# A Graph-Cut-Based Approach to Community Detection in Networks
## 5 Discussion  
In this paper, a new algorithm for community detection was proposed and some experimental results were provided. As previously mentioned, the problem of community detection has its inherent difficulties; there is no exact solution for the problem. People may have different opinions about the community structure of a given network. As seen in Section 4, the networks of bottlenose dolphins and of characters in the novel _Les Miserables_ are complicated, so that there is no universally agreed-upon community structure. Even though the modularity measure \(Q\) can provide a criterion to estimate the quality of community structures, it is only an indirect measure, and some may find a lower-scored community structure to be better than a higher-scored one.  
Considering that the problem of community detection has no exact solution, the proposed algorithm MCCD shows fairly good results with comparable \(Q\) values when applied to the example networks of Section 4. In particular, the algorithm shows satisfactory results for the barbell graph and [PERSON]'s karate club network. For the more complicated networks in Section 4, it also detects community structures well, which can be visually observed from Figures 4 and 5.  
Even though the proposed algorithm showed its feasibility via the example networks of Section 4, further evaluation of the performance of the algorithm by using various benchmarks and larger network data is needed and remains as future work. Frequently used benchmarks such as GN and LFR may be used for the evaluation. For the example networks of Section 4, MCCD takes a few seconds with typical current computers, but the time performance should be carefully investigated with larger networks and benchmarks.  
Optimization of the MCCD algorithm implementation is also left as future work. Many procedures called by MCCD may be carefully modified and implemented to reduce computation time. Modifying the algorithm so that it can be applied to detect overlapping  
Figure 5: The character network of _Les Miserables_ and the application of MCCD to the network. (**a**) The network; (**b**) the communities detected by MCCD; (**c**) the betweenness centrality values \(c_{B}(\
u)\); (**d**) the modularity values after each iteration of DIVIDE-INTO-TWO.  
community structures may be left as another element of future work. This may not be easy, however, because graph cut methods in general divide vertices without overlapping.  
Conceptualization, H.S. and J.P.; methodology, H.S.; software, H.S.; validation, H.S., J.P. and D.K.; formal analysis, H.S.; investigation, J.P. and D.K.; resources, H.S. and D.K.; data curation, H.S.; writing--original draft preparation, H.S.; writing--review and editing, J.P. and D.K.; visualization, H.S.; supervision, H.S., J.P. and D.K.; project administration, D.K.; funding acquisition, H.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported partly by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019R1C1C1008017) and partly by the Hongik University new faculty research support fund.  
Not applicable.  
The data presented in this study are available in this article and there are no other data to share.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} GN & Girvan and Newman \\ LFR & Lancichinetti, [PERSON], and Radicchi \\ MCC & Minimum Cut-based Community Detection \\ CNM & Clauset, Newman, and Moore \\ DA & Duch and Arenas \\ \end{tabular}