This paper describes a spectral method for graph-matching. We adopt a graphical models viewpoint in which the graph adjacency matrix is taken to represent the transition probability matrix of a Markov chain. The nodeorder of the steady state random walk associated with this Markov chain is determined by the co-efficent order of the leading eigenvector of the adjacency matrix. We match nodes in ...

Let G be a digraph with n vertices and A(G) be its adjacency matrix. A monic polynomial f(x) of degree at most n is called an annihilating polynomial of G if . 0 )) ( ( = G A f G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. We prove that two families of digraphs, i.e., the ladder digraphs and the difans, are annihilatingly unique by studying the similari...

Let G be a graph with adjacency matrix A and let F be a field. An F-matrix Q is a support matrix of G if A = [Q ̸=O], the zero-nonzero pattern of Q. If G has an invertible skew-symmetric support F-matrix S, the S-dual G of G is defined as the graph with adjacency matrix [S−1 ̸= O]. An analogous adjacency matrix dual, G has been examined in the literature for those bipartite graphs G with unique p...

Abstract: The structure of bus network is very significant for bus system. To evaluate the performance of the structure of bus network, indicators basing on graph theory and complex network theory are proposed. Three forms of matrices comprising linestation matrix, weighted adjacency matrix and adjacency matrix under space P are used to represent the bus network. The paper proposes a shift powe...

A lower bound on the chromatic number of a graph is derived by majorization of spectra of weighted adjacency matrices. These matrices are given by Hadamard products of the adjacency matrix and arbitrary Hermitian matrices.

With the rapid growth of online text information and user accesses, query-processing efficiency has become the major bottleneck of information retrieval (IR) systems. This paper proposes two new full-text indexing models to improve query-processing efficiency of IR systems. By using directed graph to represent text string, the adjacency matrix of text string is introduced. Two approaches are pr...

A recently developed semantic theory explains the relationship between knowledge and its representation in connectionist systems. The theory requires a mathematical model of the brain, i.e. a natural neural network. The goal of this project is to conceptualize and lay the groundwork for the development of an adjacency matrix representation of the human and rat brains. Recent data from neuroscie...

In this lecture, I will discuss the adjacency matrix of a graph, and the meaning of its smallest eigenvalue. This corresponds to the largest eigenvalue of the Laplacian, which we will examine as well. We will relate these to bounds on the chromatic numbers of graphs and the sizes of independent sets of vertices in graphs. In particular, we will prove Hoffman’s bound, and some generalizations. W...