Local 2-connected bow-tie structure of the Web and of social networks

Abstract

The explosive growth of the Web and of social networks motivates the need for analyzing the macroscopic structure of their underlying graphs. Although the characterization of the structure of a graph with respect to its pairwise connectivity has been known for over 15 years, just one subsequent study analyzed the world inside the giant strongly connected component, where it has been shown that the largest strongly connected component has its own microscopic bow-tie structure defined with respect to pairwise 2-connectivity among its vertices. In this paper, we introduce the local microscopic bow-tie structure of the largest strongly connected component, demonstrating its self-similarity property. Our experiments, conducted on the several Web graphs and social networks demonstrate clear structural differences between considered Web and social networks.