We consider a growing network in which an incoming node gets attached to the $i\mathrm{th}$ existing node with the probability ${\Pi }_i\propto {k_i}^{\beta }{\tau }_i^{\alpha }$, where $k_i$ is the degree of the $i\mathrm{th}$ node and ${\tau }_i$ its present age. The phase diagram in the $\alpha -\beta$ plane is obtained. The network shows scale-free behavior, i.e., the degree distribution $P\left(k\right)\sim k^{-\gamma }$ 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.

• Received 2 April 2004

DOI:https://doi.org/10.1103/PhysRevE.70.056103