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|Title:||Large Communities In A Scale-free Network|
|Abstract:||We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we consider a dynamic stochastic process for constructing a graph in which at each step we independently decide, with probability , whether the graph receives a new vertex or a new edge between existing vertices. The connections are then made according to a preferential attachment rule. We prove that the random graph produced by this so-called generalized linear preferential (GLP) model at time t contains a complete subgraph whose vertex set cardinality is given by , where , for any small asymptotically almost surely.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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