# On the inadequacy of nominal assortativity for assessing homophily in networks

arXiv: https://arxiv.org/abs/2211.10245 · HTML: https://mlsanity.com/paper/2211.10245/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2022.

## Built on by (most cited first, 3 of 3)

- [Y Social: an LLM-powered Social Media Digital Twin](https://mlsanity.com/paper/2408.00818/) (2024)
- [Revisiting Graph Homophily Measures](https://mlsanity.com/paper/2412.09663/) (2024)
- [The Confusion is Real: GRAPHIC -- A Network Science Approach to Confusion Matrices in Deep Learning](https://mlsanity.com/paper/2602.19770/) (2026)

## Abstract (arXiv)

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.