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

The asymptotic behaviour of the weights and the degrees in an N-interactions random graph model

“…In this paper we study the following N-interactions model (see [18]). A complete graph with m vertices we call an m-clique, for short.…”

“…At each step, the weight of a fixed vertex is increased by 1 if and only if it takes part in an interaction. As in [7], [17] and in [18], it is easy to show that the conditional probability that the jth vertex takes part in an interaction at step (n + 1) is…”

“…Proof. As in [18], the probability that an old vertex of weight W [n, j] takes part in the interaction at step (n + 1) is…”

“…A random graph model based on the interactions of three vertices was introduced and power law degree distribution in that model was proved in [7] and [8]. Instead of the three-interactions model, the interactions of N vertices (N ≥ 3 fixed) were studied in [18]. Scale-free properties for these generalized models were obtained in [17] and [18].…”

“…Instead of the three-interactions model, the interactions of N vertices (N ≥ 3 fixed) were studied in [18]. Scale-free properties for these generalized models were obtained in [17] and [18].…”