Collisions between particles in turbulent flows may be enhanced by the formation of clusters due to the preferential concentration effect. However, the internal sub-structure of the clusters remains unclear. This paper describes using the “degree of a node” and the “shortest path length” from graph theory, in combination with Voronoï analysis, to gain further insight into both the structure and internal sub-structure of a cluster. This is demonstrated on experimental measurements obtained from a confined counter-flow/jet system. A minority of the particles, which comprise large clusters, are found to have a significantly large number of neighboring particles for collisions. However, particles which comprise small clusters typically have a random number of neighbors.