Scalefree properties of weighted networks with connectivitydriven topology
Abstract
The rate equations are used to study the scalefree behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with an unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node degree at the current stage of the network evolution. Such a modification of the attachment rule is argued to accelerate considerable numerical simulations of both unweighted and weighted networks belonging to the class of investigated evolving systems. It is also proved that the studied rate equations have a solution corresponding to the total weight (concentrated at individual vertices) distribution displaying the powerlaw behavior for asymptotically large weights.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 August 2005
 DOI:
 10.1016/j.physa.2005.02.026
 arXiv:
 arXiv:condmat/0412196
 Bibcode:
 2005PhyA..354..672J
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 9 pages