Phase Transitions in an Aging Network

Abstract

We consider a growing network in which an incoming node gets attached to the $i^{th}$ existing node with the probability ${\Pi }_i\propto {k_i}^{\beta }{\tau }_i^{\alpha }$, where $k_i$ is the degree of the $i^{th}$ node and ${\tau }_i$ its present age. The phase diagram in the $\alpha -\beta$ plane is obtained. The network shows scale-free behaviour, i.e., the degree distribution $P(k)\sim k^{-\gamma }$ with $\gamma =3$ only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram.

4 pages, 4 figures Submitted to Physical Review E