Partition network into communities based on group action on sets

In this paper an improved algorithm is provided to detect communities within a network based on group action on sets (GAS). Modularity has been used as the criterion to revise the results of three previous papers, deriving a better method of partition for the network of Karate club. We developed a new method to replace the complicated GAS to achieve the same effect as GAS. Through four examples, we demonstrated that our revised approach reduced the computation amount of modularity values. Based on a branch marked example, a detailed example is provided by us to illustrate that there is too many cores in the initial stage of GAS approach to induce too many communities in the final partition. The findings shown here, will allow scholars to understand using GAS algorithm to partition a network into communities is an unreliable method.