A differential evolution box-covering algorithm for fractal dimension on complex networks

The fractality property are discovered on complex networks through renormalization procedure, which is implemented by box-covering method. The unsolved problem of box-covering method is finding the minimum number of boxes to cover the whole network. Here, we introduce a differential evolution box-covering algorithm based on greedy graph coloring approach. We apply our algorithm on some benchmark networks with different structures, such as a E.coli metabolic network, which has low clustering coefficient and high modularity; a Clustered scale-free network, which has high clustering coefficient and low modularity; and some community networks (the Politics books network, the Dolphins network, and the American football games network), which have high clustering coefficient. Experimental results show that our algorithm can get better results than state of art algorithms in most cases, especially has significant improvement in clustered community networks.