Vertex-degree sequences in complex networks: New characteristics and applications

摘要

Many complex networks exhibit a scale-free vertex-degree distribution in a power-law form ck(-gamma), where k is the vertex-degree variable and c and gamma are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to explore and analyze their vertex-degree sequences. We had shown before that, for a scale-free network of size N, if its vertex-degree sequence is k(1) < k(2) < ... < k(l), where {k(1), k(2), ..., k(l)} is the set of all unequal vertex degrees in the network, and if its power exponent satisfies gamma > 1, then the length I of the vertex-degree sequence is of order log N. In the present paper, we further study complex networks with an exponential vertex-degree distribution and prove that the same conclusion also holds. In addition, we verify our claim by showing many real-world examples. We finally discuss some applications of the new finding in various fields of science and technology. (C) 2015 Elsevier B.V. All rights reserved.