Graph entropy rate minimization and the compressibility of undirected binary graphs

With the increasing popularity of complex network analysis through the use of graphs, a method for computing graph entropy has become important for a better understanding of a network´s structure and for compressing large complex networks. There have been many different definitions of graph entropy in the literature which incorporate random walks, degree distribution, and node centrality. However, these definitions are either computationally complex or seemingly ad hoc. In this paper we propose a new approach for computing graph entropy with the intention of quantifying the compressibility of a graph. We demonstrate the effectiveness of our measure by identifying the lower bound of the entropy rate for scale-free, lattice, star, random, and real-world networks.