# A Four-Stage Algorithm for Community Detection Based on Label Propagation and Game Theory in Social Networks

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Basic Concepts

#### 3.1. The Necessity of Representing the Network

#### 3.2. Community Detection

#### 3.3. Sorensen Index

#### 3.4. Game Theory Background

## 4. The Proposed Model

#### 4.1. Important Nodes Determination

#### 4.2. Community Detection by Label Propagation

#### 4.3. Stabilized Community

#### 4.4. Assured Allocation

## 5. Analysis of the Experimental Results

_{j}) and output 0 if they are in different communities.

#### 5.1. Real Networks with Ground Truth

#### 5.2. Real Networks without Ground Truth

#### 5.3. Time Analysis of the Proposed Algorithm

#### 5.4. Benchmark Networks

## 6. Concluding Remarks and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Coscia, M.; Giannotti, F.; Pedreschi, D. A classification for community discovery methods in complex networks. Stat. Anal. Data Mining ASA Data Sci. J.
**2011**, 4, 512–546. [Google Scholar] [CrossRef] - Fortunato, S. Community detection in graphs. Phys. Rep.
**2009**, 486, 75–174. [Google Scholar] [CrossRef] - Rosvall, M.; Bergstrom, C.T. Maps of information flow reveal community structure in complex networks. arXiv
**2007**, arXiv:0707.0609. [Google Scholar] - Blondel, V.D.; Guillaume, J.-L.; Lambiotte, R.; Lefebvre, E. Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp.
**2008**, 2008, P10008. [Google Scholar] [CrossRef] - Clauset, A.; Newman, M.E.J.; Moore, C. Finding community structure in very large networks. Phys. Rev. E
**2004**, 70, 066111. [Google Scholar] [CrossRef] - Guo, K.; He, L.; Chen, Y.; Guo, W.; Zheng, J. A local community detection algorithm based on internal force between nodes. Appl. Intell.
**2019**, 50, 328–340. [Google Scholar] [CrossRef] - Li, H.-J.; Bu, Z.; Li, A.; Liu, Z.; Shi, Y. Fast and Accurate Mining the Community Structure: Integrating Center Locating and Membership Optimization. IEEE Trans. Knowl. Data Eng.
**2016**, 28, 2349–2362. [Google Scholar] [CrossRef] - Ding, X.; Zhang, J.; Yang, J. A robust two-stage algorithm for local community detection. Knowledge-Based Syst.
**2018**, 152, 188–199. [Google Scholar] [CrossRef] - Whang, J.J.; Gleich, D.F.; Dhillon, I.S. Overlapping Community Detection Using Neighborhood-Inflated Seed Expansion. IEEE Trans. Knowl. Data Eng.
**2016**, 28, 1272–1284. [Google Scholar] [CrossRef] - Nash, J. Non-cooperative games. Ann. Math.
**1951**, 54, 286–295. [Google Scholar] [CrossRef] - Cavallari, S.; Zheng, V.W.; Cai, H.; Chang, K.C.-C.; Cambria, E. Learning community embedding with community detection and node embedding on graphs. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, Singapore, 6–10 November 2017; pp. 377–386. [Google Scholar]
- Chakraborty, T.; Dalmia, A.; Mukherjee, A.; Ganguly, N. Metrics for community analysis: A survey. ACM Comput. Surv. (CSUR)
**2017**, 50, 1–37. [Google Scholar] [CrossRef] - Liu, J. Comparative analysis for k-means algorithms in network community detection. In Proceedings of the International Symposium on Intelligence Computation and Applications, Wuhan, China, 22–24 October 2010; Springer: Berlin/Heidelberg, Germany, 2010; pp. 158–169. [Google Scholar] [CrossRef]
- Ferreira, L.N.; Pinto, A.R.; Zhao, L. QK-means: A clustering technique based on community detection and K-means for deployment of cluster head nodes. In Proceedings of the 2012 International Joint Conference on Neural Networks (IJCNN), Brisbane, QLD, Australia, 10–15 June 2012; pp. 1–7. [Google Scholar] [CrossRef]
- Van Laarhoven, T.; Marchiori, E. Local network community detection with continuous optimization of conductance and weighted kernel k-means. J. Mach. Learn. Res.
**2016**, 17, 5148–5175. [Google Scholar] - Lancichinetti, A.; Fortunato, S. Consensus clustering in complex networks. Sci. Rep.
**2012**, 2, 336. [Google Scholar] [CrossRef] [PubMed] - Zhang, S.; Wang, R.-S.; Zhang, X.-S. Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Phys. A Stat. Mech. Its Appl.
**2007**, 374, 483–490. [Google Scholar] [CrossRef] - Chen, J.; Li, Y.; Yang, X.; Zhao, S.; Zhang, Y. VGHC: A variable granularity hierarchical clustering for community detection. Granul. Comput.
**2019**, 6, 37–46. [Google Scholar] [CrossRef] - Newman, M.E. Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA
**2006**, 103, 8577–8582. [Google Scholar] [CrossRef] - McSweeney, P.J.; Mehrotra, K.; Oh, J.C. A game theoretic framework for community detection. In Proceedings of the 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, Istanbul, Turkey, 26–29 August 2012; pp. 227–234. [Google Scholar]
- Zhou, L.; Lü, K.; Cheng, C.; Chen, H. A game theory based approach for community detection in social networks. In Proceedings of the British National Conference on Databases, Oxford, UK, 8–10 July 2013; Springer: Berlin/Heidelberg, Germany, 2013; pp. 268–281. [Google Scholar]
