Spectral Analysis

Synonyms

Spectral Graph Analysis; Spectral Network Analysis; Spectral Technique

Glossary

Network (graph):

A network G is a triple consisting of a node set V (G), a link set E(G), and a relation that associates each link with two nodes

Adjacency matrix:

Let G = (V (G), E(G)) be a network with V (G) = {v₁, ···, v_n}.

The adjacency matrix A(G) = (a_ij) of G is n × n matrix with a_ij = 1 if v_i is adjacent to v_j, and 0 otherwise

Eigenvalues of a graph:

All eigenvalues of the adjacency matrix A(G) of a graph G are called eigenvalues of G and denoted by

λ₁ ≥ λ₂ ≥ … ≥ λ_n

Degree diagonal matrix:

The degree diagonal matrix D(G) of a network G is the diagonal matrix whose diagonal entries are degrees of the corresponding nodes

Laplacian matrix:

The Laplacian matrix L(G) is defined be L(G) = D(G) − A(G), where D(G) is the degree diagonal matrix and A(G) is the adjacency matrix

Laplacian eigenvalues of a graph:

All eigenvalues of the Laplacian matrix L(G) of a graph Gare called the Laplacian...