Support Computation for Mining Frequent Subgraphs in a Single Graph

Defining the support (or frequency) of a subgraph is trivial when a database of graphs is given: it is simply the number of graphs in the database that contain the subgraph. However, if the input is one large graph, it is surprisingly difficult to find an appropriate support definition. In this paper we study the core problem, namely overlapping embeddings of the subgraph, in detail and suggest a definition that relies on the non-existence of equivalent ancestor embeddings in order to guarantee that the resulting support is anti-monotone. We prove this property and describe a method to compute the support defined in this way.