Minimal spanning tree analysis of regular, random and cluster structures

It is shown that a graph called the minimal spanning tree (MST) is capable of detecting several kinds of cluster structure in arbitrary points set. From a MST it is possible to deduce the average edge lengthm and the standard deviationσ, which are characteristics for the corresponding distribution. The use of a diagram involving bothm andσ makes it possible to determine the degree of order by taking a simple reading in the (m,σ) plane. It is also possible, through angular diagrams retrieved from the MST, to bring out directional properties. The method is applied to the study of the growth of granular thin films.