Significant Subgraph Mining with Multiple Testing Correction

A graph is one of the most general data types to represent structured objects, and massive amounts of structured data are now available as graphs across a wide range of domains, such as chemical compounds in PubChem [5], biological pathways in KEGG [16], protein structures in PDB [3], and social networks on the web. Analyzing such databases, that is, graph mining, has evolved into an important branch of data mining and knowledge discovery. Graph databases often include two or more distinct classes of graphs and, in many application domains, the ultimate purpose is to discover significant subgraphs that are statistically significantly enriched in one particular class of graphs. In drug discovery, for instance, chemists try to identify a key substructure of chemical compounds which is significantly associated with a particular activity, e.g., anticancer activity [30]. In a similar fashion, biologists seek substructures of proteins that are required for particular docking events [37]. 1 Finding such significant subgraphs is an open problem, as the large number of candidate subgraphs causes both a computational and a statistical problem: the computational problem is that it is often extremely expensive to check all subgraphs for enrichment, given that their number scales exponentially in the number of nodes of the largest graph in the database.