Network Structure and the Speed of Learning: Measuring Homophily Based on its Consequences

18 Pages Posted: 18 Mar 2011  

Benjamin Golub

Stanford Graduate School of Business

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Date Written: March 11, 2011

Abstract

Homophily is the tendency of people to associate relatively more with those who are similar to them than with those who are not. In Golub and Jackson (2010a), we introduced degree-weighted homophily (DWH), a new measure of this phenomenon, and showed that it gives a lower bound on the time it takes for a certain natural best-reply or learning process operating in a social network to converge. Here we show that, in important settings, the DWH convergence bound does substantially better than previous bounds based on the Cheeger inequality. We also develop a new complementary upper bound on convergence time, tightening the relationship between DWH and updating processes on networks. In doing so, we suggest that DWH is a natural homophily measure because it tightly tracks a key consequence of homophily -- namely, slowdowns in updating processes.

Keywords: networks, learning, diffusion, homophily, friendships, social networks, random graphs, convergence, speed of learning, convergence rate

JEL Classification: D83, D85, I21, J15, Z13

Suggested Citation

Golub, Benjamin and Jackson, Matthew O., Network Structure and the Speed of Learning: Measuring Homophily Based on its Consequences (March 11, 2011). Available at SSRN: https://ssrn.com/abstract=1784542 or http://dx.doi.org/10.2139/ssrn.1784542

Benjamin Golub

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

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