Ensuring Strong Dominance of the Leading Eigenvalues for Cluster Ensembles

Spectral analysis is a popular mathematical tool in analyzing a variety of network and distributed systems. For a special class of networks, called cluster ensembles, which are made of interconnected clusters, we can characterize those which exhibit strong dominance of the leading eigenvalues in terms of the cluster structure. For such systems, only these leading eigenvalues and their corresponding eigenvectors will need to be examined in studying important properties of the underlying system. This paper establishes several bounds on eigenvalue separation ratios in terms of the number of clusters, their sizes and cluster interconnection topologies.