Spectra and structure of weighted graphs

This article investigates relation between spectral and structural properties of large edge-weighted graphs. In social or biological networks we frequently look for partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them exhibit regular behavior of information flow within or between the vertex subsets. We estimate the constants bounding the volume regularity of the cluster pairs by means of spectral gaps and classification properties of eigenvectors. We will focus on the more than two clusters case.