2014/04/09 by Bhan, Ashish, Ray, Animesh
#FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Molecular Networks (q-bio.MN) #Physics and Society (physics.soc-ph) #Quantitative Methods (q-bio.QM) #Social and Information Networks (cs.SI)
paper · doi:10.48550/arxiv.1404.2374
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two simple graph parameters--the logarithm of the average cluster size and logarithm of the ratio of the edges of the graph to the theoretically maximum number of edges for that graph--that holds for all growing power law graphs. The result establishes a novel property of evolving power-law networks in the asymptotic limit of network size. Numerical simulations as well as fitting to real-world citation co-authorship networks demonstrate that the result holds for networks of finite sizes, and provides a convenient measure of the extent to which an evolving family of networks belongs to the same power-law class.