title: Canonical fitness model for simple scale-free graphs.
abstract: We consider a fitness model assumed to generate simple graphs with a power-law heavy-tailed degree sequence, P(k)[proportionality]k(-1-α) with 0<α<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 ν of a node and show analytically that it possesses nontrivial intermediate and final asymptotic behaviors. We show that the model produces P(k)[proportionality]k(-2) for large values of k independent of α. Our analytical findings are confirmed by numerical simulations.
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany.
authors.forename: F
authors.initials: F
authors.lastname: Flegel
authors.forename: I M
authors.initials: IM
authors.lastname: Sokolov
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical