# Inferring Urban Social Networks from Publicly Available Data
## 5 Discussion and Conclusions
Age- and proximity-based homophily do provide the intended benefits: imposing data-driven age-based mixing patterns is critical to guarantee the internal cohesion of single age-groups--in particular, of young people; using the real population density and penalizing physically long edges prevents a Poisson-like degree distribution; both improve the assortativity and the transitivity of the network. The clustering coefficient, however, is rather low in the friendship layer of our graph, albeit the whole social network has strong clustering thanks to the complete subgraphs used to represent data-driven households. If we introduce a variable (specifically, Lognormally distributed) sociability, we obtain the often desired heavy-tailed degree distribution. This helps connecting peripheral areas to the core of the network, especially when the average degree is small. However, sociable hubs tend to concentrate in densely populated areas, with the combined effect of exacerbating the correlation between favorable positioning and degree. The configurations that favor the rise of large hubs (i.e., Lognormal social fitness and strong penalization of long edges) slightly worsen the global transitivity, but they improve the average local transitivity. If we increase the average number of friends, most of the network distributes in just a few giant communities, a phenomenon that is amplified by a weak penalization of long edges and not affected by the distribution of the social fitness. Almost regardless of their size, the communities tend to have a large spatial extension, even though the average distance of their members is small. Finally, by controlling the penalization of long edges, we can not only control the distribution of the physical distance between adjacent nodes but also the dependence of the average degree in a tile upon the position of the tile. The variability of the degree internal to a tile is, however, entirely controlled by the social fitness. Our model is intrinsically conditioned by the meaning we give to the word \"friendship\", which is not only related to the value we assign to the average number of friends \(\mu\). For instance, the experimentally measured dependence of \(u\)'s average degree upon the density of vertices at different distances from \(u\) was already predicted by (7). However, we mostly designed this simulator as a tool to study and possibly forecast interactions, e.g., for use in computational epidemiology, even when accurate data upon such interactions are not available. When the friendship network is used to infer the likelihood of physical contacts, it may be reasonable to assume that living in a high density area implies being part of a dense subnetwork of friends that have a greater chance to physically meet. In any case, (7) also suggests that corrections to our model are possible to make it less sensitive to population density, for instance, by imposing a limit to the total sociability of each tile or using a density-aware \(D\), such as the rank-based model defined in Reference [17]. Another related element of discussion is the identification of the most suitable distribution for the social fitness parameter, or even whether this parameter should be used in the first place or not. While a heavy-tailed degree distribution characterizes many real-world networks [64], it is widely acknowledged that even sociable human beings can establish a limited amount of strong relationships [6; 66]. In other words, since our urban social graph models strong ties, whether a heavy-tail effect should be present and to what extent, is open to interpretation. A Lognormal fitness seems to yield the typical degree distribution of many real-world networks, but setting \(f_{u}\equiv 1\) still guarantees that the maximum degree of the network is 5 to 6 times greater than the mode of the distribution, which may be preferable in many practical cases.