Computational Method based on Non-Nodal Graph Expansion for Directed Percolation Model

Abstract

A simple two rooted acyclic directed graph in which each element (vertex or site) is assigned one of the states ?pen?or ?losed?with probability p or (1-p) respectively independently of all other elements is called a Directed Percolation Model. The u-v backbone in any configuration is the sub-graphs consisting of all elements which belong to at least one open path from a root u to a root v in the directed graph. The properties of this backbone in the case that G is a directed graph representing a lattice are important in understanding various properties of directed percolation model. The purpose of this article is to present a computational method which is based on two rooted acyclic non-nodal directed graphs expansion (graph without articulation point) which involves Moboius function. We present various properties of the percolation model including flicker noise by analyzing the series with Mathematica software.