Figure 3
From: Homophily influences ranking of minorities in social networks
Ranking of minorities as a function of relative group size and homophily. (A) Average cumulative degree of the minority as a function of homophily, for different minority fractions (0.1–0.5). In a balanced population (0.5, pink line), both groups share half of the links, independently of the level of homophily. As the size of the minority decreases, the inequality in the share of degree increases. In a homogeneous-mixing case (h = 0.5), the rank corresponds to the expected population size shown by the grey dashed lines. In heterophilic regimes (0 ≤ h < 0.5), the minority takes advantage of the population size effect. In homophilic regimes (0.5 < h ≤ 1), we observe that the degree of minorities is below the expectation and it is recovered only in the extreme homophilic case (h = 1) by full in-group support. (B) Fraction of minority nodes that are found in the top d% of nodes with the highest degree. The fraction of nodes belonging to the minority (fa) is set to 0.2. If the group membership does not impact the attractiveness of nodes, we expect that the presence of the minority in the top d% is the same as its relative size (dashed line). However, we see that the results are sensitive to homophily. In the heterophilic case (0 ≤ h < 0.5), minorities are over-represented in the top d%. In the homophilic case (0.5 < h ≤ 1), minorities are under-represented in the top d%. In the case of homogeneous mixing (h = 0.5) or complete homophily (h = 1.0), minorities are presented in the top d% as expected from their relative size. Note that the results for the majority group is only the complementary of those for the minority.
