The Case for Kendall's Assortativity

摘要

Since the seminal work of Litvak and van der Hofstad [12], 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 unassorta-tive. Usage of Spearman's p, or even Kendall's r was suggested as a replacement [6], but the treatment of ties was problematic for both measures. In this paper we first argue analytically that the tie-aware version of r solves the problems observed in [6], 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 r 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 r can be a practical, principled alternative.