The Magic of Networks Grown by Redirection

Abstract

We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial target or to a neighbor of this target. This exceedingly simple algorithm generates preferential attachment networks in an algorithmic time that is linear in the number of network nodes $N$. Even though preferential attachment ostensibly requires \emph{global knowledge} of the network, redirection requires only \emph{local knowledge}. We also show that changing just a \emph{single} attachment rate in linear preferential attachment leads to a non-universal degree distribution. Finally, we present unexpected consequences of redirection in networks with undirected links, where highly modular and non-sparse networks arise.

12 pages, 7 figures. For a special issue on "Statistical Physics and Complex Systems" in the Indian Journal of Physics. Version 2: small changes and additional references included. Version 3: a few minor changes and one reference added