  In many network applications nodes are stable provided they have at least k
neighbors, and a network of k-stable nodes is called a k-core. The
vulnerability to random attack is characterized by the size of culling
avalanches which occur after a randomly chosen k-core node is removed.
Simulations of lattices in two, three and four dimensions, as well as small
world networks, indicate that power-law avalanches occur in first order k-core
systems, while truncated avalanches are characteristic of second order cases.