- Hajibagheri, A.; Alvari, H.; Hamzeh, A.; Hashemi, S. Social networks community detection using the shapley value. In Proceedings of the 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISP 2012), Shiraz, Iran, 2–3 May 2012; pp. 222–227. [Google Scholar]
- Avrachenkov, K.E.; Kondratev, A.Y.; Mazalov, V.; Rubanov, D.G. Network partitioning algorithms as cooperative games. Comput. Soc. Netw.
**2018**, 5, 1–28. [Google Scholar] [CrossRef] - Zhou, X.; Cheng, S.; Liu, Y. A Cooperative Game Theory-Based Algorithm for Overlapping Community Detection. IEEE Access
**2020**, 8, 68417–68425. [Google Scholar] [CrossRef] - Alvari, H.; Hashemi, S.; Hamzeh, A. Detecting overlapping communities in social networks by game theory and structural equivalence concept. In Proceedings of the International Conference on Artificial Intelligence and Computational Intelligence, Taiyuan, China, 24–25 September 2011; Springer: Berlin/Heidelberg, Germany, 2011; pp. 620–630. [Google Scholar]
- Narayanam, R.; Narahari, Y. A game theory inspired, decentralized, local information based algorithm for community detection in social graphs. In Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012), Tsukuba, Japan, 11–15 November 2012; pp. 1072–1075. [Google Scholar]
- Havvaei, E.; Deo, N. A game-theoretic approach for detection of overlapping communities in dynamic complex networks. Int. J. Math. Comput. Methods
**2016**, 1, 313–324. [Google Scholar] - Zhao, X.; Wu, Y.; Yan, C.; Huang, Y. An algorithm based on game theory for detecting overlapping communities in social networks. In Proceedings of the 2016 International Conference on Advanced Cloud and Big Data (CBD), Chengdu, China, 13–16 August 2016; pp. 150–157. [Google Scholar]
- Moscato, V.; Picariello, A.; Sperli, G. Community detection based on game theory. Eng. Appl. Artif. Intell.
**2019**, 85, 773–782. [Google Scholar] [CrossRef] - Zhou, L.; Yang, P.; Lü, K.; Wang, L.; Chen, H. A fast approach for detecting overlapping communities in social networks based on game theory. In Proceedings of the British International Conference on Databases, Oxford, UK, 10–12 July 2015; Springer: Berlin/Heidelberg, Germany, 2015; pp. 62–73. [Google Scholar]
- Sorensen, T.A. A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. Biol. Skar.
**1948**, 5, 1–34. [Google Scholar] - Myerson, R.B. Game Theory: Analysis of Conflict; Harvard University Press: Cambridge, MA, USA, 1997. [Google Scholar]
- You, X.; Ma, Y.; Liu, Z. A three-stage algorithm on community detection in social networks. Knowl.-Based Syst.
**2019**, 187, 104822. [Google Scholar] [CrossRef] - Newman, M.E.; Girvan, M. Mixing patterns and community structure in networks. In Statistical Mechanics of Complex Networks; Springer: Berlin/Heidelberg, Germany, 2003; pp. 66–87. [Google Scholar]
- Pons, P.; Latapy, M. Computing communities in large networks using random walks. In Proceedings of the International Symposium on Computer and Information Sciences, Istanbul, Turkey, 26–28 October 2005; Springer: Berlin/Heidelberg, Germany, 2005; pp. 284–293. [Google Scholar]
- Newman, M.E.J. Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E
**2006**, 74, 036104. [Google Scholar] [CrossRef] [PubMed] - Raghavan, U.N.; Albert, R.; Kumara, S. Near linear time algorithm to detect community structures in large-scale networks. Phys. Rev. E
**2007**, 76, 036106. [Google Scholar] [CrossRef] - Newman, M.E.J.; Girvan, M. Finding and evaluating community structure in networks. Phys. Rev. E
**2004**, 69, 026113. [Google Scholar] [CrossRef] - Danon, L.; Diaz-Guilera, A.; Duch, J.; Arenas, A. Comparing community structure identification. J. Stat. Mech. Theory Exp.
**2005**, 2005, P09008. [Google Scholar] [CrossRef] - Lusseau, D. The emergent properties of a dolphin social network. Proc. R. Soc. B Boil. Sci.
**2003**, 270, S186–S188. [Google Scholar] [CrossRef] - Zachary, W.W. An Information Flow Model for Conflict and Fission in Small Groups. Anthropol. Res.
**1977**, 33, 452–473. [Google Scholar] [CrossRef] - Lancichinetti, A.; Fortunato, S.; Radicchi, F. Benchmark graphs for testing community detection algorithms. Phys. Rev. E
**2008**, 78, 046110. [Google Scholar] [CrossRef] - Chen, M.; Kuzmin, K.; Szymanski, B.K. Community Detection via Maximization of Modularity and Its Variants. IEEE Trans. Comput. Soc. Syst.
**2014**, 1, 46–65. [Google Scholar] [CrossRef] - Aghaalizadeh, S.; Afshord, S.T.; Bouyer, A.; Anari, B. A three-stage algorithm for local community detection based on the high node importance ranking in social networks. Phys. A Stat. Mech. Its Appl.
**2020**, 563, 125420. [Google Scholar] [CrossRef] - Peters, H. Game Theory: A Multi-Leveled Approach; Springer: Berlin/Heidelberg, Germany, 2015. [Google Scholar]

