if they are even aware of one another's contributions during individual mapping sessions. Crandall et al. [32] proposed a model of spatio-temporal co-occurrences to infer social ties between Flickr users. By dividing space into squares of size s, the authors state that 'two people A and B co-occurred in a given s × s cell C, at temporal range t, if both A and B took photos geo-tagged with a location in cell C within t days of each other'. This model assumes that two people who took a picture at the same place, defined as a s × s cell, and at the same time are more likely to know each other. This assumption is related to Flickr pictures which image capture date and time are recorded by receivers contained in cameras or mobile phones, such as digital clocks and GPS. In contrast with Flickr, where users often take dated geo-tagged pictures in the field, OSM users may map remote areas from their desktop computer as well as in the field by using a mobile phone. Moreover, the timestamp of each contribution corresponds to the date of the data upload. Therefore, from this point of view, inferring social ties between OSM contributors based on their spatio-temporal contributions may seem irrelevant. However, there are local OSM communities that organise mapping parties or mapathons in which contributors simultaneously contribute to the same area, sometimes on a given theme, for example, collecting information on the wheelchair accessibility of public places<fnref n="6" />. In this case, linking OSM contributors who contributed at the same time and in the same area should reveal these collaborations and thus the contributors who involve themselves in this kind of group event. Apart from mapping parties, there might also be implicit collaboration between participants who contribute to the same place and at the same time. For instance, two contributors who simultaneously map the same area without correcting each other may reveal some kind of partnership. Therefore, it may be worthwhile to design spatio-temporal graphs that make it possible to reveal these potential types of collaboration.

We suggest modelling spatio-temporal collaboration based on two graphs: a cotemporal network and a co-location network. The co-temporal network aims to connect contributors who contribute at approximately the same time, while the co-location network will connect contributors who participate in the same area. Considering a contributor i who participates in OSM, let schedule_i be the set of temporal intervals of all of the changesets that are produced by i, given that a changeset contains a start date and an end date. Let ActivityArea_i be the set of mapping areas of i, which can be delimited by the geographical footprints of the contributions produced by i. Some methods can be found in the literature [13, 16] to compute the mapping areas of OSM contributors.

Let $E_{co-temporal} = (i, j, w_{co-temporal})$ be the set of temporally connected contributors, in other words, contributors whose contribution schedules overlap. The challenge here is to define $w_{co-temporal}$ so that the more similar the schedules of two contributors are, the more connected they will be, i.e. the higher $w_{co-temporal}$ will be. A solution could be to define $w_{co-temporal}$ in a similar manner to Crandall et al. [32], but considering too large of a temporal range t might connect too many contributions together and thus erase the most relevant co-temporal contributions.

Let $totalduration()$ be a function that returns the total duration of a set of temporal intervals. Therefore, $totaldurationschedule_i \cap schedule_j$ returns the sum of the duration of the intersection of the temporal intervals of contributor i's changesets and contributor j's changesets. Besides, $totalduration()$ has the following properties:

$$ schedule_i \cap schedule_j = \emptyset \Rightarrow totaldurationschedule_i \cap schedule_j = 0 \quad (6) $$

$$ totaldurationschedule_i \cap schedule_j = totaldurationschedule_i + totaldurationschedule_j \quad (7) $$

One can argue that while most ordinary people in the same time zone do have similar schedules in their daily lives, there are users who make use of automatic tools to contribute to the maps. Therefore, building a co-temporal graph would also allow us to identify the accounts that continuously contribute in an automated way, because they will be connected to many contributors. This information is useful for qualifying both the contributor's mode of practice and the resulting contributions.

The same reasoning can be extended to the definition of the weighting of the edges of the co-location graph. Let $E_{co-location} = (i, j, w_{co-location})$ be the set of spatially connected contributors, in other words, contributors whose mapping areas overlap, such as:

<footnote n="6">⁶https://www.geog.uni-heidelberg.de/gis/mappingparty_en.html</footnote>
$$w_{co-location} = \frac{S(ActivityArea_i \cap ActivityArea_j)}{S(ActivityArea_i \cup ActivityArea_j)} \qquad (8)$$

having $S()$, a function that returns the total area of the input set of mapping areas, which can be a set of polygons. $S()$ has the same properties as the ones previously given for the totalduration() function. Figure 6 illustrates the proposed definitions.

<figure><img src="image_11.png" /><figcaption>Figure 6: Examples of (a) a co-location graph and (b) a co-temporal graph between three contributors.</figcaption></figure>

To detect collaborations which occurred during mapping events only, $w_{co-temporal}$ should be defined in a different way to quantify the relative overlap of the changeset dates that best match between two sets of schedules. In addition, a $w_{co-temporal}$ should quantify the relative overlap of the mapping areas that best match geometrically. To this end, we could define two functions $sim_T()$ and $sim_S()$ that respectively compute the similarity between two temporal intervals and two mapping areas. For the temporal issue, $sim_T()$ would, for instance, calculate the differences in the start dates and the end dates between one of $i$'s changesets and one of $j$'s. The smaller the date differences are, the more similar the changeset dates are. Therefore, to capture the maximum value of similarity between two sets of schedules, $w_{co-temporal}$ could be redefined as:

$$w_{co-temporal} = \max(sim_T(d_i, d_j)) \quad d_i \in schedule_i, \quad d_j \in schedule_j \qquad (9)$$

and $w_{co-location}$ can be defined the same way, as $sim_S()$ is a two-dimensional extension of $sim_T()$.

