From a structure to a tree

Abstract

A graph is decomposed into a series of overlapping clusters. The tightness of a cluster is measured by the trace of the third power of the interaction matrix of the graph. The clusters are linked to form a new graph, which is decomposed into a tree according to the closeness of the clusters: the concept of the closeness is analogus to the general gravitational law. The initial graph is not restricted to a series of binary relationships: both nodes and links may be assigned weights, and the links may be directed and asymmetric.