Dynamics of k-core percolation in a random graph

Details Dynamics of k-core percolation in a random graph Dynamics of k-core percolation in a random graph

2008-08-06

arxiv.org/abs/0808.0766v2

J. Phys. A: Math. Theor. 42 (2009) 075005

Physics

Condensed Matter

Statistical Mechanics

16 pages, 4 figures

Scientific paper

10.1088/1751-8113/42/7/075005

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.

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