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In recent years many algorithms have been developed for finding patterns ingraphs and networks. A disadvantage of these algorithms is that they usesubgraph isomorphism to determine the support of a graph pattern; subgraphisomorphism is a well-known NP complete problem. In this paper, we propose analternative approach which mines tree patterns in networks by using subgraphhomomorphism. The advantage of homomorphism is that it can be computed inpolynomial time, which allows us to develop an algorithm that mines treepatterns in arbitrary graphs in incremental polynomial time. Homomorphismhowever entails two problems not found when using isomorphism: (1) two patternsof different size can be equivalent; (2) patterns of unbounded size can befrequent. In this paper we formalize these problems and study solutions thateasily fit within our algorithm.

Mining Patterns in Networks using Homomorphism