# Inferring Urban Social Networks from Publicly Available Data
### Related Work
#### 1.1.2 Social and Contact Network Models  
A number of random graph models, proposed across decades of research, have been widely used in computational social sciences [7]. The lack of available data about real-world social ties fostered the choice of rather simple models (e.g., Erdos-Renyi [30], Barabasi-Albert [31], and Watts-Strogatz [32]) which rely on just a few, easy to explain, assumptions. While these models capture in a simple and elegant way some essential features of different kinds of complex networks, it is well know that, in practice, they have significant limitations. Models designed to mimic the scale-free degree distribution emerging in many real networks, for instance, may fail to yield the expected clustering structure [33]. Exponential random graphs have been shown to overcome some of these limits [34; 35]. Generally speaking, a possible adjustment to those models consists in introducing a _homophily_ principle [36], according to the widely acknowledged insight that individuals tend to localize with their peers [37; 38]. Among other aspects, such as education or economy, age emerged as a critical element in the formation of social ties [10; 39; 40; 41], possibly thanks to the availability of age-related data at different spatial scales [42]. As far as we know, however, there are no quantitative studies that report the relative frequency of social links (i.e., relationships) by age, and previous network models that incorporate real data on social mixing by age are designed to generate synthetic physical interactions. Another widely studied type of homophily is spatial proximity, which gives rise to the so-called _spatial networks_. Most authors considered variations of well known random network models obtained by embedding the vertices in a metric space. The imposed spatial constraints influence the topological properties of the network [43; 44] and the imposed penalty on \"long\" edges causes the spatial distribution of the vertices to impact on clusters, path lengths, degree distribution, and more [5; 45]. Again, there is not much research about data-driven spatial social network models, in which the location of the individuals can be retrieved from real data. A somehow corresponding problem consists in inferring social or contact networks from real data. For _virtual_ populations, e.g., online social networks, relationships and actually occurred interactions may be directly retrieved [12; 17; 46; 47], at least to some extent. The dependability of this information is, however, debatable because the virtual population may convey significantly different information with respect to self-reported friendships [48]. When the focus is, instead, on the physical interactions among the individuals of a population, a synthetic version of the population may be created on the basis of census and/or survey data [49]. The final goal is the definition of a set of _human mixing patterns_ (i.e., the frequency of contacts among people of different ages and/or in different places) which allow to reproduce the dynamics of the network, for instance, to model the diffusion of a disease in real populations [49; 50; 51; 52]. This approach usually requires to focus on a set of primary social settings (e.g., households, schools and workplaces) and to collect sample data (e.g., surveys, questionnaires, diaries, mobility, etc.) [15; 53; 51], possibly integrated with mobile/traffic/wearable sensors data [8; 48; 54; 55] or online tools [52]. These data may be used to directly extract setting-specific _contact matrices_[9; 15; 51; 53], or to recreate _realistic_ instances of such social settings and synthetic agendas used to feed an agent-based simulator by which agent-to-agent interactions are reproduced [9; 54; 56; 57; 58]. It is worth noting that these studies target physical contacts rather than relationships. While they provide valuable information about social mixing patterns, they do not aim to define a network of strong social ties.