Similarities Between Biological and Social Networks in Their Structural Organization

Abstract

A branching tree is a tree that is generated through a multiplicative branching process starting from a root. A critical branching tree is a branching tree in which the mean branching number of each node is 1, so that the number of offspring neither decays to zero nor flourishes as the branching process goes on. Moreover, a scale-free branching tree is a branching tree in which the number of offspring is heterogeneous, and its distribution follows a power law. Here we examine three structures, two from biology (a phylogenetic tree and the skeletons of a yeast protein interaction network) and one from social science (a coauthorship network), and find that all these structures are scale-free critical branching trees. This suggests that evolutionary processes in such systems take place in bursts and in a self-organized manner.