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

http://dueallamenouno.comunita.unita.it/2012/02/04/i-nemici-dei-miei-nemici/