### 3.2.2 OSM operation-based layers

All of the papers cited in section 2.2 are based on OSM edit operations. As these graphs are all slightly different, they can all be considered as potential layers of our model. The similarity between these graphs certainly makes the multiplex network redundant, but experiments will determine which layers are relevant in the network and which should be abandoned.
To model interactions based on the remaining OSM operations (see Section 2.1), extra graphs should be contemplated. Thus, we define a use graph and a suppression graph. The use graph can be related to Wikipedia's norm network defined in [28], where nodes are Wikipedia articles and an edge directed from article A to article B represents the fact that article A contains a hyperlink to article B. In that case, the content of article A relies on article B. In the context of OSM, if *i* uses *w* OSM node contributions that were authored by *j* to edit a new OSM way contribution, or if *i* uses *w* OSM node and way contributions that were authored by *j* to edit a new OSM relation contribution, then

$$ (i, j, w) \in E_{use} \qquad (10) $$

For instance, if a contributor maps a bus line based on 10 bus stops that were authored by another contributor, the latter will probably be more reliable (given the number of used nodes) than a contributor who has only one node that has been used (for example, to connect a street in order to create a street junction). This graph assumes that the more a contributor's contributions are being used, the more reliable they must be. Likewise, if *i* deletes *w* objects that were last authored by *j*, then

$$ (i, j, w) \in E_{suppression} \qquad (11) $$

If *i* made *w* edits to the *v* + 1 version of an OSM object whose version *v* was authored by *j*, then

$$ (i, j, w) \in E_{co-edit} \qquad (12) $$

If *i* edited the *v* + 1 version of *w* OSM objects whose versions *v* - *n* (*n* ∈ N) were authored by *j*, then

$$ (i, j, w) \in E_{collaboration-breadth} \qquad (13) $$

If, among all of the objects that *i* edited after *j*, *w* is the maximum number of times *i* edited (directly or not) an object after *j*, then

$$ (i, j, w) \in E_{collaboration-depth} \qquad (14) $$

Besides, we should note that if $(i, j, w) \in E_{collaboration-breadth}$, then $\exists w' | (i, j, w') \in E_{collaboration-depth}$, and it is true the other way round.

If *i* and *j* edited at least one object in common, then

$$ (i, j) = (j, i) \in E_{co-contribution} \qquad (15) $$

For further details on the aforementioned graphs, the reader is referred to [7] for the co-edit graph model, to [10] for the breadth and depth of collaboration models, and to [9] for the co-contribution graph model.

### 3.2.3 Tag-editing style layers

In the multiplex social network proposed by Kazienko et al. [30] to analyse Flickr users, one layer gathers user relations based on tags. In this layer, the contributors who use at least one common tag to describe their photos are connected. Similarly, we can transpose this tag-based relation graph to the OSM case. In OSM, a tag is a (key, value) pair. Contributors who add common tag keys somehow follow a common standard for map feature description, and even more if they add the same (key, value) pairs. Additionally, contributors who tag-edit the same type of objects constitute a group of similar editors who are specialised in one action. For instance, contributors who only add the tag 'building = yes' will be strongly connected, and their group will realize a behaviour pattern. Therefore, we define a key-based relation graph and a tag-based relation graph such that if $(i, j, w) \in E_{key-based}$, then

$$ w = \frac{NK_{ij}}{NK_i} \qquad (16) $$

where $NK_{ij}$ is the number of common tag keys for *i* and *j*, and $NK_i$ is the number of tag keys used by *i*.

If $(i, j, w) \in E_{tag-based}$, then
$$w = \frac{NT_{ij}}{NT_{i}} \qquad (17)$$

where $NT_{ij}$ is the number of common tags for i and j, and $NT_{i}$ is the number of tag used by i.

### 3.2.4 Geometric-editing style layers

As well as for the tag-editing style layers, the geometric-editing style layers should be integrated into our multiplex network to detect specific contribution styles. In this manner, we may connect contributors who geometrically edit objects to change their level of detail [33], for instance, by adding additional nodes to existing ways. In the same vein, contributors who played a part in the evolution of the maturity of the same object could be connected in another graph. For instance, a contributor who creates a closed way to map a building that was initially mapped as a node would be connected to the author of the node-described building [34].

