Dynamics of k-core percolation in a random graph

Abstract

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.

16 pages, 4 figures

References in corpus (4)

• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Finite size scaling for the core of large random hypergraphs
• Dynamics of k-core percolation