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

Christos Giatsidis (1) , Dimitrios M. Thilikos (2, 3) , Michalis Vazirgiannis (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 Department of Mathematics [Athens]
3 ALGCO - Algorithmes, Graphes et Combinatoire

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 between its nodes. A variety of measures are proposed to evaluate different quality aspects 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 commu- nity 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 essen- tially 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 synthetic and real-world graphs such as Wikipedia, DBLP, and ArXiv and report interesting results at the graph as well at the node level.

Mots clés: Graph mining; Community evaluation metrics; Degeneracy; Directed cores

Domaines: Web; Recherche d'information [cs.IR]; Réseaux et télécommunications [cs.NI]; Mathématique discrète [cs.DM]

Christos Giatsidis, Dimitrios M. Thilikos, Michalis Vazirgiannis. D-cores: measuring collaboration of directed graphs based on degeneracy. Knowledge and Information Systems (KAIS), 2012, 35 (2), pp.311 - 343. ⟨10.1007/s10115-012-0539-0⟩. ⟨lirmm-00846768⟩