Homomorphism density is a concept from combinatorics and graph theory that deals with the frequency of the occurrence of one graph within another graph. More formally, it relates to the density of homomorphisms from one graph to another.
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For finite graphs , the homomorphism density is the probability that a uniformly random map is a graph homomorphism. For bipartite graphs with prescribed vertex classes, the random map is chosen separately and uniformly into the corresponding classes.