Relating Network Structure to Diffusion Properties through Stochastic Dominance by Matthew O. Jackson and Brian W. Rogers * Revised: December 15, 2006 Forthcoming, Advances in Theoretical Economics † Abstract We examine the spread of a disease or behavior through a social net- work. In particular, we analyze how infection rates depend on the dis- tribution of degrees (numbers of links) among the nodes in the network. We introduce new techniques using first- and second order stochastic dominance relationships of the degree distribution in order to compare infection rates across different social networks. JEL Classification Numbers: D85, A14, C71, C72. Keywords: Diffusion, Infection, SIS, Networks, Social Networks * Jackson: Department of Economics, Stanford Unversity, Stanford, Cal- ifornia 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: jacksonm@stanford.edu and b- rogers@kellogg.northwestern.edu; web sites: http://www.stanford.edu/∼jacksonm and www.kellogg.northwestern.edu/faculty/rogers b/personal/. We gratefully acknowledge financial 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. † This paper appeared previously as part of “Search vs Random Attachment and the For- mation 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