Temporal effects in the growth of networks

Temporal effects in the growth of networksMatu´ˇs Medo, Giulio Cimini, Stanislao GualdiPhysics Department, University of Fribourg, CH-1700 Fribourg, Switzerland(Dated: September 28, 2011)We show that to explain the growth of the citation network by preferential attachment (PA), onehastoaccept thatindividualnodesexhibitheterogeneousfitnessvaluesthatdecaywith time. Whileprevious PA-based models assumed either heterogeneity or decay in isolation, we propose a simpleanalytically treatable model that combines these two factors. Depending on the input assumptions,theresulting degree distribution shows an exponential, log-normal or power-law decay, which makesthe model an apt candidate for modeling a wide range of real systems.Over the years, models with preferential attachment Before specifying a model and attempting to solve it,(PA) were independently proposed to explain the distri- we turn to data to provide support for our hypothesisbutionofthe number ofspecies ina genus[1], the power- of decaying relevance. We use here the citation datalaw distribution of the number of citations received by provided by the American Physical Society (APS) whichscientific papers [2] and the number of links pointing to contains all 450084 papers published by the APS fromWWW pages [4]. A theoretical description of this class 1893 to 2009 together with their 4691938 citations ofof processes and the observationthat they generally lead other papers from APS journals. It is ...