The problem of deciding whether a graph contains another graph appears in various applications. For solving this problem efficiently, we developed a numerical method to detect non-subgraphs, graphs which are not subgraphs of other graphs, by comparing eigenvalues of graphs. In this paper, we propose a method to make the detection more efficient by comparing of eigenvalues of graphs decomposed according to labels of the vertices and the edges. The new approach not only reduces the cost of computing eigenvalues but also increases the possibility of detecting non-subgraphs. The experimental evaluation shows the effectiveness of the proposed method.