Canonical fitness model for simple scale-free graphs

We consider a fitness model assumed to generate simple graphs with a power-law heavy-tailed degree sequence, P(k) proportional to k(1-alpha) with 0 < alpha < 1, in which the corresponding distributions do not possess a mean. We discuss the situations in which the model is used to produce a multigraph and examine what happens if the multiple edges are merged to a single one and thus a simple graph is built. We give the relation between the (normalized) fitness parameter r and the expected degree nu of a node and show analytically that it possesses nontrivial intermediate and final asymptotic behaviors. We show that the model produces P(k) proportional to k(-2) for large values of k independent of alpha. Our analytical findings are confirmed by numerical simulations. DOI: 10.1103/PhysRevE.87.022806