《Assortative mixing in networks》.pdfVIP

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 2 A network is said to show assortative mixing if the nodes in the network that have many connec- 0 tions tend to be connected to other nodes with many connections. We define a measure of assortative 0 mixing for networks and use it to show that social networks are often assortatively mixed, but that 2 technological and biological networks tend to be disassortative. We propose a model of an assortative y network, which we study both analytically and numerically. Within the framework of this model we a find that assortative networks tend to percolate more easily than their disassortative counterparts M and that they are also more robust to vertex removal. 0 2 Many systems take the form of networks—sets of ver- rather than just p k . In this paper, we will usually be tices joined together by edges—including social networks, interested not in the total degree of such a vertex, but in ] computer networks, and biological networks [1, 2, 3]. A the remaining degree—the number of edges leaving the n n variety of models of networks have been proposed and vertex other than the one we arrived along. This number - studied in the physics literature, many of which have is one less than the total degree and hence is distributed s been successful at reproducing features of networks in the in proportion to (k + 1)p k+1 . The correctly normalized i d real world