RANDOM EVOLVING NETWORKS UNDER THE DIAMETER AND AVERAGE CONNECTIVITY CONSTRAINT

摘要

In this paper, the growth of random networks under the constraint that the diameter, defined as the average shortest path length between all nodes, and the average connectivity k remains approximately constant is studied. We show that if the network maintains the form of its degree distribution and the maximal degree k_c is a N-dependent cutoff function k_c (N) < N, then the degree distribution would be approximately power-law with an exponent between 2 and 3. The distribution exponent has little relationship with the average degree . The diameter constraint can be interpreted as an environmental selection pressure, which could explain the scale-free nature of networks.