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Author  |
Newman, M.E.J. |
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Title |
Mixing patterns in networks |
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Journal Article |
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Year |
2003 |
Publication |
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics |
Abbreviated Journal |
Phys Rev E Stat Nonlin Soft Matter Phys |
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Volume |
67 |
Issue |
2 Pt 2 |
Pages |
026126 |
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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. |
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Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA |
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English |
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ISSN |
1539-3755 |
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Notes |
PMID:12636767 |
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Call Number |
Equine Behaviour @ team @ |
Serial |
5215 |
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Author |
Newman, M.E.J. |
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Title |
The Structure and Function of Complex Networks |
Type |
Journal Article |
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Year |
2003 |
Publication |
SIAM Review |
Abbreviated Journal |
SIAM Rev. |
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Volume |
45 |
Issue |
2 |
Pages |
167-256 |
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Keywords |
networks; graph theory; complex systems; computer networks; social networks; random graphs; percolation theory |
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Abstract |
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks. |
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Siam |
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Call Number |
Equine Behaviour @ team @ |
Serial |
5214 |
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