# Inferring Urban Social Networks from Publicly Available Data
## 5 Discussion and Conclusions  
We have defined and implemented a probabilistic model of the strong social ties binding the population of a given territory, organized into households. Despite the abundance of related empirical and modeling studies, there is no general agreement concerning the mechanisms behind the formation of urban social networks. Our model is, therefore, designed on top of just a few clear assumptions: (i) not all individuals are equally sociable;  
Figure 11: **(Florence)** Impact of switching from \(f_{u}\equiv 1\) to \(f_{u}\sim 1+\mathcal{LN}(\ln(2),0.25)\) on the degree distribution of each tile. In both cases, \(\mu=10\) and \(D(u,v)=d(u,v)^{-2}\). \(f_{u}\) has no impact on the mean degree of each tile (**a**), but setting \(f_{u}\sim 1+\mathcal{LN}(\ln(2),0.25)\) yields individuals with very different sociability inside each tile (**b**). (**a**) Difference of the _mean_ degree of each tile between the configuration with \(f_{u}=1+\mathcal{LN}(\ln(2),0.25)\) and the configuration with \(f_{u}\equiv 1\). **(b**) Difference of the _maximum_ degree of each tile between the configuration with \(f_{u}=1+\mathcal{LN}(\ln(2),0.25)\) and the configuration with \(f_{u}\equiv 1\). Figure 10: **(Florence)** Heatmaps of the population and of the average degree per tile of the considered territory. The average degree is obtained for a graph with \(f_{u}\sim 1+\mathcal{LN}(\ln(2),0.25)\), \(\mu=10\) and \(D(u,v)=d(u,v)^{-\beta}\), for both \(\beta\in\{0.5,2\}\). With \(\beta=0.5\) **(b)**, the mean degree is weakly correlated with the population density, contrarily to what happens when \(\beta=2\) **(c)**. (ii) the geographical distance and the age difference play a role in the probability that two individuals become friends; (iii) we shall make use of all available data, bearing in mind their shortcomings. An overview of the main features of the model can be found in Reference [22], where the potential of the proposed framework is confirmed by the results of a set of epidemic simulations on the obtained network. In this paper, we instead provided a detailed analysis and an extensive experimental validation to assess the robustness and the flexibility of our model. The main goal of this work is permitting the recreation of synthetic social networks in the common circumstance where aggregated demographic data and some estimate of the age mixing patterns are the only available information. The ubiquitous use of online social networks and wearable sensors offers the opportunity to analyze networks that span the globe, but the extent to which they can be used to track real geographical networks and infer relationships is still an open question. On the other hand, social surveys are rarely available and intrinsically limited in the size of the reconstructed network. Data related to mobile (and/or landline) phone calls may seem a good compromise, but they are also difficult to acquire, often disaggregated among several operators, and variable in terms of pervasiveness and geographical resolution. Our tool addresses these issues providing a way to simulate a population within an arbitrary territory, whose individuals may be positioned with (almost) arbitrary precision, and for which the social mixing patterns can be inherited from any already existing dataset. We extensively evaluated the resulting social network and its dependence on system parameters, considering three Italian cities that differ for both the size of the population and the geography of the territory. We found that setting the average number of friends to 5 is sufficient to obtain a giant component that almost spans the entire network, even in the absence of household edges.