K-cores in Time-evolving Co-authorship Graphs : A Case Study on DBLP

A k-core of a graph is a maximal subgraph whose nodes have degree at least k in that subgraph. A node can appear in multiple k-cores. The core number of a node is the largest k among its k-cores. The degeneracy of a graph is the maximum core number among its nodes. Applications of k-cores and core numbers are numerous, including community detection and modeling spread on a network. We present a study of k-cores on the DBLP co-authorship graphs over 30 years starting at 1980. Our key observations are as follows. (1) Over time, collaborations, in terms of co-authorships, have increased dramatically. From 1980 to 2010, the number of papers has increased 38 times and the number of authors has increased 64.6 times, but the number of co-authorship relations has increased 153.7 times and the degeneracy of the co-authorship graph has increased 7.1 times. Specifically, the 1980 graph has a degeneracy of 11 (which means that it has one maximal subgraph where the authors have at least 11 co-authors), while the 2010 graph has a degeneracy of 78 (which means that it has one maximal subgraph where the authors have at least 78 co-authors). (2) The k-cores with the largest k values in the DBLP co-authorship graphs are often cliques (representing a specific publication). (3) We observe two types of authors. The first type consists of authors with large core numbers. They have relatively few papers but many co-authors per paper. The second type consists of high-degree authors who have more papers but few co-authors per paper.