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.

翻译：名义同配性（或离散同配性）被广泛用于表征网络中的群体混合模式与同质性，使研究者能够分析群体间的相互作用方式。本文证明，当应用于群体规模不均等且混合不对称的网络时，该测度存在严重缺陷。我们通过解析方法刻画了这些缺陷，并利用合成网络与实证网络表明，名义同配性未能考虑群体失衡与群体间不对称相互作用，从而得出不准确的混合模式描述。我们提出调整后的名义同配性，并证明该调整能恢复不同混合程度网络中的预期同配性。此外，我们还提出一种通过估计组间与组内连接倾向来评估不对称混合的解析方法。最后，我们讨论该方法如何揭示真实网络中隐藏的混合模式。