Characterization of Graphs Using Degree Cores

Abstract

Generative models are often used in modeling real world graphs such as the Web graph in order to better understand the processes through which these graphs are formed. In order to determine if a graph might have been generated by a given model one must compare the features of that graph with those generated by the model. We introduce the concept of a hierarchical degree core tree as a novel way of summarizing the structure of massive graphs. The degree core of level kis the unique subgraph of minimal degree k. Hierarchical degree core trees are representations of the subgraph relationships between the components of the degree core of the graph, ranging over all possible values of k. We extract features related to the graph's local structure from these hierarchical trees. Using these features, we compare four real world graphs (a web graph, a patent citation graph, a co-authorship graph and an email graph) against a number of generative models.