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## An Integer Programming Approach and Visual Analysis for Detecting Hierarchical Community Structures in Social Networks (2015)

### Citations

3045 | Some Methods for Classification and Analysis of Multivariate Observations
- MacQueen
- 1967
(Show Context)
Citation Context ...tecting community structures based on conventional graph clustering methods have been proposed, including the hierarchical clustering algorithm [12, 8, 25], graph partitioning [1], k-means clustering =-=[23]-=-, particle swarm optimization [3], and bee colony optimization [18]. Subsequently, novel methods for detecting community structures were proposed. For example, [43] proposed an IP method that applied ... |

1508 |
Community structure in social and biological networks
- Girvan, Newman
(Show Context)
Citation Context ...grounds or interests interact frequently and generally gather together to form one or several communities. A structure with multiple communities for the social network is called a community structure =-=[6, 7, 27]-=-, e.g., nodes with the same color that belong to the same community, which is encircled by blue dots (Figure 1(a)). Hence, differing from previous studies using cluster analysis, the degree of similar... |

601 |
Uncovering the overlapping community structure of complex networks in nature and society
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- 2005
(Show Context)
Citation Context ... Networks Many studies found that the detected community structure may have sophisticated relations, including hierarchical community relationships [5, 11, 35] and overlapping community relationships =-=[29, 30]-=-. In hierarchical community structures, a hierarchical relationship exists among communities, i.e., a community can be divided further into multiple subcommunities. On the other hand, community struct... |

285 | Comparing community structure identification
- Danon, D́ıaz-Guilera, et al.
- 2005
(Show Context)
Citation Context ...grounds or interests interact frequently and generally gather together to form one or several communities. A structure with multiple communities for the social network is called a community structure =-=[6, 7, 27]-=-, e.g., nodes with the same color that belong to the same community, which is encircled by blue dots (Figure 1(a)). Hence, differing from previous studies using cluster analysis, the degree of similar... |

275 |
Mixing patterns in networks
- Newman
(Show Context)
Citation Context ...etected community structure. As the NMI value increases, the quality of the community structure increases. Aside from these measures for detected community structures, the modularity metric (Q value) =-=[26, 28]-=- has been a very popular quality measure. The Q value is the sum of differences of the fraction of all links within each community minus the expected value of the same quantity in a network in which n... |

245 |
M: Hierarchical structure and the prediction of missing links in networks
- Clauset, Moore, et al.
(Show Context)
Citation Context .... Each community may have subcommunities based on the strong similarities among individuals, such that the hierarchical relationship forms a nested structure called a hierarchical community structure =-=[5, 11, 35]-=- (Figure 1(a)), and the hierarchical relationship is represented by a tree-like dendrogram (Figure 1(b)), in which each community is represented by a node and the hierarchical relationship is represen... |

168 | Empirical comparison of algorithms for network community detection
- Leskovec, Lang, et al.
- 2010
(Show Context)
Citation Context ...ty structure was found after each ant determined its community. To assess the quality of detected community structures, various similarity or quality measures were applied, including internal density =-=[19]-=-, normalized mutual information (NMI) [6], and function-modularity intensity [38]. To minimize difference among different communities, [19] used the proposed internal density to compute the density of... |

119 | Iterative optimization and simplification of hierarchical clusterings.
- Fisher
- 1996
(Show Context)
Citation Context ...Detection of Community Structures Various methods for detecting community structures based on conventional graph clustering methods have been proposed, including the hierarchical clustering algorithm =-=[12, 8, 25]-=-, graph partitioning [1], k-means clustering [23], particle swarm optimization [3], and bee colony optimization [18]. Subsequently, novel methods for detecting community structures were proposed. For ... |

118 |
Self-similar community structure in a network of human interactions
- Guimera, Danon, et al.
- 2003
(Show Context)
Citation Context ...t hierarchical levels to assist in identifying the inner structure of a network. Hence, hierarchical community structures have been detected in many complex networks. As well, numerous studies (e.g., =-=[32, 36, 4, 34, 14]-=-) have proposed approaches to detect hierarchical structures in complex networks, and applied their approaches to real social networks. Notably, [32] improved the agglomerative algorithm and objective... |

