D-cores: Measuring collaboration of directed graphs based on degeneracy

Community detection and evaluation is an important task in graph mining. In many cases, a community is defined as a subgraph characterized by dense connections or interactions among its nodes. A large variety of measures have been proposed to evaluate the quality of such communities - in most cases ignoring the directed nature of edges. In this paper, we introduce novel metrics for evaluating the collaborative nature of directed graphs - a property not captured by the single node metrics or by other established community evaluation metrics. In order to accomplish this objective, we capitalize on the concept of graph degeneracy and define a novel D-core framework, extending the classic graph-theoretic notion of k-cores for undirected graphs to directed ones. Based on the D-core, which essentially can be seen as a measure of the robustness of a community under degeneracy, we devise a wealth of novel metrics used to evaluate graph collaboration features of directed graphs. We applied the D-core approach on large real-world graphs such as Wikipedia and DBLP and report interesting results at the graph as well at node level.