First Passage Properties of the Erd\"os-Renyi Random Graph

ORAL

Abstract

We study the first-passage properties of the Erd\"os-Renyi random graph. Using an effective medium approximation we find that the mean-first-passage time between pairs of nodes is insensitive to the fraction $p$ of occupied links. This prediction is tested by numerical simulation. However, the inverse first moment exhibits non-monotonic behavior with $p$ near the percolation transition that can be understood on physical grounds.

Authors

  • Vishal Sood

    • CNLS Los Alamos National Laboratory

  • Sidney Redner

    • CNLS LANL, Los Alamos NM 87545, USA
    • Boston University
    • CNLS Los Alamos National Laboratory

  • Daniel ben-Avraham

    • Department of Physics, Clarkson University, Postdam NY 13699, USA
    • Clarkson University