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.
Categories: cond-mat.stat-mech