Assortative mixing

Assortative/disassortative mixing in graph theory is the extent to which nodes connect preferentially to other nodes with similar characteristics.

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For example, in a sexual network individuals tend to choose partners who are similar in age, race, sexual orientation, marital status, socioeconomic status, religion, or locale. These characteristics can have influences on epidemic spread, mainly HIV. Assortative mixing is involved in the phenomenon of "super-spreaders" of sexually transmitted diseases; a small fraction of the population that is very sexually promiscuous can act as a conduit for the disease to spread within the group over wide distances, and from that group to other social groups. An example of this phenomenon is the population subgroup formed by truck drivers and prostitutes.

Assortative mixing by degree refers to graphs in which high degree nodes connect frequently to other high degree nodes. A formal definition is given in M.E.J. Newman Assortative Mixing in Networks, Phys. Rev. Lett. 89, 208701 (2002). Interestingly, all simple connected graphs have negative assortativity.

See also

• Homophily

Bibliography

• Catanzaro, Michele; Caldarelli, Guido; Pietronero, Luciano. Social network growth with assortative mixing. Physica A 338, 119 (2004).
• M.E.J. Newman Assortative Mixing in Networks, Phys. Rev. Lett. 89, 208701 (2002)
• Ganesh Bagler and Somdatta Sinha, Assortative mixing in Protein Contact Networks and protein folding kinetics, Bioinformatics, 23, 1760--1767 (2007)