**Figure 2.**The NMI results for the Four-Stage Algorithm (FSA) and other approaches in the networks with ground truth.

**Figure 3.**Modularity results for the Four-Stage Algorithm (FSA) and other approaches in the networks with ground truth.

**Figure 4.**The NMI values of the four-stage algorithm on the benchmark networks based on (

**a**) ε, (

**b**) ω.

Important nodes Determination |

$1:\mathrm{Input}:\mathrm{An}\mathrm{undirected}\mathrm{and}\mathrm{unweighted}\mathrm{network}\mathrm{G}=\left(\mathrm{V},\mathrm{E}\right)$ 2: Output: The important node’s set $\mathrm{C}=\{{\mathrm{v}}_{1}$,${\mathrm{v}}_{2},\dots ,{\mathrm{v}}_{\mathrm{n}}$} 3:$\mathrm{C}=\left\{{\mathrm{v}}_{1}\right\}$ 4:$\mathrm{for}\mathrm{all}\left({\mathrm{v}}_{\mathrm{j}}\in \mathrm{V},{\mathrm{v}}_{\mathrm{j}}\notin \mathrm{C}\right)\mathrm{do}$ 5: $\mathrm{if}\left(\mathrm{d}\left({\mathrm{v}}_{\mathrm{j}},{\mathrm{v}}_{\mathrm{i}}\right)\ge \mathrm{Avd}\right)$ 6: $\mathrm{C}=\mathrm{C}\cup \left\{{\mathrm{v}}_{\mathrm{j}}\right\}$ 7: end if 8:Return C 9:end for |

