Papers by Keyword: Resistance Distance

Abstract: We propose a new clustering method that uses a similarlity metric deived from electrical resistance networks. The proposed metric allows us to quantify the mutual relevancy between data objects or nodes. We show how to derive the metric from the data collection and how to apply it to various application contexts. Our theoretical analyses and experiments show the excellent potential of the method to identifying clusters of networks and to improving data clustering performance on a number of data sets.

Abstract: On the basis of electrical network theory, Klein and Randić [Journal of Mathematical Chemistry 12 (1993) 81-9 proposed the novel concept of resistance distance. They view a graph as an (resistive) electrical network by considering each edge of the graph as a unit resistor. Then the resistance distance between any two vertices is defined as the effective resistance between these two nodes in the corresponding electrical network. In the present work, an interesting identity on resistance distances is obtained, that is, the sum of the resistance distance between end-vertices of an edge e of a plane graph G and the resistance distance between end-vertices of the dual edge e^* of e in the dual graph G^* of G is equal to one.