Via Technology Review:

Why do networks die?

‘”David Garcia and pals at the Swiss Federal Institute of Technology in Zurich, give us an answer of sorts. These guys have carried out a digital “autopsy” on Friendster using data collected about the network before it gave up the ghost.

They say that when the costs–the time and effort–associated with being a member of a social network outweigh the benefits, then the conditions are ripe for a general exodus. The thinking is that if one person leaves, then his or her friends become more likely to leave as well and this can cascade through the network causing a collapse in membership.

But Garcia and co point out that the topology of the network provides some resilience against this. This resilience is determined by the number of friends that individual users have.

So if a big fraction of people on a network have only two friends, it is highly vulnerable to collapse. That’s because when a single person exits, it leaves somebody with only one friend. This person is then likely exit leaving another with only one friend and so on. The result is a cascade of exists that sweeps through the network.

However, if a large fraction of people on the network have, say, ten friends, the loss of one friend is much less likely to trigger a cascade.

So the fraction of the network with a certain number of friends is a crucial indicator of the network’s vulnerability to cascades.

Garcia and co examined this fraction–they call it k-core distribution–for networks such as Friendster, Myspace and Facebook and the results are telling. “We ?nd that the di?erent online communities have di?erent k-core distributions,” they say.

Of course, communities that are vulnerable in this way don’t automatically fail. Before that can happen, the cost-to-benefit ratio must drop to a level that makes individuals likely to leave. It is the combination of a low cost-to-benefit ratio and a vulnerable k-core distribution that is fatal for social networks.”