Analysis of Average Communicability in Complex Networks

摘要

The average communicability of a complex network is an important measure of the efficiency of information exchange in the entire network. The optimization of average communicability is a significant problem in network design for various applications in science and engineering. Since the search for the topology that achieves the highest average communicability is a very difficult problem due to the enormous size of the solution space, the genetic algorithm is a good choice for search. From numerical simulation, we discover a positive correlation between the variance of the degree distribution with the average communicability of the network. This correlation is then proven mathematically, with applications to the comparison for the average communicability of two networks with the same number of nodes and links using the largest eigenvalues of their adjacency matrices.