Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10482131 | Physica A: Statistical Mechanics and its Applications | 2012 | 6 Pages |
Abstract
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k into k nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p, or splitting with probability 1âp. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
E.R. Colman, G.J. Rodgers,