Phase Transitions in an Aging Network

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We consider a growing network in which an incoming node gets attached to the ith existing node with the probability Πᵢ ∝ kᵢβτᵢα, where kᵢ is the degree of the ith node and τᵢ its present age. The phase diagram in the α-β plane is obtained. The network shows scale-free behaviour, i.e., the degree distribution P(k) k⁻γ with γ=3 only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram.