Quasistatic scale-free networks

A network is formed using the N sites of a one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree k(in)=2. N links are then introduced to this network, each link starts from a distinct node, the other end being connected to any other node with degree k randomly selected with an attachment probability proportional to k(alpha). Tuning the control parameter alpha, we observe a transition where the average degree of the largest node <k(m)(alpha,N)> changes its variation from N0 to N at a specific transition point of alpha(c). The network is scale free, i.e., the nodal degree distribution has a power law decay for alpha> or = alpha(c).