### 3.2.5 Motivation and discussion

The assets of this multiplex collaboration network are manifold. First, as was mentioned earlier, each layer (or graph) of the system may present a specific piece of information that contributes to a better understanding of the complexity of the relationships between contributors. Second, some graphs may not highlight relevant elements on their own, whereas if they are studied in combination with another graph, they could add realistic features, providing valuable information to qualify the data. For instance, if two contributors map the same area several times without editing each other's contributions, on the one hand, it may reveal some kind of collaboration in the sense that they somehow agree with each other's work. On the other hand, two contributors who map the same area and edit the same elements may either show some disagreement or some improvement between them. These two pieces of information can be found in a co-location graph, which highlights the fact that they contributed to the same place, and in a width or depth of collaboration graph, which connects the contributors who have edited one another. The co-location graph is not meant to be used alone. If the graph is taken independently, the most salient features extracted from this graph may give an incorrect (or incomplete) reflection of reality. However, our study assumes that the multiplex model should balance the results found in each graph and thus get a better grasp of the real collaboration in the platform.

Of course, as the graphs are built only on the contributions, contributors who communicate only through chatting tools will not be connected. But if they do interact by contributing to the same spatio-temporal area, or to the same objects, or using any other visible operations on the data, this link will be represented in the system.

The way that each graph's weighting is defined can lead to edges that bear different physical dimensions. The multiplex network's definition enables us to consider any graph that has a dimensional weighting or not, as long as the analysis based on the obtained network does not mix everything. It is totally possible to contemplate a multistep analysis that takes into account some specific layers of the network. For instance, it could be possible to first select the contributors who are involved in a spatiotemporal collaboration, then to deeply analyse their interactions by studying the network's layers that deal with OSM edit operations.

As the core of our proposed approach is in the multiplex model, we acknowledge the lack of details in the spatio-temporal layers (section 3.2.1), as they were inspired by the work on Flickr data and therefore, should be readapted for VGI data. Some proposed graphs, such as the collaboration graphs based on edits, are more tangible than the others because they tackle the same issues as our study, whereas the others deal with assumptions that need to be refined. Therefore, the utility of each graph layer needs to be experimentally verified, but it does not bring into question the point of the proposed model.

# 4 Experiments

## 4.1 OpenStreetMap datasets

Our case study required us to retrieve OSM history data to capture interactions on each OSM object. OSM history dumps are available under a PBF format on the Planet OSM website<sup>7</sup>. However, OSM data extracts by country or by region can be downloaded on Geofabrik's free download server<sup>8</sup>. Historical raw data were imported into a PostgreSQL database using a Python script.

<footnote n="7"><sup>7</sup>https://planet.openstreetmap.org/</footnote>

<footnote n="8"><sup>8</sup>http://download.geofabrik.de/</footnote>
Multiplex networks were constructed based on the data contained in a given spatiotemporal window. Our main experiment is based on the contributions in the Ile de la Cité area in Paris (France) between 2012 and 2015. To show that the modelling of a multiplex network is independent of the dataset, two extra multiplex networks are also constructed based on two different spatio-temporal windows: Stuhr (Germany) between 2009 and 2013 and Kathmandu (Nepal) between 2014 and 2017. The analysis of these areas is less detailed than the one of Ile de la Cité (IDC), for they only aim at demonstrating the generalisability of the multiplex analysis to different datasets.

From a temporal point of view, contributions are queried according to a two-stage procedure. First, we retrieve the latest versions of all objects located in a spatial window regarding the lower boundary of the temporal window. Second, every edit produced within the spatio-temporal window is added to the dataset. Then, all of the graphs are generated on the GeOxygen open-source platform<fnref n="9" /> [35].

## 4.2 Multiplex analysis of Paris

This case study focuses on the sequential collaboration mode in the Paris IDC dataset. Therefore, the experimental multiplex network is composed of the following five layers: co-edit graph, breadth of collaboration graph, depth of collaboration graph, cocontribution graph and use graph.

### 4.2.1 Participation

As contributors are not necessarily connected with others in every layer of a multiplex network, we computed the multiplex coefficient participation $P_i$, which quantifies the distribution of node $i$'s neighbours through the layers of the system [31]:

$$P_i = \frac{\alpha}{\alpha - 1} \cdot \left[ 1 - \sum_{m=1}^{\alpha} \left( \frac{k_i^{[m]}}{o_i} \right)^2 \right] \quad (18)$$

where $\alpha$ indicates the number of layers in the multiplex network, here, $\alpha = 5$ layers for Paris IDC multiplex network. $k_i^{[m]}$ is the unweighted degree of node $i$ in the $m^{th}$ layer of the multiplex network. This metric quantifies the number of neighbours for a given node; therefore, it considers the undirected degree of the node, which is the sum of its indegree and its outdegree. Then, $o_i$ is the overlapping degree of node $i$ defined as:

$$o_i = \sum_{m=1}^{\alpha} k_i^{[m]} \quad (19)$$

The multiplex participation coefficient $P_i$ takes a value between 0 and 1; the coefficient equals 0 when all of the node's neighbours are concentrated in one layer and 1 when the node has the same number of neighbours in every layer of the multiplex network. We note that the multiplex participation coefficient cannot be computed when the multiplex network is composed of $\alpha < 2$ layers or when $o_i = 0$. The former case does not affect us. However, in the latter case, we will note $P_i = null$ when a contributor is isolated in all layers of the network. $P_i = null$ means that the contributor $i$ participated without interacting with any other contributor.

