arXiv:cond-mat/0205405v1 [cond-mat.dis-nn] 20 May 2002 Assortative mixing in networks M. E. J. Newman Department of Physics, University of Michigan, Ann Arbor, MI 48109–1120 and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 A network is said...
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arXiv:cond-mat/0205405v1 [cond-mat.dis-nn] 20 May 2002 Assortative mixing in networks M. E. J. Newman Department of Physics, University of Michigan, Ann Arbor, MI 48109–1120 and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 A network is said to show assortative mixing if the nodes in the network that have many connec- tions tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal. Many systems take the form of networks—sets of ver- tices joined together by edges—including social networks, com
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