Canonical fitness model for simple scalefree graphs
Abstract
We consider a fitness model assumed to generate simple graphs with a powerlaw heavytailed degree sequence, P(k)∝k^{1α} 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)∝k^{2} for large values of k independent of α. Our analytical findings are confirmed by numerical simulations.
 Publication:

Physical Review E
 Pub Date:
 February 2013
 DOI:
 10.1103/PhysRevE.87.022806
 arXiv:
 arXiv:1211.5498
 Bibcode:
 2013PhRvE..87b2806F
 Keywords:

 89.75.Hc;
 89.75.Da;
 Networks and genealogical trees;
 Systems obeying scaling laws;
 Physics  Physics and Society;
 Computer Science  Social and Information Networks
 EPrint:
 6 pages, 2 figures