Community Detection (Label Propagation) |

$1:\mathrm{Input}:\mathrm{Ranking}\mathrm{nodes}\mathrm{C}=\{{\mathrm{v}}_{1}$,${\mathrm{v}}_{2},\dots ,{\mathrm{v}}_{\mathrm{n}}$} 2: Output: The communities $\mathrm{S}=\{{\mathrm{S}}_{1}$,${\mathrm{S}}_{2},\dots ,{\mathrm{S}}_{\mathrm{n}}$} 3:${\mathrm{S}}_{\mathrm{i}}=\left\{{\mathrm{v}}_{{\mathrm{i}}_{\mathrm{j}}}\right\},{\mathrm{v}}_{{\mathrm{i}}_{\mathrm{j}}}\in \mathrm{C}$ 4:$\mathrm{for}\mathrm{all}\left(\mathrm{u}\in \mathrm{S}\mathrm{and}\mathrm{v}\in \mathrm{V}-\mathrm{C}\right)\mathrm{do}$ 5: $\mathrm{if}\left({\mathrm{S}}_{\mathrm{Sorenson}}\left(\mathrm{u},\mathrm{v}\right)=\mathrm{true}\right)$ 6: ${\mathrm{S}}_{\mathrm{i}}={\mathrm{S}}_{\mathrm{i}}\cup \left\{\mathrm{v}\right\}$ 7: end if $8:\mathrm{S}=\mathrm{S}\cup {\mathrm{S}}_{\mathrm{i}}$ 9: Return S 10:end for |

Community Combination (Cooperative game) |

$1:\mathrm{Input}:\mathrm{The}\mathrm{initial}\mathrm{communities}\mathrm{S}=\{{\mathrm{S}}_{1}$,${\mathrm{S}}_{2},\dots ,{\mathrm{S}}_{\mathrm{n}}$} 2:Output: $\mathrm{Reduced}\mathrm{and}\mathrm{stabilized}\mathrm{communities}\mathsf{\gamma}=\{{\mathrm{C}}_{1}$,${\mathrm{C}}_{2},\dots ,{\mathrm{C}}_{\mathrm{n}}$} $3:\mathsf{\gamma}=\left\{\right\}$ 4: $\mathrm{for}\mathrm{all}\left({\mathrm{S}}_{\mathrm{i}},{\mathrm{S}}_{\mathrm{j}}\in {\mathrm{S}\mathrm{and}\mathrm{S}}_{\mathrm{i}}\ne {\mathrm{S}}_{\mathrm{j}}\right)\mathrm{do}$ 5: $\mathrm{if}\Delta \mathrm{u}\left({\mathrm{S}}_{\mathrm{ij}}\right)\Delta \mathrm{u}\left({\mathrm{S}}_{\mathrm{j}}\right)\Delta \mathrm{u}\left({\mathrm{S}}_{\mathrm{j}}\right)0\mathrm{then}$ 6: $\mathsf{\gamma}=\{$ ${\mathrm{S}}_{\mathrm{ij}}\}-\left\{{\mathrm{S}}_{\mathrm{i}}\right\}-\left\{{\mathrm{S}}_{\mathrm{j}}\right\}$ 7: else 8: Return $\mathsf{\gamma}$ 9: end else 10: end if 11: end for (Repeat until no coalition willing to join the other one to improve itself) |

