Weighted Betweenness and Algebraic Connectivity

One of the better studied topology metrics of complex networks is the second smallest eigenvalue of the Laplacian matrix of a network’s graph, referred to as the algebraic connectivity mN-1. This spectral metric plays a decisive role in synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph...

Graphs with given diameter maximizing the algebraic connectivity

We propose a class of graphs G?D(n1, n2, ..., nD+1), containing of a chain of D+1 cliques Kn1 , Kn2 , ..., KnD+1, where neighboring cliques are fully-interconnected. The class of graphs has diameter D and size N = ? 1?i?D+1ni. We prove that this class of graphs can achieve the maximal number of links, the minimum average hopcount, and more...