Automatic Selection of Number of Clusters in Networks Using Relative Eigenvalue Quality

In communication networks, it is often useful to partition the networks into disjoint clusters so that hierarchical protocols, such as hierarchical routing, can be used. Many clustering techniques have been developed for this purpose, including connectivity-based, centroid-based, and spectral methods. One issue with all of these methods is how to select an appropriate number of clusters from the structure of the network. In this paper, we consider clustering techniques based on spectral graph theory in which the relations among nodes in a communication network are mapped onto a graph. We consider techniques that are designed to minimize the multiway normalized cut, a metric that tries to simultaneously minimize the number of edges cut between clusters while balancing the volumes of the clusters. We develop a new method for determining the number of clusters based on the eigenvalues of a normalized graph Laplacian matrix by comparing the eigenvalues to the statistics of a certain type of random cut of the graph. Performance results are presented to demonstrate the effectiveness of our algorithm.