Assured Allocation (non-Cooperative game) |

$1:\mathrm{Input}:\mathrm{The}\mathrm{reduced}\mathrm{and}\mathrm{stabilized}\mathrm{communities}\mathrm{achieved}\mathrm{by}\mathrm{cooperative}\mathrm{game}\mathsf{\gamma}=\{{\mathrm{C}}_{1}$,${\mathrm{C}}_{2},\dots ,{\mathrm{C}}_{\mathrm{n}}$} 2:Output: $\mathrm{Assured}\mathrm{node}\mathrm{allocation}\mathrm{and}\mathrm{final}\mathrm{stable}\mathrm{community}\mathrm{structure}\mathrm{C}=\{{\mathrm{C}}_{1}$,${\mathrm{C}}_{2},\dots ,{\mathrm{C}}_{\mathrm{n}}$} $3:\mathsf{\delta}=\left\{\right\}$ 4:$\mathrm{for}\mathrm{all}\left(\mathrm{x}\in {\mathrm{C}}_{\mathrm{i}}\right)\mathrm{do}$ $5:\mathsf{\delta}=\mathrm{C}-{\mathrm{C}}_{\mathrm{i}}$ 6: $\mathrm{for}\mathrm{all}\left({\mathrm{C}}_{\mathrm{j}}\in \mathsf{\delta}\right)\mathrm{do}$ $7:\mathrm{if}\left(\Delta {\mathrm{u}}_{\mathrm{x}}\left({\mathrm{C}}_{\mathrm{i}}\right)\right)\mathsf{\omega}$ 8: ${\mathrm{C}}_{\mathrm{j}}={\mathrm{C}}_{\mathrm{j}}+\left\{\mathrm{x}\right\}$ 9: end if $10:\mathrm{if}\left(\Delta {\mathrm{u}}_{\mathrm{x}}\left({\mathrm{C}}_{\mathrm{j}}\right)\right)\mathsf{\epsilon}$ 11: ${\mathrm{C}}_{\mathrm{i}}={\mathrm{C}}_{\mathrm{i}}-\left\{\mathrm{x}\right\}$ 12: end if 13: Return ${\mathrm{C}}_{\mathrm{i}},{\mathrm{C}}_{\mathrm{j}}$ 14:end for (Repeat until nodes do not eager to join new community and leave their current communities) |

Dataset | NMI | Modularity | ||||
---|---|---|---|---|---|---|

Label Propagation | Cooperative Game | Non-Cooperative Game | Label Propagation | Cooperative Game | Non-Cooperative Game | |

Karate | 0.3428 | 06948 | 0.8737 | 0.0015 | 0.2797 | 0.2890 |

Dolphin | 0.2672 | 0.4888 | 0.8649 | 0.0119 | 0.2864 | 0.2991 |

Polbooks | 0.3363 | 0.5036 | 0.8701 | 0.0064 | 0.0785 | 0.0884 |

Football | 0.6845 | 0.5003 | 0.7261 | 0.0058 | 0.3705 | 0.3924 |

**Table 3.**Shows that the FSA algorithm has detected a close number of communities to the ground truth.

Methods | Networks | Karate | Dolphin | Polbooks | Football | |
---|---|---|---|---|---|---|

