Mixed membership estimation for social networks

In economics and social science, network data are regularly observed, a thorough understanding of the community structure facilitates comprehension economic patterns activities. Consider an undirected with n nodes K communities. We model using Degree-Corrected Mixed-Membership (DCMM) model, where for each node i=1,2,…,n, there exists membership vector πi=(πi(1),πi(2),…,πi(K))′, πi(k) is weight that i puts on k, 1≤k≤K. comparison to well-known stochastic block (SBM), DCMM permits both severe degree heterogeneity mixed memberships, making it more realistic general. present efficient approach, Mixed-SCORE, estimating vectors all other parameters. This approach inspired by discovery delicate simplex in spectral domain. derive explicit error rates Mixed-SCORE algorithm demonstrate rate-optimal over broad parameter space. Our findings provide novel statistical tool analysis, which can be used understand formations, extract nodal features, identify unobserved covariates dyadic regressions, estimate peer effects. applied political blog network, two trade networks, co-authorship citee obtained interpretable results.