Fig. 1

Statistics of network models. All networks have \(N = 5000\) nodes, where each node joins the network with \(l = 2\) edges and 20% of the nodes are minority. We set \(h = 0.8\), \(e_o = 1\), \(\alpha = 1\) and \(p_d = 0.6\). a Degree distributions. BA, Homophily BA, and Diversified Homophily BA all heavy-tailed degree distributions because of preferential attachment. b Basic Statistics. As expected, Random Network has dyadicity and heterophilicity of 1. For all network models expect Random Network, dyadicity in the minority group is larger than dyadicity in the majority group. The diversified versions of network models have larger heterophilicity compared to their undiversified versions because of the inter-group edges in the diversified versions. Homophily BA and BA have the smallest average shortest path lengths and diameters due to the presence of hubs. Diversified Homophily and Diversified Homophily BA have the largest average shortest path length and diameter. c Social Captial Equality Measures. For each equality measure, we sort the generative network models from most equal (left) to least equal (right). The earth mover distance is the distance between the degree distributions of the minority and majority groups. Homophily BA has the largest earth mover distance, while Random Network has the smallest distance. The power inequality is the ratio of the average degree in the minority group to the average degree in the majority group. The moment glass ceiling is the ratio of the second moment of degree distribution in the minority group to the second moment of degree distribution in the majority group. For Power Inequality and Moment Glass Ceiling, the minority nodes have the most advantage in Diversified Homophily BA, while the majority nodes have the most advantage in Homophily BA.