We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the node-normalized cut (also called cut ratio) and the edge-normalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria. The energy model that corresponds to the edge-normalized cut differs from the other ...

Definition 1.1. Given a (undirected) graph G = (V,E), the maximum cut δ(U) for U ⊆ V is the cut with maximal value |δ(U)|. The Maximum Cut Problem consists of finding a maximal cut. We let MaxCut(G) = max{|δ(U)| : U ⊆ V } be the value of the maximum cut in G, and MaxCut′ = MaxCut(G) |E| be the normalized version (note that both normalized and unnormalized maximum cut values are induced by the s...

This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our algorithm instead uses a minimum volume enclosing ellipsoid for them. We show that the algorithm shares similarity with the ellipsoidal rounding algorithm for separ...

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of minimizing normalized cut. However unlike spectral approaches, the proposed algorithm scales to graphs with millions of nodes and edges. The algorithm consists of...