title: Groupies in multitype random graphs.
abstract: A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
authors.affiliation: Department of Mathematics, Tongji University, Shanghai, 200092 China.
authors.forename: Yilun
authors.identifier: 0000-0002-2817-3400
authors.initials: Y
authors.lastname: Shang
keywords: Degree; Groupie; Multitype; Random graph