Percolation in Random Graphs: A Finite Approach

Abstract

We propose an approach to calculate the critical percolation threshold for finite-sized Erdos-Renyi digraphs using minimal Hamiltonian cycles. We obtain an analytically exact result, valid non-asymptotically for all graph sizes, which scales in accordance with results obtained for infinite random graphs using the emergence of a giant connected component as marking the percolation transition. Our approach is general and can be applied to all graph models for which an algebraic formulation of the adjacency matrix is available.