In the Paris multiplex network, $P_i = null$ for almost 40% of the total set of contributors (Table 1). These contributors did not interact with anyone through OSM editing (they did not edit nor were edited) nor through OSM object use (they did not use other contributors' objects and their contributions were not used by others). Therefore, regarding the implemented multiplex network, these contributors can be qualified as isolated contributors. An analysis of their contributions should reveal further information on their trustworthiness.

<table><caption>Table 1: Multiplex participation coefficients are computed on each multiplex network. Paris IDC 2-layer network corresponds to Paris IDC multiplex network, where only the use graph and the co-edition graph were kept.</caption><thead><tr><th>Area</th><th>Paris IDC</th><th>Paris IDC 2-layer network</th><th>Stuhr</th><th>Kathmandu</th></tr></thead><tbody><tr><td>Total contributors</td><td>532</td><td>532</td><td>132</td><td>1861</td></tr><tr><td>P<sub>i</sub> = null</td><td>39%</td><td>39%</td><td>24%</td><td>39%</td></tr><tr><td>P<sub>i</sub> = 0</td><td>2%</td><td>46%</td><td>18%</td><td>12%</td></tr><tr><td>P<sub>i</sub> > 0</td><td>59%</td><td>15%</td><td>58%</td><td>47%</td></tr></tbody></table>

<footnote n="9">⁹https://github.com/IGNF/geoxygene</footnote>
We found that $P_i \neq 0$ for only nine contributors: they represent approximately 2% of the non-isolated contributors. These contributors only participate in the use graph. Besides, as the co-edit, breadth of collaboration, depth of collaboration, and co-contribution graphs all refer to the OSM edit operation, if a contributor participates in one of these four graphs, they necessarily participate in the other three graphs. The strong similarity between these graphs accounts for the right-skewed distribution of the multiplex participation coefficient values (see Figure 7(a)).

<figure><img src="image_12.png" /><figcaption>Figure 7: Histograms of the multiplex participation coefficient, (a) five-layered network, (b) two-layered network composed of the co-edit graph and the use graph on Paris IDC.</figcaption></figure>

To observe contributors’ participation in OSM editing and object use operations, we computed the multiplex participation coefficient on a balanced multiplex network that is composed of one layer per operation in the Paris IDC area: the co-edit graph stands for edit operation, and the use graph stands for use operation. The distribution of $P_i$ in Figure 7(b) depicts that the majority of non-isolated contributors have $P_i < 0.1$. Actually, in this two-layered network, $P_i = 0$ for 246 contributors, i.e. 75% of the non-isolated contributors. Among these, 96% of the contributors only participate in the co-edit graph. Therefore, non-isolated contributors primarily interact through OSM object edits. Regarding only the multiplex participation coefficient, we can already draw initial analysis of OSM contributor profiles:

1. Isolated contributors participated through OSM object creation only, and they had not been edited by others yet. The behaviour of these contributors is closely related to a simultaneous collaboration mode.

2. Non-isolated contributors' behaviour is related to a sequential collaboration mode. Among them, we can differentiate contributors who operate through object editing only, object use only or both. Furthermore, contributors who participate in object editing only (for instance) can either edit, be edited or both. So, we need to verify the edges' direction to more accurately qualify the collaboration between contributors. For instance, a contributor whose contributions are widely edited but are never used appears less trustworthy than a contributor who edits a lot and whose contributions are widely used.

### 4.2.2 Community detection

The aim of this paper is to study contributors' behaviour, particularly their collaborative actions. To this end, we attempted to detect communities in our multiplex network to explore any evidence of collaboration groups, and if so, what can be inferred when it comes to OSM contributors and their contributions. Community detection in graphs, also known as graph clustering, is an unsupervised classification method consisting of grouping similar nodes together. According to Schaeffer [36], "Graph clustering is the task of grouping the vertices of the graph into clusters taking into consideration the edge structure of the graph in such a way that there should be many edges within each cluster and relatively few between the clusters." Figure 8 illustrates a graph clustering example.

Literature highlights three approaches for community detection in multiplex networks [37]. The first approach consists of aggregating all of the multiplex network's layers to reduce them to a mono-dimensional graph. Detecting community in such a graph can be done using classical clustering methods. The second approach is to apply clustering methods in
<figure><img src="image_13.png" /><figcaption>Figure 8: Example of graph clustering in a Facebook community. Detected communities may reveal underlying social information, for instance they represent people from the same family, the same working place or the same school.</figcaption></figure>

each layer of the network, then detect communities from these intermediary communities. Hmimida and Kanawati [37] proposed a third approach, which is a bottom-up method that simultaneously explores all layers of the network, starting from specific contributors who are initially chosen as 'seeds' of future communities. In our case, we chose the layer aggregation approach because it is the simplest method: communities are detected only once, and classical methods can be used. Kazienko et al. [30] also used the layer aggregation approach to analyse the proposed model of multidimensional social network.

