Analysis of Average Communicability in Complex Networks
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.
KeywordsGenetic algorithm Complex networks Communicability Eigenvalue and eigenvector Rewiring
- 1.Scott, J.: Social Network Analysis. Sage, New York (2012)Google Scholar
- 13.Wilkov, R.S.: Design of computer networks based on a new reliability measure. In: Fox, I. (ed.) Proceedings of the Symposium on Computer-Communications Networks and Teletraffic, pp. 371–384. Polytechnic Institute of Brooklyn, Brooklyn (1972)Google Scholar
- 23.Costa, L., Rodrigues, F.: What is there between any two nodes in a complex network? Arxiv.org (2008). http://arxiv.org/abs/0801.4068. Accessed 16 Mar 2016
- 24.Amaral, L., Ottino, J.: Complex networks. Eur. Phys. J. B Condens. Matter 38(2), 147–162 (2004)Google Scholar
- 29.Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, London (2016). http://www.cambridge.org/ar/academic/subjects/sociology/sociology-general-interest/social-network-analysis-methods-and-applicationsMATHGoogle Scholar