Co-authorship, rational Erdős numbers, and resistance distances in graphs

Alexandru T. Balaban () and Douglas J. Klein
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Alexandru T. Balaban: Texas A&M University
Douglas J. Klein: Texas A&M University

Scientometrics, 2002, vol. 55, issue 1, No 3, 59-70

Abstract: Abstract The Erdős number (EN) for collaborative papers among mathematicians was defined as indicating the topological distance in the graph depicting the co-authorship relations, i. e., EN = 1 for all co-authors of Paul Erdős; EN = 2 for their co-authors who did not publish jointly with Erdős; etc. A refinement of this notion uses resistance distances leading to rational Erdős numbers (REN), which (as indicated by their name) are rational numbers. For acyclic graphs, EN = REN, but for graphs with circuits these numbers differ. Further refinements are possible using weighted edges in the co-authorship graph according to the number of jointly authored papers.

Date: 2002
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DOI: 10.1023/A:1016098803527

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