Hruz, Tomas; Peter, Ueli Nongrowing preferential attachment random graphs. (English) Zbl 1237.05189 Internet Math. 6, No. 4, 461-487 (2010). Summary: We consider an edge rewiring process that is widely used to model the dynamics of scale-free weblike networks. This process uses preferential attachment and operates on sparse multigraphs with \(n\) vertices and \(m\) edges. We prove that its mixing time is optimal and develop a framework that simplifies the calculation of graph properties in the steady state. The applicability of this framework is demonstrated by calculating the degree distribution, the number of self-loops, and the threshold for the appearance of the giant component. Cited in 1 Document MSC: 05C80 Random graphs (graph-theoretic aspects) 05C82 Small world graphs, complex networks (graph-theoretic aspects) 60C05 Combinatorial probability 05C07 Vertex degrees 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:edge rewiring process; weblike networks; preferential attachment; sparse multigraphs; mixing time; degree distribution; number of self-loops; giant component × Cite Format Result Cite Review PDF Full Text: DOI Euclid