Social networks amplify inequalities due to fundamental mechanisms of social tie formation such as homophily and triadic closure. These forces sharpen social segregation reflected in network fragmentation. Yet, little is known about what structural factors facilitate fragmentation. In this paper we use big data from a widely-used online social network to demonstrate that there is a signicant relationship between social network fragmentation and income inequality in cities and towns. We find that the organization of the physical urban space has a stronger relationship with fragmentation than unequal access to education, political segregation, or the presence of ethnic and religious minorities. Fragmentation of social networks is signicantly higher in towns in which residential neighborhoods are divided by physical barriers such as rivers and railroads and are relatively distant from the center of town. Towns in which amenities are spatially concentrated are also typically more socially segregated. These relationships suggest how urban planning may be a useful point of intervention to mitigate inequalities in the long run.

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Figure 1: Income inequality correlates with network fragmentation in towns. (A) Cumulative distribution of income in a relatively equal town (Ajka, green line) and a relatively unequal one (G¨od¨oll˝o, blue line). (B) The social network structure in Ajka, the sample town that has low income inequality. (C) The social network structure in G¨od¨oll˝o, the sample town that has high income inequality. (D) Income inequality (measured by the Gini index) correlates with the fragmentation of social network within the town (Pearson’s r = 0.44 for towns larger than 15,000 population). (E) Network fragmentation intensifies income inequality stronger in those towns where initial inequality is high. , the marginal effect of town social network fragmentation (Fi) on the Gini of the town in 2016 (Gi,2016), becomes significant around the mean of the Gini in 2011 (Gi,2011) i.e. at ZGi,2011 = 0. It increases as Gi,2011 grows. In the subplot
we plot the correlation between town Gini scores in 2011 and 2016 (Gi,2011 and Gi,2016.) When studying social network fragmentation within towns, we consider only those links in iWiW, for which both ends correspond to person in the same town. We apply the community detection method known as Louvain algorithm [30]. This method partitions the individuals of the network in town i into groups by optimizing a measure called modularity Qi that compares the density of edges within groups to the density across groups [31]. Mathematically.