# Inferring Urban Social Networks from Publicly Available Data  
[PERSON]  
1 Istituto per le Applicazioni del Calcolo \"[PERSON]\", Consiglio Nazionale delle Ricerche, 00185 Rome, Italy; [EMAIL_ADDRESS] (E.M.); [PERSON]ESS] (M.B. ); [EMAIL_ADDRESS] (A.C.); [EMAIL_ADDRESS] (M.C. ); [EMAIL_ADDRESS] (D.T. ); [PERSON]DDRESS] (L.R.Z.) [PERSON]  
1  
[PERSON]  
1  
[PERSON]  
1  
1 Istituto per le Applicazioni del Calcolo \"[PERSON]\", Consiglio Nazionale delle Ricerche, 0 agents. On the one hand, our social graph may be used to simulate situations in which friends and relatives may go out together, organize public or private meetings, and are, in general, more likely to interact. This can be achieved by using _proximity_, measured on the network, as a driving factor in the simulation of contacts and events. On the other hand, the fact that the social graph is embedded into the urban landscape makes it possible to consider both geographical constraints and social ties to comprehend how specific places of aggregation foster interactions. Finally, this network can be used as a standalone tool to characterize urban social relations patterns and to understand how these patterns are influenced by the geography and the demography of a given territory. The edges of our spatial network describe stable interpersonal relationships of two types: intra-household (e.g., kinship) and friendship. Once the organization of the population into households has been inferred from the available data, the household network can be defined quite naturally as a set of _cliques_ (i.e., complete subgraphs), one for each household. However, the design of an accurate model for friendships is not so straightforward. Most simulation-based social studies claim a lack of reliable data and, therefore, model social networks by using general random graph models, such as Erdos-Renyi (ER), Small-world, or Scale-free graphs [7]. However, survey-based interaction networks, notoriously biased towards strong relationships [8], do not seem to follow any well-known simple random model [9]. Inspired by both empirical studies [10; 11; 12; 13] and previous modeling attempts [14] of real world social networks, we designed our friendship network model on top of the fundamental assumption that the probability \(\Pr[u,v]\) of two agents \(u\) and \(v\) being friends is ultimately governed by three key factors:  
1. their age group, whose role in the edge creation process can be described by means of a \(n\times n\) social mixing matrix \(S=\{s_{i,j}\}\), where \(s_{i,j}\) measures the frequency of relationships among individuals of age groups \(i\) and \(j\);
2. their geographical distance, whose impact can be controlled through a suitable non-increasing function \(D(u,v)\) of the distance \(d(u,v)\) between \(u\) and \(v\);
3. their sociability (i.e., the propensity of each of them to have friends), measured in our model by a _social-fitness score_\(f_{u}\) associated to each agent \(u\). While \(f_{u}\) and \(D\) might be adjusted to the type and strength of the social ties that one aims at reproducing, the coefficients \(s_{i,j}\) should instead be derived from social survey data, when possible. Even in the absence of information about social _relationships_, publicly available data regarding patterns of physical _contacts_ and _interactions_ should be regarded as a valuable source to estimate the ratios of intra- and inter-age group connections. In the proposed model, thus, \(D\) and \(f_{u}\) only impact on the selection of edges that exist between any two groups \(i\) and \(j\), whereas the overall social mixing structure defined by the data-driven \(S\) is preserved, at least on average.