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.