Self-adaptive Louvain algorithm: Fast and stable community detection algorithm based on the principle of small probability event

Community structure is an important structure feature of complex networks. Due to its speed, effectiveness and simplicity, the Louvain algorithm is widely used to detect community structure planted in the network topology. Speeding up the Louvain algorithm, enabling the analysis of larger graphs in a shorter time and maintaining the accuracy of result, can benefit the research of networks in many fields. We here propose the Random Self-adaptive Neighbors Louvain algorithm as a new improved Louvain algorithm. The principle of small probability event is used to infer the number of neighbors to pick up randomly. The accuracy, speed and fluctuation of our method are compared with those of the original Louvain algorithm and the Random Neighbor Louvain algorithm. The results show that the RSNL can obtain as good partition as that of the original Louvain in a faster speed. On the networks without distinct community structures, the RSNL is faster and more accurate than the RNL. A new measure, equivalent computing time, is proposed to show the expectation runtime of the algorithm to obtain a relatively good partition. The comparison of this measure shows that the RSNL algorithm can make the best performance among the three algorithms in most cases.