Minimal spanning tree: A new approach for studying order and disorder

We develop a new approach for studying order and disorder in sets of particles. This approach is based on a graph constructed from the set of points locating the positions of the particles. This graph, which is called the minimal spanning tree, allows us to deduce two parameters, namely, the average edge length $m$ and the standard deviation $\sigma$, which are characteristic of the repartition to be studied. The method is applied to particles of an aggregated lithium thin film deposited on a dielectric substrate. These particles are found to be partially ordered. The use of a diagram involving both $m$ and $\sigma$ turns out to be a powerful tool for the determination of the degree of order in very various systems.