Spatial autocorrelation, of which Geary’s c has traditionally been a popular measure, is fundamental to spatial science. This paper provides new perspective on c. We discuss this using concepts from spectral graph theory/linear algebraic theory. More precisely, we provide three types representations for it: (a) Laplacian representation, (b) Fourier transform and (c) Pearson’s correlation coeffi...

With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacian. We shall show that spectral properies (the eigenvalues and eigenvectors) of these matrices pro...

Spectral graph theory is a fast developing field in modern discrete mathematics with important applications in computer science, chemistry and operational research. By merging combinatorial techniques with algebraic and analytical methods it creates new approaches to hard discrete problems and gives new insights in classical Linear Algebra. The proposed minisymposium will bring together leading...

Let us first review some basic random graph models. The most popular is perhaps the Erdös-Rényi model, denoted by G(n, p) for some n ∈ N and p ∈ [0, 1]. In this model, there is a set of vertices V (with n = |V |), and the edge set over V is determined randomly by ( n 2 ) biased coin tosses. Initially, there are no edges: E := ∅. Then, for each pair of vertices u, v ∈ V , independently flip a co...

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