We aggregate the five layers of the Paris IDC multiplex network into an undirected weighted graph. The weight of edge (u, v) in the aggregated graph corresponds to the total number of edges (u, v) found in the different layers of the multiplex network, which is between 1 and 5 in a five-layered network. Clauset et al. [38] proposed an algorithm for community detection based on the maximisation of the modularity Q, a value quantifying the good distribution into communities by maximising the number of edges inside communities and minimising their number outside communities. More recently, Blondel et al. [39] proposed the Louvain algorithm based on the same approach, which is supposed to perform better with respect to modularity optimisation. In addition, the Louvain algorithm for community detection is already implemented in the Gephi open-source software and was successfully exploited by Heaberlin and DeDeo [28] to detect communities in the Wikipedia network.
Community detection in the aggregated graph returns 13 communities with a modularity of Q = 0.37 (see Figure 9). According to Clauset et al. [38], when Q>0.3, a significant community structure has been found in an unweighted graph. However, our experiment deals with a weighted graph, and it is not guaranteed that this precise threshold is still valid for a weighted graph. Therefore, in what follows, we further study the detected communities. Five communities are composed of only two nodes; among the remaining 8 communities, two configuration types stand out: contributor-centred communities and unorganised groups. Contributor-centred communities are groups composed of small contributors who are sparsely connected to one another but are all connected to a big contributor in the sense of his/her high node degree.

<figure><img src="image_14.png" /><figcaption>Figure 9: Detected communities using Louvain algorithm on the Paris IDC aggregated network. Node size is proportional to the degree of centrality. User IDs are anonymised.</figcaption></figure>

In terms of degree of centrality, the unorganised group appears to be less hierarchically organised (see Figure 10). For the sake of privacy, we designate contributors by anonymised identifiers in the following analysis.

### 4.2.3 Community analysis

The distribution of nodes' degrees in both communities (Figure 10) is depicted in Figure 11. The distribution of nodes' degrees in the 210284-centred community is compliant with our initial observation: the community is composed of a central user and smaller contributors. The distribution of the unorganised group shows that there is also a central
<figure><img src="image_15.png" /><figcaption>Figure 10: Two distinct configurations observed in the detected communities of the Paris IDC area: (a) contributor-centred community, (b) unorganised community. Node size is proportional to the degree of centrality. User IDs are anonymised.</figcaption></figure>

contributor in this community. Contrary to the former community, though there are nodes having an intermediate degree of centrality, which make the central contributor less apparent. The clustering coefficient of a node quantifies the connection between its neighbours. In other words, it measures the ‘Friend of a Friend’ principle [40]. Battiston et al. [31] define the clustering coefficient of node i as:

$$C_i = \frac{\sum_{j \neq i, k \neq i} a_{ij} \cdot a_{jm} \cdot a_{mi}}{k_i (k_i - 1)} \quad (20)$$

<figure><img src="image_16.png" /><figcaption>Figure 11: Distribution of the degree of centrality values: (a) unorganised community, (b) 210284-centred community.</figcaption></figure>

Histograms of the clustering coefficient of the communities depicted in Figure 10 are shown in Figure 12. We observe that the distribution of the clustering coefficient in the 210284-centred community is split into two classes: nodes have
either a very low clustering coefficient or a very high clustering coefficient. Nodes having a low clustering coefficient are small contributors who are only connected to the community's central user, while nodes having a high coefficient are small contributors who are connected both to the central user and to each other. In the unorganised group, the clustering coefficient distribution is smoother, as there are nodes having an intermediate clustering coefficient. Therefore, the observed configurations differ from the existence of the intermediate degree and mid-clustered nodes in one of the unorganised communities, which makes it look less hierarchical than the user-centred community.

<figure><img src="image_17.png" /><figcaption>Figure 12: Distribution of the clustering coefficient values: (a) unorganised community, (b) 210284-centred community.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 13: Distribution of the nodes' outdegree values (y-axis) to their indegree values (x-axis) in two communities of the co-edit graph: (a) contributor-centred community, (b) unorganised group.</figcaption></figure>

Figures 13–15 represent nodes from the two communities extracted in Figure 10 in the plane (indegree, outdegree) of each layer of the multiplex layer. Throughout the different layers of the multiplex network, the contributor-centred community maintains a similar configuration: most of its members are characterised by a low *indegree*; outdegree* except for one node having both high outdegree and high indegree. Each time, this node happens to be the community centre (210284). Consequently, this contributor is very active because his/her collaboration is located both on modification and use operations. Although his/her contributions are edited by many members from his/her community, some members also use them to build their own contributions.
<figure><img src="image_19.png" /><figcaption>Figure 14: Distribution of the nodes’ outdegree values (y-axis) to their indegree values (x-axis) in two communities of the breadth of collaboration graph: (a) contributor-centred community, (b) unorganised group.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Figure 15: Distribution of the nodes’ outdegree values (y-axis) to their indegree values (x-axis) in two communities of the use graph: (a) contributor-centred community, (b) unorganised group.</figcaption></figure>

