A Lower Bound for Algebraic Connectivity based on Connection Graph Stability Method

2009/09/15 by Ali Ajdari Rad, Rad, Ali Ajdari, Mahdi Jalili +3
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.0909.2782

arxiv created 2009/09/15 · arxiv updated 2009/12/01

Abstract

In this paper a tight lower bound for algebraic connectivity of graphs (second smallest eigenvalue of the Laplacian matrix of the graph) based on connection-graph-stability method is introduced. The connection-graph-stability score for each edge is defined as the sum of the length of all the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is lower bounded by the size of the graph divided by the maximum connection graph stability of the edges.

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