# Modularity-Based Incremental Label Propagation Algorithm for Community Detection
## 4 Conclusions and Future Work  
This paper proposed a new approach, namely MILPA, to detect community structures in networks. While it is an improved version of LPA, MILPA has several unique features. The major difference is that it takes the incremental strategy to carry out label propagation which is the opposite of LPA. In the incremental strategy, MILPA always centers on the node with the highest intensity and starts to find other neighbors that are closely connected, so it greatly reduces the randomness of the algorithm. Experiment results have shown that this strategy can speed up the convergence of label propagation and greatly reduce the randomness of the process. Another feature of MILPA is the introduction of modularity optimization, which enables some nodes to be moved into more appropriate communities to produce a better partition. This is a key factor of the proposed method to have better performance  
Figure 6: The modularity of different methods in eight real-world networks.  
than LPA. Due to this operation, however, MILPA is slower than LPA which has linear time complexity. Complexity analysis and improvements of MILPA will be important tasks in our future research.  
One point that cannot be ignored is the execution order of the algorithm, that is, incremental label propagation first and modularity-based label updating later. This combination, i.e., staged operation, makes MILPA outperform GN, LPAMP, and Fastgreedy which are also based on modularity optimization. The three existing methods do not take this operation but find the best community by modularity optimization every time they move nodes, so it is easy for them to fall into local optimal solutions. Interestingly, Louvain, the best algorithm which is based on modularity optimization, takes the staged operation too. Thus, this phenomenon sheds some light on the design of community detection algorithms.  
There is also one important advantage of MILPA. Experiments on LFR benchmark networks demonstrated that it can find community structure of a network even it is not obvious. As the community structure of synthetic networks becomes more and more difficult to distinguish, the performance of other algorithms (including Louvain) declines significantly, but the proposed algorithm maintains a high detection performance. MILPA therefore may be viewed a high-quality competitor when new methods are tested in LFR networks.  
In summary, the proposed MILPA has a number of major improvements over traditional LPA and it can be considered as an important supplement of community detection techniques for its performance superiority to many modularity-based methods. In the future work, we will focus on the time complexity of the algorithm to further improve the performance of the algorithm. We will also consider developing our algorithm to weighted networks and directed networks and generalizing it to larger networks.  
The authors designed the experiment together. [PERSON]. ([PERSON]), [PERSON] and [PERSON] performed the experiment. [PERSON] and [PERSON]. ([PERSON]) carried out the analyses. [PERSON]. ([PERSON]), [PERSON], [PERSON] and [PERSON] wrote the manuscript. All authors reviewed the manuscript. [PERSON]. ([PERSON]) and [PERSON] contributed equally to this work. [PERSON]. ([PERSON]) and [PERSON] are co-first authors. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Key R&D Program of China under Grant 2019 YFB1704700; in part by the National Natural Science Foundation of China under Grants 61573257, 71690234, 61873191, 61973237 and 71690234; in part by the Science and Technology Commission of Shanghai Municipality under Grant 19 JG0500700.  
The authors declare no conflict of interest.