Relating Network Structure to Di¤usion Properties through Stochastic Dominance by Matthew O. Jackson and Brian W. Rogers Draft: December 15, 2006 Forthcoming in Advances in Economic Theoryy

We examine the spread of a disease or behavior through a social network. In particular, we analyze how infection rates depend on the distribution of degrees (numbers of links) among the nodes in the network. We introduce new techniques using …rstand second order stochastic dominance relationships of the degree distribution in order to compare infection rates across di¤erent social networks. JEL Classi…cation Numbers: D85, A14, C71, C72. Keywords: Di¤usion, Infection, SIS, Networks, Social Networks Jackson: Department of Economics, Stanford Unversity, Stanford, California 94305, USA; Rogers: Managerial Economics and Decision Sciences (MEDS), Kellogg School of Management, 2001 Sheridan Rd., Jacobs Center 5th Floor, Evanston, IL 60208-2009, USA; emails: [email protected] and [email protected]; web sites: http://www.stanford.edu/ jacksonm and www.kellogg.northwestern.edu/faculty/rogers_b/personal/. We gratefully acknowledge …nancial support under NSF grant SES-0316493, the Lee Center for Advanced Networking, and a SISL/IST fellowship. We thank Dunia Lopez-Pintado for helpful comments and conversations. yThis paper appeared previously as part of “Search vs Random Attachment and the Formation of Large Networks”by the same authors. That paper was split, with part becoming this paper and the other part being Jackson and Rogers [4]. 1