To explore in depth the role of contributor 210284, we focus on their relationship with contributor 860686, who is the next most central contributor in the community. To that end, Table 2 lists the weights of the edges linking these two nodes in all the layers of the multiplex network. The collaboration between these two contributors is broader than it is deep, meaning that the intensity of the collaboration is characterised by a high number of edited objects rather than a series of edits on one unique object. Moreover, as the edge weight in the co-edit graph is similar to the edge weight in the breadth of collaboration graph, the contributors directly edited each other’s contributions. We note that contributor 860686 used contributor 210284’s nodes in order to make his/her own OSM ways on 14 occasions. Therefore, even if the former widely edits the latter’s contributions, he/she is also willing to use them to create other objects, revealing a sign of confidence towards the central contributor. Besides, regarding contributor 86086’s actions, we can infer that they are also a very committed contributor.

In all of the layers, the unorganised group plots are more scattered than the contributor-centred group plots. By dividing the plot into four dials (as in Figure 13), we see that the nodes are distributed in all the dials (Figure 14(b)). Therefore, the contributors of this group are quite heterogeneous in terms of indegree/outdegree participation.
<table><caption>Table 2: Edges (210284,86086) and (86086,210284) in the Paris IDC multiplex network.</caption><thead><tr><th>Graph</th><th>Weight of edge (210284,86086)</th><th>Weight of edge (86086, 210284)</th></tr></thead><tbody><tr><td>Co-edit</td><td>74</td><td>89</td></tr><tr><td>Breadth of collaboration</td><td>75</td><td>89</td></tr><tr><td>Depth of collaboration</td><td>1</td><td>1</td></tr><tr><td>Use</td><td>14</td><td>N\A</td></tr></tbody></table>

Actually, the unorganised groups that were detected in the aggregated graph are far from being unorganised in the different layers of the multiplex network. This is due to the aggregation process, which merges edges that are scattered in different layers, leading to artificial connections between contributors in the aggregated graph. As a solution, we may filter edges whose weight is under a threshold in order to retain only the most meaningful relationships. The filtering process may be done at two different stages: either before graph aggregation, in which case filtering would remove weak interactions in each layer, or after aggregation, to remove generally weak relationships. However, in that case, relationships that are not repeated in several layers are removed. Therefore, having filtered the layers as follows:

* Co-edit layer: keeping edges whose $w > 3$

* Collaboration breadth layer: keeping edges whose $w > 3$

* Collaboration depth layer: keeping edges whose $w > 2$

A merged graph is built from the aggregation of the filtered graphs with the other layers. Then, community detection is run once more on this aggregated graph. Such a filtering process presents the advantage of removing the redundancy that the co-edit, breadth of collaboration and depth of collaboration layers contained. Figure 16 depicts a new community composition. We observe that the initial 210284-centred community includes nodes having a higher degree of centrality and its configuration is less user-centred. The unorganised group is composed of fewer nodes with a low degree of centrality. These communities are composed of contributors who are bound by a stronger relationship than in the initial community; therefore, a deeper analysis on these groups may more accurately reveal collaborative behaviours.

<figure><img src="image_21.png" /><figcaption>Figure 16: Detected communities of a multiplex network in which thresholds are applied on edit layers: (a) 210284-centred community, (b) unorganised community. Node size is proportional to degree. User IDs are anonymised.</figcaption></figure>

## 4.3 Independence of the multiplex network regarding the spatio-temporal area

This subsection aims to demonstrate that the multiplex network can still be used when considering other spatio-temporal windows. To this end, multiplex networks were constructed using the Stuhr and Kathmandu datasets described earlier.
Compared to the five-layer multiplex network of Paris IDC, these two networks are similarly computed, but with the differences that the co-contribution graph was dropped, while a suppression graph, a co-location graph and a co-temporal graph were added to the set of layers. The co-temporal and co-location graph weightings are both defined by a relative overlap (as proposed in section 3.2.1). In total, the Stuhr and Kathmandu multiplex networks are each composed of seven layers.

Community detection was run on the aggregated graphs of the Stuhr and Kathmandu multiplex networks, having the same thresholds applied on the edition-based layers of the networks before aggregation, as was described for Paris IDC. We could visually identify the same configurations (Figures 17 and 18). Table 3 summarises the distribution of clustering coefficient values in these newly detected communities. In both areas, almost half of the nodes in user-centred communities have a very low clustering coefficient (between 0 and 0.1). Communities that were labelled unorganised have either an important portion of medium clustering coefficient values (between 0.1 and 0.8), as it is the case for the Stuhr unorganised community, or an important portion of high clustering coefficient values (between 0.8 and 1), as it is the case for the Kathmandu unorganised community. This basic analysis of the Stuhr and Kathmandu datasets shows that a multiplex network can be built for any spatio-temporal area. Further analysis should clearly be conducted to better understand the collaboration mechanisms at work for these two areas, but this was not the point of our analysis.

