On the inadequacy of nominal assortativity for assessing homophily in networks

TL;DR

This paper reveals the limitations of nominal assortativity in accurately measuring homophily in networks with unequal group sizes and asymmetric interactions, proposing adjustments and new methods for better analysis.

Contribution

The authors identify shortcomings of nominal assortativity and introduce adjusted measures and analytical methods to better capture mixing patterns in complex networks.

Findings

Nominal assortativity fails with unequal group sizes.

Adjusted assortativity recovers expected mixing patterns.

New analytical method uncovers hidden mixing in real networks.

Abstract

Nominal assortativity (or discrete assortativity) is widely used to characterize group mixing patterns and homophily in networks, enabling researchers to analyze how groups interact with one another. Here we demonstrate that the measure presents severe shortcomings when applied to networks with unequal group sizes and asymmetric mixing. We characterize these shortcomings analytically and use synthetic and empirical networks to show that nominal assortativity fails to account for group imbalance and asymmetric group interactions, thereby producing an inaccurate characterization of mixing patterns. We propose adjusted nominal assortativity and show that this adjustment recovers the expected assortativity in networks with various level of mixing. Furthermore, we propose an analytical method to assess asymmetric mixing by estimating the tendency of inter- and intra-group connectivities. Finally, we discuss how this approach enables uncovering hidden mixing patterns in real-world networks.