Construction of velocity similarity graph for velocity field analysis in granular intruder motion

We present a method based on graph community detection algorithms to analyse velocity fields induced by an intruder particle impinging upon a stationary bed of particles. Based on velocity relations between the pairs of adjacent particles, the “velocity similarity” graphs are built where the graph vertices represent the particles and the edge weights are calculated according to the velocities of the respective particle pairs. A few different expressions for the edge weights are tested. Based on the graph, a Louvain community detection algorithm with the “geographic” null model is used to identify the goups of particles moving in a coordinated manner, represented in the graph as a community of vertices, for which the community detection algorithms developed for graph analysis can be applied. Selection of the expression of the graph edge weights based on the velocities of the respective particles influences the resulting graph structure and thereby has an influence on the community detection results.