The Case for Kendall’s Assortativity
Since the seminal work of Litvak and van der Hofstad , it has been known that Newman’s assortativity [14, 15], being based on Pearson’s correlation, is subject to a pernicious size effect which makes large networks with heavy-tailed degree distributions always unassortative. Usage of Spearman’s \(\rho \), or even Kendall’s \(\tau \) was suggested as a replacement , but the treatment of ties was problematic for both measures. In this paper we first argue analytically that the tie-aware version of \(\tau \) solves the problems observed in , and we show that Newman’s assortativity is heavily influenced by tightly knit communities. Then, we perform for the first time a set of large-scale computational experiments on a variety of networks, comparing assortativity based on Kendall’s \(\tau \) and assortativity based on Pearson’s correlation, showing that the pernicious effect of size is indeed very strong on real-world large networks, whereas the tie-aware Kendall’s \(\tau \) can be a practical, principled alternative.
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