<figure><img src="image_22.png" /><figcaption>Figure 17: Two distinct configurations in the detected communities of Stuhr: (a) contributor-centred community, (b) unorganised community. Node size is proportional to degree. User IDs are anonymised.</figcaption></figure>

<table><caption>Table 3: Clustering coefficient value distribution of the communities depicted in Figures 17 and 18.</caption><thead><tr><th rowspan="2">Cluster coefficient (value intervals)</th><th colspan="2">Stuhr</th><th colspan="2">Kathmandu</th></tr><tr><th>User centred</th><th>Unorganised</th><th>User centred</th><th>Unorganised</th></tr></thead><tbody><tr><td>[0, 0.1]</td><td>41.2%</td><td>21.6%</td><td>46.4%</td><td>32.7%</td></tr><tr><td>[0.1, 0.5]</td><td>11.8%</td><td>17.4%</td><td>14.2%</td><td>0.6%</td></tr><tr><td>[0.5, 0.8]</td><td>9.8%</td><td>17.4%</td><td>14.6%</td><td>18.5%</td></tr><tr><td>[0.8, 1]</td><td>37.3%</td><td>39.1%</td><td>24.9%</td><td>48.2%</td></tr></tbody></table>

# 5 Discussion

The key question regarding the centred communities is as follows: does a community centre behave like a moderator? Goodchild and Li [1] defined a moderator as a user who contributes a lot and whose contributions are sparsely edited. The analysis of one specific contributor-centred community is not sufficient to generalise to the qualification of communities that share the same configuration. Ideally, each community should be similarly studied. Nevertheless, we focus on the participation of their contributor-centres (see Table4).

We note that contributor 17397 barely contributed during the studied period, though their contributions formed more than half of the visible contributions in January 2013. Therefore, this community is composed of members who
<figure><img src="image_23.png" /><figcaption>Figure 18: Two distinct configurations in the detected communities of Kathmandu: (a) contributor-centred community, (b) unorganised community. Node size is proportional to degree. User IDs are anonymised.</figcaption></figure>

<table><caption>Table 4: Activity of contributors having the highest node degree in the set of nodes after 1 January 2013 of the Paris IDC area.</caption><tr><td>Central user ID</td><td>210284</td><td>1198200</td><td>158937</td><td>17397</td></tr><tr><td>Created nodes</td><td>3600</td><td>130</td><td>600</td><td>0</td></tr><tr><td>Created ways</td><td>15</td><td>9</td><td>40</td><td>0</td></tr><tr><td>Edited nodes</td><td>1500</td><td>500</td><td>2200</td><td>1</td></tr><tr><td>Edited ways</td><td>500</td><td>260</td><td>340</td><td>20</td></tr><tr><td>Day activity (%)</td><td>60</td><td>20</td><td>60</td><td>20</td></tr><tr><td>Night activity (%)</td><td>40</td><td>80</td><td>40</td><td>80</td></tr><tr><td>Weekdays activity (%)</td><td>90</td><td>70</td><td>25</td><td>60</td></tr><tr><td>Weekend activity (%)</td><td>10</td><td>30</td><td>75</td><td>40</td></tr></table>

massively edited 17397's contributions, which may imply that they are low quality data. However, contributor 17397 is the target of 46 contributors in the use graph, of which two contributors use 17397's nodes more than a thousand times to create their own OSM ways. So, 17397's nodes are not necessarily of poor quality, since they were exploited by other users. The participation of contributor 17397 may have helped the other users to contribute in OSM by editing their objects. From this point of view, contributor 17397 behaved more like a pioneer, whereas the other contributor-centres, who are more active in the period of analysis, acted like moderators.

In addition, we observe that the other contributor-centres' contributions are mainly automated edits and come from the open data platform of Paris or from the city cadastre. Accordingly, these contributors can be considered experts. To classify them in the typology proposed by Coleman et al. [4], we need to access their personal information, which is impossible on OSM. Thus, the analysis of the temporal participation of the main contributors of the dataset may provide some guesses in this respect (see Table 4). A professional is more likely to contribute on weekdays and during the day, whereas an amateur may contribute more during his/her spare time, that is, after work hours on weekdays or during the weekends. On these grounds, contributors 210284 and 17397 behave like professionals, while contributors 1198200 and 158937 appear similar to amateurs. However, as most of their contributions are automated edits, their active participation was not required. Therefore, inferring the contributors' expertise via this route is quite debatable.

Through this application example, we demonstrate that a substantial contributor who has been widely edited does not fit in the moderator profile as defined by Goodchild and Li [1], but this user appears to encourage smaller contributors to
participate by editing their objects. In this way, this type of contributor increases collaboration (through data editing) on the features they created and consequently boosts the quality of the resulting data [3]. Yet, considering only the initial version of their contributions, the data are a priori inaccurate or incomplete, but likely to be kept in the database to be improved later. Additionally, a contributor whose nodes are intensely used can be considered as trustworthy by the community. Furthermore, the informational-trust concept conveys trust to a contribution that is authored by a trustworthy contributor [21]. Therefore, according to this concept, nodes that were used by other contributors can be qualified as trustworthy.

