Abstract-This study describes a chance discovery method for network that use betweeness centrality and similarity. In prior research of chance discovery, in the chance discovery process, it is required that analysts infer chance from visualized network, because it is difficult that to solve problem like to guess the cause from the data such as non-parametric problem. However, this reasoning process has problem that chance discovery is difficult because chance discovery depends on experience or background knowledge of analysts. Therefore, to solve this problem, we pay attention the mathematical element with the network, and propose chance index that is index of network. Chance index have three calculation methods: the sum of the reciprocal, the product of the reciprocal, and the average reciprocal. Using the proposal method on three kinds of data, results show that proposal method is useful method and chance index that use average reciprocal is most useful calculation method.