Scale-free property for degrees and weights in an N-interactions random graph model

2013/09/17 by Fazekas, István, Porvázsnyik, Bettina
#05C80 #60G42 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.4258

Abstract

A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The weight of a given vertex is the number of the interactions of the vertex. The asymptotic behaviour of the graph is studied. Scale-free properties both for the degrees and the weights are proved. It turns out that any exponent in (2,∞) can be achieved. The proofs are based on discrete time martingale theory.

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