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Proximity catch digraphs (PCDs) are based on proximity maps which yieldproximity regions and are special types of proximity graphs. PCDs are based onthe relative allocation of points from two or more classes in a region ofinterest and have applications in various fields. In this article, we provideauxiliary tools for and various characterizations of PCDs based on theirprobabilistic behavior. We consider the cases in which the vertices of the PCDscome from uniform and non-uniform distributions in the region of interest. Wealso provide some of the newly defined proximity maps as illustrative examples.

A Probabilistic Characterization of Random Proximity Catch Digraphs and the Associated Tools