Complex scale-free networks with tunable power-law exponent and clustering

摘要

We introduce a network evolution process motivated by the network ofcitations in the scientific literature. In each iteration of the process a nodeis born and directed links are created from the new node to a set of targetnodes already in the network. This set includes $m$ "ambassador" nodes and $l$of each ambassador's descendants where $m$ and $l$ are random variablesselected from any choice of distributions $p_{l}$ and $q_{m}$. The processmimics the tendency of authors to cite varying numbers of papers included inthe bibliographies of the other papers they cite. We show that the degreedistributions of the networks generated after a large number of iterations arescale-free and derive an expression for the power-law exponent. In a particularcase of the model where the number of ambassadors is always the constant $m$and the number of selected descendants from each ambassador is the constant$l$, the power-law exponent is $(2l+1)/l$. For this example we deriveexpressions for the degree distribution and clustering coefficient in terms of$l$ and $m$. We conclude that the proposed model can be tuned to have the samepower law exponent and clustering coefficient of a broad range of thescale-free distributions that have been studied empirically.