Probabilities of homomorphic mappings from multiple graphs

Abstract Each partition of a population defines a homomorphic mapping of sociometric graphs onto a corresponding set of image graphs. For sets of images selected by substantive importance, the expected number of mappings is calculated when the array of sociometric graphs is drawn at random with equal probabilities. Upper and lower bounds are computed for the probability of finding at least one mapping from an array to the given images, and for the expected number of mappings given that there is at least one. Results of small Monte Carlo trials are reported.