What's in a word graph evaluation and enhancement of word lattices?

During the last few years, word graphs have been gaining increasing interest within the speech community as the primary interface between speech recognizers and language processing modules. Both development and evaluation of graph-producing speech decoders require generally accepted measures of word graph quality. While the notion of recognition accuracy can easily be extended to word graphs, a meaningful measure of word graph size has not yet surfaced. We argue, that the number of derivation steps a theoretical parser would need to process all unique sub-paths in a graph could provide a measure that is both application oriented enough to be meaningful and general enough to allow a useful comparison of word recognizers across different applications.