Being edited is not equivalent to being corrected. Although this aspect was not addressed in our analysis, it should be interesting to distinguish whether a contributor was corrected or completed. As the co-edit graph combines both operations, future work may consist in breaking down the co-edit graph according to the completion and correction operations. For now, though, the positive side of our case study is the discovery of a new contributor profile that we could term a *pioneer*: their contributions appear to encourage beginners or small contributors to participate. Therefore, the quality of the corresponding contributions may be enhanced as they benefited from one or several cross-checks. Additionally, it could be useful to make an aggregated graph that keeps mutual and directed edges, in order to improve community detection. In that case, the co-contribution graph would not be taken into account.

In this case study, communities of only two members were not analysed. As we cannot know for now whether this configuration is due to the chosen spatio-temporal window of analysis, it can be interesting to analyse OSM contributors to a broader area and over a longer period. The community detection for this new area would determine whether this configuration survives or not. It should be noted, though, that the point of our analysis is not to demonstrate the occurrence of a specific pattern of collaboration in every region -in this case the experiment would require several countries as a test case - but to provide some insight into the potential of modelling a multiplex network to study contributors’ collaborations to infer knowledge about the quality of the contributions.

Isolated contributors also deserve deeper investigation. Indeed, not being edited nor used could mean different things. On the one hand, the corresponding contributions may be top-quality data that are not designed for building ways, for instance, points of interest. On the other hand, these contributions may be recent data with respect to the temporal window of analysis, so that edits of these data are temporally out of bounds. On this matter, the collaborative behaviour of OSM contributors is inferred from the whole temporal window. Consequently, the experiment does not allow us to observe the change in the collaborative behaviour of a contributor for now. A potential solution is to observe temporal changes through dynamic multiplex networks [41].

# 6 Conclusion

This paper proposed to analyse contributors' behaviour by implementing a multiplex network that gathers various types of collaboration between OSM contributors. The model makes use of existing graphs from the literature and includes additional graphs that address other aspects of collaboration. In this way, through our case study, we were able to distinguish between contributors who contribute in sequential and simultaneous modes of collaboration, thanks to the use of a multiplex network.

Beyond these results, we could discover interesting features regarding the collaborative behaviour of OSM contributors on the Paris area, particularly great OSM contributors. The analysis of their behaviour made it possible to infer a priori assumptions as to the quality of the underlying contributions, although a second quality procedure is clearly needed to assess the overall data quality, where additional criteria should be taken into account. Even if this first step is not enough to qualify VGI data properly, having information on contributors is useful to assess the quality of contributions even when no reference dataset is available for comparison: in this case, the informational trust concept can still be applied [21].

The perspectives on our work are manifold; as mentioned in the previous section, analysing wider areas would yield additional interesting information, and even more by implementing all of the layers that were presented in Section 3. Adding layers in the multiplex network would refine the qualification of contributors. Furthermore, experimenting with other methods for graph analysis may lead to different results. For instance, the detected communities will surely be different if we perform graph clustering on each layer of the system to determine multiplex clusters. Likewise, the seed-centric approach [37] may also reveal other configurations of community.

Furthermore, our use case relies on experimental choices, for instance, the implementation of a two-layered network to study multiplex participation (see Section 4.2.1) and the application of an edge threshold to each graph (see Section 5). Varying the number of layers or the edge threshold values would validate the choice of our model's parameters and quantify their importance. For instance, which layers can be dropped without changing the composition and the structure
of the communities? What are the thresholds to apply on the graphs' edges to obtain relevant communities? These questions fall within the need to study the sensitivity of the used methods.

The detected communities result from the optimisation of the modularity, which is a graph structural quantity. However, it does not say anything about the contributions. Therefore, digging deeper into the contributions of the communities should lead to a better comprehension of these communities. For instance, what are the contributions that result from a coediting community? Are they primarily points of interest, buildings, roads or vegetation? Or maybe these co-editings do not specialise a specific type of geographic element. The only way to find this out is to more thoroughly study the contributions' details as a next step.

Our first analysis was focused on great contributors rather than the small ones, who mainly compose the majority of OSM contributors. Small contributors are oftentimes left aside in existing research, and analysing them would make it possible to better identify the anonymous crowd of OSM. Besides, a non-prolific user is not necessarily less trustworthy. This type of contributor may be picky but more thorough when it comes to his/her actions, making the corresponding contributions of a higher quality. Above all, the results extracted from our model should be integrated in a global process that aims at qualifying OSM data, and why not, other VGI data from sources such as Geo-Wiki or Foursquare. To this end, contributor behaviours should be studied for other VGI projects, to highlight common VGI contribution patterns that are not limited to OpenStreetMap.

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