Partition network into communities based on group action on sets

- We use modularity values to solve the incomplete algorithm of Zhang et al. (2011).
- Our revised algorithm reduced the computation amount of modularity values.
- We provide our intersection-union operation to replace the GAS algorithm.
- The GAS algorithm of Zhang et al. (2011) will result in too many cores in the initial stage and then too many communities.
- We point out the Burnside Theorem, cited in Zhang et al. (2011) that is no use to decide the number of communities.

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.