Improved Semi-Deterministic Scheme to Generate Limited Scale-Free Networks

In this paper, we consider the problem of constructing scale-free networks in a semi-deterministic manner. Scale-free networks have several favorable properties as the topology of interconnection networks such as the short diameter and the quick message propagation. The proposed algorithm is an extension of the Bulut's algorithm for constructing scale-free networks with designated minimum degree k and maximum degree m, such that: 1) it determines the ideal number of edges derived from the ideal degree distribution, and 2) after connecting each new node to k existing nodes as in the Bulut's algorithm, it adjusts the number of edges to the ideal value by conducting add/removal of edges. We prove that such an adjustment is always possible if the number of nodes in the network exceeds m2/k+m.