A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration

A novel method for analyzing the inverse problem of topological indices of graph is proposed in this paper, which applies the data mining technique to classification of graphs according to topological indices. Differing from the way of using topological indices to categorize graphs into different isomorphic classes, this method aims at dividing molecular graphs with n vertices into several compact classes according to their topological indices. Then the chemical and physical features of each kind of graph can be researched and new compounds can be found, which has great significance on bio-medical filed. In the experiment, three classes of simple connected graphs with 5, 6 and 7 vertices, respectively, are investigated and analyzed using the proposed method, the experimental results show the validity of it. However, there are still some problems needed to be researched further, such as selecting the vector of topological indices for clustering, selecting the distance between the vectors of topological indices, choosing the aspects to analyze the properties of each kind of graph after clustering, etc.