PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Efficient computation of Ihara coefficients using the Bell polynomial recursion
Samuel Bulò, Edwin Hancock, Furqan Aziz and Marcello Pelillo
Linear Algebra and its Applications 2011.

Abstract

The Ihara zeta function has proved to be a powerful tool in the analysis of graph structures. It is determined by the prime cycles of a finite graph G=(V,E) and can be characterized in terms of a quasi characteristic polynomial of the adjacency matrix T of the oriented line graph associated to G. The coefficients of this polynomial, referred to as Ihara coefficients, have been used to characterize graphs in a permutation-invariant manner, and allow for an efficient evaluation of the Ihara zeta function. In this paper we present a novel method for computing the Ihara coefficients. We first establish a characterization of the Ihara coefficients in terms of complete Bell polynomials and, by exploiting a recursive relation for the latter, we show how the Ihara coefficients can be efficiently computed in O(|E|2), provided that the eigenvalues of T are known.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8499
Deposited By:Edwin Hancock
Deposited On:03 February 2012