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Long-range assortativity

Pablo I. Fierens*

Leandro Chaves Rêgo†

  • Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Bloco 910, Campus do Pici, Fortaleza, CEP: 60440-554 Ceará, Brazil and Programa de Pós-Graduação em Engenharia de Produção, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego, 1235, Cidade Universitária, Recife, CEP: 50.740-550 Pernambuco, Brazil

  • *Contact author: pfierens@itba.edu.ar
  • †Contact author: leandro@dema.ufc.br
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Phys. Rev. E 114, 054308 – Published 6 November, 2026

DOI: https://doi.org/10.1103/8sqq-6mym

Abstract

The study of homophily in networks usually involves investigating whether nodes have a tendency to make more direct connections with similar nodes than what would happen in a random network. However, the study of homophily between nodes that are not directly connected is also of interest. Remarkably, even though there is a vast literature on long-range degree homophily, just a few works have investigated other properties, but only considering linear relations among scalar attributes of the nodes. In this work, we put forth a measure of long-range homophily that can deal with nonscalar and noncategorical node attributes and enables the analysis of nonlinear relations. This measure can be viewed as an extension of the usual Newman assortativity, as it is based on the comparison of the similarity of node attributes in a given network to that expected in a nonhomophilic network where connections are randomly made while preserving node degrees. We show the application of the measure in a few real-world examples, some of which exhibit a nontrivial long-range homophilic behavior.

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Phys. Rev. E 114, 054308– Published 6 November, 2026
  • Received 26 February 2026
  • Accepted 22 October 2026
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