Testing for Homogeneity Using Minimum Spanning Trees

The problem of assuring homogeneity in the exposed surfaces of materials that are manufactured from particle composites arises in many applied contexts. A major issue in solving the problem is the need to quantify our intuitive notion of homogeneity in a way that permits scientific judgment. This article starts with an example from materials science and explores a mathematical formulation of homogeneity that is based on a network interpretation of how the particles are distributed. In this approach, minimum spanning trees are found to be the right tool.