Evaluation Approaches | ||||||

Ground Truth | Q | 0.37 | 0.38 | 0.41 | 0.55 | |

C | 2 | 2 | 3 | 12 | ||

FSA | Q | 0.37 | 0.44 | 0.53 | 0.61 | |

NMI | 0.87 | 0.89 | 87 | 0.9 | ||

C | 2 | 2 | 4 | 10 | ||

TS | Q | 0.42 | 0.38 | 0.52 | 0.6 | |

NMI | 0.71 | 0.89 | 0.55 | 0.9 | ||

C | 4 | 2 | 4 | 10 | ||

Louvain | Q | 0.42 | 0.52 | 0.52 | 0.6 | |

NMI | 0.59 | 0.48 | 0.51 | 88 | ||

Fast Greedy | Q | 0.38 | 0.5 | 0.5 | 0.55 | |

NMI | 0.69 | 0.61 | 0.53 | 0.7 | ||

Infomap | Q | 0.4 | 0.52 | 0.52 | 0.6 | |

NMI | 0.7 | 0.5 | 0.49 | 0.92 | ||

LPA | Q | 0.4 | 0.5 | 0.5 | 0.6 | |

NMI | 0.7 | 0.69 | 0.57 | 0.92 | ||

Eigenvector | Q | 0.39 | 0.49 | 0.49 | 0.47 | |

NMI | 0.68 | 0.45 | 0.71 | 0.52 | ||

Walktrap | Q | 0.35 | 0.49 | 0.51 | 0.6 | |

NMI | 0.5 | 0.54 | 0.54 | 0.9 |

**Table 4.**The performance and the number of extracted communities in real networks without ground truth.

Networks | FSA | TS | Louvain | FastGreedy | Infomap | LPA | Eigenvector | Walktrap | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C | Q | C | Q | C | Q | C | Q | C | Q | C | Q | C | Q | C | Q | |

Lesmis | 6 | 0.55 | 6 | 0.54 | 6 | 0.56 | 5 | 0.50 | 9 | 0.55 | 8 | 0.53 | 6 | 0.55 | 8 | 0.52 |

Adjnoun | 7 | 0.31 | 7 | 0.29 | 7 | 0.29 | 7 | 0.29 | 2 | 0.01 | 10 | 0.24 | 1 | 0.00 | 25 | 0.22 |

Jazz | 3 | 0.45 | 3 | 0.44 | 4 | 0.44 | 4 | 0.44 | 7 | 0.28 | 3 | 0.39 | 2 | 0.28 | 11 | 0.44 |

Networks | FSA | Louvain | Infomap | LPA | Walktrap |
---|---|---|---|---|---|

Karate | 0.0007 | 0.1061 | 0.0200 | 0.0041 | 0.0039 |

Football | 0.0009 | 0.1082 | 0.0170 | 0.0032 | 0.0059 |

Dolphin | 0.0010 | 0.1078 | 0.0181 | 0.0023 | 0.0041 |

Polbooks | 0.0014 | 0.1101 | 0.0208 | 0.0031 | 0.0049 |

Lesmis | 0.0011 | 0.1090 | 0.0095 | 0.0029 | 0.0051 |

Jazz | 0.0034 | 0.1890 | 0.1098 | 0.0078 | 0.0090 |

Adjnoun | 0.0021 | 0.1001 | 0.0971 | 0.0034 | 0.0058 |

NMI | Modularity | |||||
---|---|---|---|---|---|---|

n | Label Propagation | Coalition | Individual | Label Propagation | Coalition | Individual |

50 | 0.3224 | 0.9049 | 0.9321 | 0.0244 | 0.5008 | 0.6127 |

100 | 0.4029 | 0.9267 | 0.9526 | 0.0010 | 0.5320 | 0.5340 |

150 | 0.4849 | 0.9602 | 0.9731 | 0.0168 | 0.6972 | 0.7321 |

200 | 0.5413 | 0.8387 | 0.9606 | 0.0299 | 0.6896 | 0.7487 |

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## Share and Cite

**MDPI and ACS Style**

Torkaman, A.; Badie, K.; Salajegheh, A.; Bokaei, M.H.; Ardestani, S.F.F.
A Four-Stage Algorithm for Community Detection Based on Label Propagation and Game Theory in Social Networks. *AI* **2023**, *4*, 255-269.
https://doi.org/10.3390/ai4010011

**AMA Style**

Torkaman A, Badie K, Salajegheh A, Bokaei MH, Ardestani SFF.
A Four-Stage Algorithm for Community Detection Based on Label Propagation and Game Theory in Social Networks. *AI*. 2023; 4(1):255-269.
https://doi.org/10.3390/ai4010011

**Chicago/Turabian Style**

Torkaman, Atefeh, Kambiz Badie, Afshin Salajegheh, Mohammad Hadi Bokaei, and Seyed Farshad Fatemi Ardestani.
2023. "A Four-Stage Algorithm for Community Detection Based on Label Propagation and Game Theory in Social Networks" *AI* 4, no. 1: 255-269.
https://doi.org/10.3390/ai4010011