This paper describes an improved chance index for chance discovery. A chance is an important event or circumstance that can be used by analysts to make decisions. Discovery chance, i.e., chance discovery, is important for knowledge to be used effectively in understanding the background and causes hidden in a dataset. However, chance discovery depends on analyst's inference. Therefore, we propose a chance index that quantitatively evaluates chance. The method is based on betweenness centrality and the strength of co-occurrence. This study improves the accuracy of chance index by considering cluster information.