Dynamics of k-core percolation in a random graph

Mami Iwata, Shin-ichi Sasa

Published 2008-08-06, updated 2009-01-22Version 2

We study the edge deletion process of random graphs near a k-core percolation point. We find that the time-dependent number of edges in the process exhibits critically divergent fluctuations. We first show theoretically that the k-core percolation point is exactly given as the saddle-node bifurcation point in a dynamical system. We then determine all the exponents for the divergence based on a universal description of fluctuations near the saddle-node bifurcation.