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2009•arXiv (Cornell University)Open access

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

Ali Ajdari Rad, Mahdi Jalili, Martin Hasler

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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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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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Available 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.

Key concepts: Connection (principal bundle), Algebraic number, Graph, Upper and lower bounds, Algebraic connectivity, Stability (learning theory), Mathematics, Computer science

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