Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computation. In this paper we describe a spectral method which can be used to partition graphs into nonoverlapping subgraphs. In particular, we demonstrate how the Fiedler-vector of the Laplacian matrix can be used to decompose graphs into non-overlapping neighbourhoods that can be used for the purposes of both matching and clustering.
Qiu and Hancock REF used the Fiedler vector of the Laplacian matrix to decompose graphs into smaller subgraphs to simplify the complexity of inexact graph matching.
Graph Matching and Clustering Using Spectral Partitions
Pattern Recognition
Computer Science Mathematics