Social networks that balance themselves

4 May 2012
16:30
Professor Steven Strogatz
Abstract
<p><span>&nbsp;</span><span>Consider a fully-connected&nbsp;social&nbsp;network of people, companies,</span><br /><span>or&nbsp;countries, modeled as an undirected complete graph with real numbers on</span><br /><span>its&nbsp;edges. Positive edges link friends; negative edges link enemies.</span><br /><span>I'll&nbsp;discuss two simple models of how the edge weights of such&nbsp;networks</span><br /><span>might&nbsp;evolve over time, as they seek a balanced state in which "the enemy of</span><br /><span>my&nbsp;enemy is my friend." The mathematical techniques involve elementary</span><br /><span>ideas&nbsp;from linear algebra, random graphs, statistical physics, and</span><br /><span>differential&nbsp;equations. Some motivating examples from international</span><br /><span>relations and&nbsp;social&nbsp;psychology will also be discussed.&nbsp;This is joint work</span><br /><span>with Seth Marvel, Jon&nbsp;Kleinberg, and Bobby Kleinberg.</span><span>&nbsp;</span></p>