"'Structural balance theory applies in situations where there's a lot of social stress -- gossip disparaging to one person, countries feeling pressure, companies competing -- where we need to make alliances and find our friends and enemies,' said Cornell Ph.D. candidate Seth Marvel, lead author of a paper explaining the research published during the week of Jan. 3, 2011, in the online edition of the Proceedings of the National Academy of Sciences with co-authors Jon Kleinberg, the Tisch University Professor of Computer Science, Robert Kleinberg, assistant professor of computer science, and Steven Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics.
People may form alliances based on shared values, or may consider the social consequences of allying with a particular person, Marvel said. 'The model shows that the latter is sufficient to divide a group into two factions,' he said."
An interesting example of how social groups can break in to factions. It is hard though to see how this could be tracked in a real web based social network, though I have seen it happen.
Likely patterns of defriending Facebook or unfollowing on Twitter could indicate a process like this is happening. But this model assumes your social graph is the real relationships between people and not an artifact of using the social network.
For example in Second Life you could follow group memberships to see if this is happening. But a limitation on the number of groups any avatar can have could make it difficult to know if fractions are forming or not. In Second Life it would not be until two or mire united SIMs that form an Island break off in to islands that you can be sure a fraction split has happened.