In this paper we show how inexact multisubgraph matching can be solved using methods based on the projections of vertices (and their connections) into the eigenspaces of graphs - and associated clustering methods. Our analysis points to deficiencies of recent eigenspectra methods though demonstrates just how powerful full eigenspace methods can be for providing filters for such computationally intense problems. Also presented are some applications of the proposed method to shape matching, information retrieval and natural language processing.