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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 onconnection-graph-stability method is introduced. The connection-graph-stabilityscore for each edge is defined as the sum of the length of all the shortestpaths making use of that edge. We prove that the algebraic connectivity of thegraph is lower bounded by the size of the graph divided by the maximumconnection graph stability of the edges.

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