Measuring Similarity Between Mathematics Research and Its References Using Bibliographic Coupling

Abstract

1 Introduction Originally formalized in the 1960s [1], Bibliographic Coupling is a metric used to determine the similarity between two pieces of research by measuring the amount of overlap in their references. Applied to a research publication and its references this metric can provide insight into how similar the research is to the work on which it built, and vice versa. 2 Objective The primary objective of this research is to develop a deeper understanding of how mathematics research develops overtime, specifically how similar publications are to research which proceeded it. This research uses multiple bibliographic coupling metrics as a measure of this similarity be- tween mathematics research publications and the research they reference, as well as determining if the style of research or a high number of citations received by a reference impacts it. 3 Methods This study uses Web of Science citation and reference data from 1900-2017 as its dataset for bibliographic coupling analysis. This overlap is measured in three ways. The first is basic Bibliometric Coupling Strength, defined set-theoretically by Rousseau, Leo, & Guns [2] as |A ̄ ∩ B ̄| where A and B are publications and A ̄ and B ̄ are their reference sets. The other two metrics are both proportional, the first being a measure of the proportion of overlap in the citing publication and the second the proportion of overlap in the cited publication. More formally, if publication B cites publication A then these two measures are defined as |A ̄ ∩ B ̄|/|A ̄| and |A ̄ ∩ B ̄|/(|B ̄ − A|). These measure are used instead of the single relative coupling strength introduced by Sen & Gan [3] as the analysis aims to measure similarity in both directions, how similar the publication is to publications it references as well as how similar the publication referenced is to the publications citing it. The analysis uses Web of Science category designations to determine if the amount of bibliographic coupling differs in Mathematics, Applied Mathematics, and Mathematics, Interdisciplinary Applications categorized publications in-toto, as well as overtime. A secondary analysis is run focused on highly cited research to see if more highly cited publications have a different similarity relationship with the research citing it. References [1] M. M. Kessler. Bibliographic coupling between scientific papers. American Documentation, 14(1):10–25, 1963. [2] Ronald Rousseau, Egghe Leo, and Raf Guns. Publication and Citation Anal- ysis. Chandos Publishing, January 2018. [3] Subir K SEN and Shymalkg K Gan. A mathematical extension of the idea of bibliographic coupling and its applications. Annals of Library Science and Documentation, 30(2):78–82, 1983.