Mixing patterns in networks

M. E. J. Newman
Phys. Rev. E 67, 026126 – Published 27 February 2003
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Abstract

We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.

  • Received 26 September 2002

DOI:https://doi.org/10.1103/PhysRevE.67.026126

©2003 American Physical Society

Authors & Affiliations

M. E. J. Newman

  • Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120
  • Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501

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Vol. 67, Iss. 2 — February 2003

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