Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
978232 | Physica A: Statistical Mechanics and its Applications | 2007 | 10 Pages |
Abstract
General conditions for the appearance of the power-law distribution of total weights concentrated in vertices of complex network systems are established. By use of the rate equation approach for networks evolving by connectivity-governed attachment of every new node to p⩾1 exiting nodes and by ascription to every new link a weight taken from algebraic distributions, independent of network topologies, it is shown that the distribution of the total weight w asymptotically follows the power law, P(w)â¼w-α with the exponent αâ(0,2]. The power-law dependence of the weight distribution is also proved to hold, for asymptotically large w, in the case of networks in which a link between nodes i and j carries a load wij, determined by node degrees ki and kj at the final stage of the network growth, according to the relation wij=(kikj)θ with θâ(-1,0]. For this class of networks, the scaling exponent Ï describing the weight distribution is found to satisfy the relationship Ï=(λ+θ)/(1+θ), where λ is the scaling index characterizing the distribution of node degrees, n(k)â¼k-λ.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
W Jeżewski,