Local rewiring rules for evolving complex networks

• Published in: Physica A 2014-12, Vol.416, p.80-89
• Main Authors: Colman, E.R., Rodgers, G.J.
• Format: Article
• Language: English
• Subjects: Attachment; Detaching; Detachment; Extreme values; Links; Networks; Random networks; Rewiring; Statistical mechanics
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2014.08.046

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global rewiring and local rewiring. During a rewiring phase a node is randomly selected, one of its out-going edges is detached from its destination then re-attached to the network in one of two possible ways; either globally to a randomly selected node, or locally to a descendant of a descendant of the originally selected node. Although the probability of attachment to a node increases with its connectivity, the probability of detachment also increases, the result is an exponential degree distribution with a small number of outlying nodes that have extremely large degree. We explain these outliers by identifying the circumstances for which a set of nodes can grow to very high degree. •An analysis of the class of directed network with fixed out-degree.•A stochastic model is introduced that incorporates growth, local and global rewiring.•Degree distribution converges to an exponential form.•When the rewiring is mostly local, small sets of nodes dominate and accumulate many links.