Spectral Graph Theory: Eigen Values Laplacians and Graph Connectivity
Jitender Kumar, B. Archana, Ramya Muralidharan
Abstract
Spectral graph theory investigates how graph structures and specific matrix eigenvalues of adjacency matrices and Laplacian matrices relate to each other. The following paper explains fundamental spectral graph theory concepts by analyzing eigenvalues alongside Laplacians which help evaluate graph connectivity. The spectral characteristics of these matrices provide crucial insights into the graph structure that include properties regarding connectivity as well as expansion features and operational reliability. The paper explains essential theorems alongside applications and methodology of spectral analysis.
Topics & Concepts
Spectral graph theoryGraphMaterials scienceGraph theoryGraph energyStatistical physicsVoltage graphDiscrete mathematicsLine graphMathematicsCombinatoricsPhysicsGraph theory and applicationsComplex Network Analysis TechniquesTopological and Geometric Data Analysis