Statistical analyses of cyclic and starlike hierarchical dominances in directed graphs.

Abstract

The mathematical framework of matrix decomposition implies the possibility to perform statistical analyses of directed graphs focused on the distributions of the independent cyclic and starlike hierarchical components. In this approach the weighted directed graphs with n nodes are built up as a linear combination of starlike graphs with n outgoing edges and a suitable set of three-edge cyclic subgraphs. The applicability of this approach is illustrated by quantifying several general features: e.g., ratio of the cyclic and hierarchical components and asymmetry in the hierarchical components. The applicability of these methods is illustrated by considering the averages over random directed graphs and comparing these values with those characterizing simple directed graphs of tournaments.