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The Case for Kendall’s Assortativity

  • Paolo Boldi
  • Sebastiano VignaEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 882)

Abstract

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 unassortative. Usage of Spearman’s \(\rho \), or even Kendall’s \(\tau \) 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 \(\tau \) 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 \(\tau \) 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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly

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