8. The apparatus of claim 7 , wherein the means for mapping comprises extending the first database graph by creating dummy vertices and dummy edges wherein every vertex and every edge of first database graph has a corresponding element in the second database graph.
7. A computer-implemented apparatus for conducting a database graph query, comprising: (a) means for obtaining a first database graph and a second database graph, wherein the first database graph and second database graph each have two or more vertices and one or more edges; (b) means for mapping the first database graph to the second database graph, wherein: (i) each vertex in the first database graph has a corresponding vertex in the second database graph; and (ii) each edge in the first database graph has a corresponding edge in the second database graph; wherein the means for mapping (b) comprises: (1) computing an initial similarity matrix for the first database graph and the second database graph, wherein each entry of the similarity matrix represents a weight similarity of each vertex of the first database graph to each vertex of the second database graph; (2) creating a priority queue comprised of vertex pairs based on the weight similarity, wherein each vertex pair comprises a vertex from the first database graph and a most similar vertex from the second database graph based on the weight similarity; (3) processing the priority queue by: (i) marking a first vertex pair in the priority queue as matched; (ii) assigning a higher similarity weight to unmatched vertex pairs that are neighbors to the first vertex pair; (iii) repeating steps (3)(i) and (3)(ii) for each subsequent vertex pair in the priority queue until all vertices in the first database graph have been marked as matched; (c) means for creating a graph closure tree comprised of a union of the first database graph and the second database graph based on the mapping, wherein each node of the graph closure tree comprises a graph closure of the node's children and each child of a leaf node comprises a database graph; and (d) means for conducting a graph query based on the graph closure tree.