New Method for Estimating the Tree-Likeness of Graphs and Its Application for Tracing the Robustness of Complex Networks

This article presents the original metric of the minimum cyclic reachability distribution providing the foundation for assessing the topological tree-likeness of the large-scale sparse graphs. The conceptual sense enclosed in the proposed metric lies in interpreting the similarity of the analyzed graph to a tree based on the position of each its vertex in the structure of the graph's paths. With a view to demonstrate the theoretical value of the introduced metric, the article deals with its applying for discovering the dependence of the topological tree-likeness of the random graphs on the parameters of their generation. Finally, the article illustrates the usage of the designed metric for estimating the robustness of the complex networks and pursues the experimental analysis of the graph model constructed for the real-world power transmission network.