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In this paper, we show how inexact graph matching (that is, the correspondence between sets of vertices of pairs of graphs) can be solved using the renormalization of projections of the vertices (as defined in this case by their connectivities) into the joint eigenspace of a pair of graphs and a form of relational clustering, An important feature of this eigenspace renormalization projection clustering (EPC) method is its ability to match graphs with different number of vertices. Shock graph-based shape matching is used to illustrate the model and a more objective method for evaluating the approach using random graphs is explored with encouraging results. Index Terms--Inexact multisubgraph matching, eigendecomposition, eigenspace projections, correspondence clustering, shape matching, random graphs.

Graph eigenspaces have been used to encode many different properties of graphs. In this paper we explore how such methods can be used for solving inexact graph matching (the matching of sets of vertices in one graph to those in another) having the same or different numbers of vertices. In this case we explore eigen-subspace projections and vertex clustering (EPS) methods. The correspondence algorithm enables the EPC method to discover a range of correspondence relationships from one-to-one vertex matching to that of inexact (many-to-many) matching of structurally similar subgraphs based on the similarities of their vertex connectivities defined by their positions in the common subspace. Examples in shape recognition and random graphs are used to illustrate this method. [ABSTRACT FROM AUTHOR]