Assortative mixing

In the study of complex networks, the term assortative mixing refers to a bias in favor of connections between network nodes with similar characteristics. [cite journal
author = M. E. J. Newman
year = 2003
title = Mixing patterns in networks
journal = Physical Review E
volume = 67
pages = 026126
url = http://arxiv.org/abs/cond-mat/0209450] In the specific case of social networks, assortative mixing is also known as homophily. The rarer disassortative mixing is a bias in favor of connections between dissimilar nodes.

In social networks, for example, individuals commonly choose to associate with others of similar age, nationality, location, race, income, educational level, religion, or language as themselves. [cite journal
author = M. McPherson, L. Smith-Lovin, and J. M. Cook
year = 2001
title = Birds of a feather: Homophily in social networks
journal = Annual Review of Sociology
volume = 27
pages = 415-444
doi = 10.1146/annurev.soc.27.1.415] In networks of sexual contact, the same biases are observed, but mixing is also disassortative by gender – most partnerships are between individuals of opposite sex.

Assortative mixing can have effects, for example, on the spread of disease: if individuals have contact primarily with other members of the same population groups, then diseases will spread primarily within those groups. Many diseases are indeed known to have differing prevalence in different population groups, although other social and behavioral factors affect disease prevalence as well, including variations in quality of health care and differing social norms.

Assortative mixing is also observed in other (non-social) types of networks, including biochemical networks in the cell, [cite journal
author = S. Maslov and K. Sneppen
year = 2002
title = Specificity and stability in topology of protein networks
journal = Science
volume = 296
pages = 910-913
url = http://arxiv.org/abs/cond-mat/0205380] computer and information networks, [cite journal
author = R. Pastor-Satorras, A. Vázquez, and A. Vespignani
year = 2001
title = Dynamical and correlation properties of the Internet
journal = Physical Review Letters
volume = 87
pages = 258701
url = http://arxiv.org/abs/cond-mat/0105161] and others.

Of particular interest is the phenomenon of assortative mixing by degree, meaning the tendency of nodes with high degree to connect to others with high degree, and similarly for low degree. Because degree is itself a topological property of networks, this type of assortative mixing gives rise to more complex structural effects than other types. Empirically it has been observed that most social networks mix assortatively by degree, but most networks of other types mix disassortatively, [cite journal
author = M. E. J. Newman
year = 2002
title = Assortative mixing in networks
journal = Physical Review Letters
volume = 89
pages = 208701
url = http://arxiv.org/abs/cond-mat/0205405] although there are exceptions. [cite journal
author = G. Bagler and S. Sinha
year = 2007
title = Assortative mixing in protein contact networks and protein folding kinetics
journal = Bioinformatics
volume = 23
pages = 1760
url = http://arxiv.org/abs/0711.2723]

ee also

*Complex network
*Graph theory
*Homophily

References