A new small-world network created by Cellular Automata

In this paper, we generate small-world networks by the Cellular Automaton based on starting with one-dimensional regular networks. Besides the common properties of small world networks with small average shortest path length and large clustering coefficient, the small-world networks generated in this way have other properties: (i) The edges which are cut in the regular network can be controlled that whether the edges are reconnected or not, and (ii) the number of the edges of the small-world network model equals the number of the edges of the original regular network. In other words, the average degree of the small world network model equals to the average degree of the original regular network. (C) 2016 Elsevier B.V. All rights reserved.