Finding recurring residue packing patterns, or spatial motifs, that characterize protein structural families is an important problem in bioinformatics. To this end, we apply a novel frequent subgraph mining algorithm to three graph representations of protein threedimensional (3D) structure. In each protein graph, a vertex represents an amino acid. Vertex-residues are connected by edges using three approaches: first, based on simple distance threshold between contact residues; second using the Delaunay tessellation from computational geometry, and third using the recently developed almostDelaunay tessellation approach. Applying this approach to a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, we typically identify several hundred common subgraphs equivalent to common packing motifs found in the majority of proteins in the family. We also use the counts of motifs extracted from proteins in two different SCOP families as input ...