A GraphCutBased Approach to Community Detection in Networks
Abstract
:1. Introduction
2. Prior Works
3. Methods
3.1. Network and Community Structure
3.2. Minimum Cut
3.3. The Betweenness Centrality
3.4. The DIVIDEINTOTWO Algorithm
Algorithm 1: The DIVIDEINTOTWO algorithm. 
Input: A connected graph $G=(V,E)$ Output: $C=\{{C}_{1},{C}_{2}\}$, a partition of G

3.5. Modularity: A Quality Measure
3.6. The Proposed Algorithm
Algorithm 2: The MCCD algorithm. 
Input: A connected graph $G=(V,E)$ Output: $C=\{{C}_{1},\dots ,{C}_{k}\}$, a community structure of G

Algorithm 3: The kMCCD algorithm. 
Input: A connected graph $G=(V,E)$ and a desired number of communities k Output: $C=\{{C}_{1},\dots ,{C}_{k}\}$, a community structure of G

4. Results
4.1. Example 1: A Simple Network
4.2. Example 2: Zachary’s Karate Club Network
Algorithm  GN  FN  CNM  DA  MCCD 

Modularity  0.401  0.381  0.381  0.419  0.372 
4.3. Example 3: The Social Network of Bottlenose Dolphins
4.4. Example 4: The Characters Network of Les Misérables
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
GN  Girvan and Newman 
LFR  Lancichinetti, Fortunato, and Radicchi 
MCCD  Minimum Cutbased Community Detection 
CNM  Clauset, Newman, and Moore 
DA  Duch and Arenas 
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Shin, H.; Park, J.; Kang, D. A GraphCutBased Approach to Community Detection in Networks. Appl. Sci. 2022, 12, 6218. https://doi.org/10.3390/app12126218
Shin H, Park J, Kang D. A GraphCutBased Approach to Community Detection in Networks. Applied Sciences. 2022; 12(12):6218. https://doi.org/10.3390/app12126218
Chicago/Turabian StyleShin, Hyungsik, Jeryang Park, and Dongwoo Kang. 2022. "A GraphCutBased Approach to Community Detection in Networks" Applied Sciences 12, no. 12: 6218. https://doi.org/10.3390/app12126218