The issue of graph recognition has been not always investigated until today though the subjects on the document image understanding are very interest and have proposed many methods/systems. This is partly because the graph reading is not yet sufficiently recognized in the practical applications, and partly because the graph recognition is more difficult than the ordinary document analysis/recognition. In this paper, we address an analysis problem of graph structures: especially, we concentrate on the recognition method of composite elements on bar graphs. The knowledge about layout structures is called the layout knowledge. We propose the representation form of this layout knowledge clearly, and make it explicit that our approach based on this layout knowledge can analyze/recognize the graph structures effectively.