On the relationship between set-based and network-based measures of gender homophily in scholarly publications

TL;DR

This paper compares set-based and network-based measures of gender homophily in scholarly co-authorship, demonstrating their equivalence under certain conditions and clarifying how to interpret these metrics.

Contribution

It establishes the theoretical equivalence between set-based and network-based gender homophily measures in co-authorship networks.

Findings

Set-based and network-based measures are mathematically equivalent with proper weighting.

The paper clarifies the interpretation of gender homophily metrics in scholarly networks.

Provides a framework for consistent measurement of gender homophily across different methods.

Abstract

There is an increased interest in the scientific community in the problem of measuring gender homophily in co-authorship on scholarly publications (Eisen, 2016). For a given set of publications and co-authorships, we assume that author identities have not been disambiguated in that we do not know when one person is an author on more than one paper. In this case, one way to think about measuring gender homophily is to consider all observed co-authorship pairs and obtain a set-based gender homophily coefficient (e.g., Bergstrom et al., 2016). Another way is to consider papers as observed disjoint networks of co-authors and use a network-based assortativity coefficient (e.g., Newman, 2003). In this note, we review both metrics and show that the gender homophily set-based index is equivalent to the gender assortativity network-based coefficient with properly weighted edges.