# Inferring Urban Social Networks from Publicly Available Data
## Appendix C Results for the City of Viterbo  
The same analysis discussed in Sections 3 and 4 for the city of Florence has been carried out for the cities of Viterbo and Sabaudia. Except for a few details, mostly ascribable to differences in the demographics and in the geography of the considered territories, the same observations and conclusions drawn for the case of Florence apply to these other two cities, as confirmed by the results shown in this and the next appendix. In the following,we report all plots and tables for the city of Viterbo, which are by all means analogous to those already presented for Florence.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{6}{c}{**(a) Friendship Network for \(\mu=5\). Expected Values for an ER Graph with \(\mu=5\): \(\langle\)dist\(\rangle\approx 6.9\), \(C=7.5\)e-05.**} \\ \hline \hline \multirow{2}{*}{**Population**} & \multirow{2}{*}{\(\mathbf{D(u,v)}\)} & \multirow{2}{*}{\(\langle\)dist\(\rangle\)} & \multirow{2}{*}{\(C\)} & \multirow{2}{*}{\(\rho\)} & \multirow{2}{*}{\(\mathbf{\#\)\(\mathbf{\text{Comp.}}\)}} & \multirow{2}{*}{**Giant \%**} \\ \cline{1-1} \cline{5-6}  & & & & & & \\ \hline homogeneous & 1 & 7.08 & 8.2e-05 & \(-\)5.06e-04 & 458.9 & 99.3\% \\ homogeneous & \(d(u,v)^{-0.5}\) & 7.04 & 8.2e-05 & 0.005 & 546.9 & 99.2\% \\ homogeneous & \(d(u,v)^{-2}\) & 7.15 & 7.95e-04 & 0.13 & 1022.1 & 98.4\% \\ real & 1 & 7.08 & 8.2e-05 & \(-\)1.91e-04 & 463.1 & 99.3\% \\ real & \(d(u,v)^{-0.5}\) & 6.94 & 9.2e-05 & 0.02 & 1053.9 & 98.4\% \\ real & \(d(u,v)^{-2}\) & 6.44 & 0.00025 & 0.2 & 9137.3 & 84.0\% \\ \hline \multicolumn{6}{c}{**(b) Friendship Network for \(\mu=10\). Expected Values for an ER Graph with \(\mu=10\): \(\langle\)dist\(\rangle\approx 4.82\), \(C=1.5\)e-04.**} \\ \hline \hline \multicolumn{6}{c}{\(\mu=10\)} \\ \hline \multirow{2}{*}{**Population**} & \multirow{2}{*}{\(\mathbf{D(u,v)}\)} & \multirow{2}{*}{\(\langle\)dist\(\rangle\)} & \multirow{2}{*}{\(C\)} & \multirow{2}{*}{\(\rho\)} & \multirow{2}{*}{\(\mathbf{\#\)\(\mathbf{\text{Comp.}}\)}} & \multirow{2}{*}{**Giant \%**} \\ \hline homogeneous & 1 & 5.08 & 1.52e-04 & \(-\)5.31e-04 & 4.1 & 100.0\% \\ homogeneous & \(d(u,v)^{-0.5}\) & 5.06 & 1.56e-04 & 0.011 & 8.0 & 100.0\% \\ homogeneous & \(d(u,v)^{-2}\) & 5.23 & 0.0016 & 0.22 & 42.9 & 99.9\% \\ real & 1 & 5.08 & 1.56e-04 & \(-\)9.15e-04 & 4.8 & 100.0\% \\ real & \(d(u,v)^{-0.5}\) & 5.04 & 1.69e-04 & 0.04 & 55.8 & 99.9\% \\ real & \(d(u,v)^{-2}\) & 5.17 & 0.0005 & 0.31 & 4461.6 & 92.6\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: (**Viterbo**) Main features of the friendship graph \(G_{\text{F}}\) as the population type, \(D(u,v)\) and \(\mu\) vary, for constant \(f_{u}\) and \(S\). \(\langle\)dist\(\rangle\) is the average path length, \(C\) is the global clustering coefficient, \(\rho\) is the degree assortativity, “# comp.” denotes the number of connected components, and “giant %” denotes the percentage of nodes in the giant component.  
Figure A8: **(Viterbo)** Distribution of the size of the connected components other than the giant for friendship graphs with \(\mu=5\) and \(\mu=10\). The lines show the mean, whereas the error bars (with “caps\") represent the 95% confidence interval computed over each set of runs.  
Figure A9: (**Viterbo**) Overview of the urban social graph for the city of Viterbo. Each plot shows the average with confidence interval for 10 independent runs with the same configuration. (**a**) Size of the largest 50 connected components. (**b**) Size of the largest 50 clusters (Louvain). (**c**) Degree distribution with Lognormal fit. (**d**) Geographical distance between adjacent vertices. (**e**) Mean and max intra-cluster geographical distances. (**f**) Mean distance to all other vertices vs. Degree.  
Figure A10: Modularity of the obtained clustering structure—distribution for 10 independent runs per configuration.