Patterns of Link Reciprocity in Directed Networks

Diego Garlaschelli and Maria I. Loffredo
Phys. Rev. Lett. 93, 268701 – Published 20 December 2004

Abstract

We address the problem of link reciprocity, the nonrandom presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.

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  • Received 23 April 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.268701

©2004 American Physical Society

Authors & Affiliations

Diego Garlaschelli1,2 and Maria I. Loffredo2,3

  • 1Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 Siena, Italy
  • 2INFM UdR Siena, Via Roma 56, 53100 Siena, Italy
  • 3Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Pian dei Mantellini 44, 53100 Siena, Italy

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Issue

Vol. 93, Iss. 26 — 31 December 2004

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