58 |
Why so many clustering algorithms – A Position Paper”
- Estivill-Castro
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(Show Context)
Citation Context ...n which the nodes within each cluster are strongly connected with each other (i.e., interactions within the same cluster are strong), and the links between two different clusters are connected weakly =-=[10, 20, 47]-=-. Extended from cluster analysis, the individuals with similar backgrounds or interests interact frequently and generally gather together to form one or several communities. A structure with multiple ... |

44 |
Finding and evaluating community structure
- Newman, Girvan
(Show Context)
Citation Context ... differing from previous studies using cluster analysis, the degree of similarity is regarded as the evaluation criterion for detecting/partitioning community structures in social or complex networks =-=[28]-=-. Recent works further investigated the hierarchical relationships in community structures. Each community may have subcommunities based on the strong similarities among individuals, such that the hie... |

23 |
Extremal optimization for graph partitioning
- Boettcher, Percus
- 2001
(Show Context)
Citation Context ...s Various methods for detecting community structures based on conventional graph clustering methods have been proposed, including the hierarchical clustering algorithm [12, 8, 25], graph partitioning =-=[1]-=-, k-means clustering [23], particle swarm optimization [3], and bee colony optimization [18]. Subsequently, novel methods for detecting community structures were proposed. For example, [43] proposed a... |

23 |
GA-NET: a genetic algorithm for community detection in social networks.
- Pizzuti
- 2008
(Show Context)
Citation Context ...ticle swarm optimization was applied to detect community structures, and experimental results showed that the isolated nodes can be detected with increased ease. A genetic algorithm (GA) developed in =-=[31]-=- to solve the community detection problem with a single-objective function based on community score; the quality of the detected community structures was better than that of the previous GA approaches... |

5 | Enhancing community detection using a network weighting strategy
- Meo, Ferrara, et al.
(Show Context)
Citation Context ...grounds or interests interact frequently and generally gather together to form one or several communities. A structure with multiple communities for the social network is called a community structure =-=[6, 7, 27]-=-, e.g., nodes with the same color that belong to the same community, which is encircled by blue dots (Figure 1(a)). Hence, differing from previous studies using cluster analysis, the degree of similar... |

5 |
Detecting community structure in complex networks using simulated annealing with k-means algorithms.
- Liu, Liu
- 2010
(Show Context)
Citation Context ...oposed in [15] to solve the community structure detection problem with a multi-objective function, improving the single-objective function designed in [31]. The k-means algorithm was first adopted by =-=[22]-=- to find an initial solution, which considered link length between nodes in a network, and then applied the simulated annealing algorithm to detect community structures. Experimental results showed th... |

4 |
Detecting hierarchical structure in networks
- Herlau, Mørup, et al.
- 2012
(Show Context)
Citation Context ... 2s(c) (d) Figure 4: (a) Dendrogram of the detected hierarchical community structure for Zachary’s karate club network. (b) Drawing of our detected structure. (c) Drawing of the structure detected by =-=[17]-=-. (d) Drawing of the structure detected by [24]. Nodes in the two super communities at level 2 are connected strongly with nodes 1 and 34, respectively (Figures 4(a) and 4(b)). In the real Zachary’s k... |

4 | Overlapping community structures and their detection on social networks
- Nguyen, Dinh, et al.
- 2011
(Show Context)
Citation Context ... Networks Many studies found that the detected community structure may have sophisticated relations, including hierarchical community relationships [5, 11, 35] and overlapping community relationships =-=[29, 30]-=-. In hierarchical community structures, a hierarchical relationship exists among communities, i.e., a community can be divided further into multiple subcommunities. On the other hand, community struct... |

3 |
MONTECCHIANI F.: Fast layout computation of clustered networks: Algorithmic advances and experimental analysis
- DIDIMO
(Show Context)
Citation Context ...Detection of Community Structures Various methods for detecting community structures based on conventional graph clustering methods have been proposed, including the hierarchical clustering algorithm =-=[12, 8, 25]-=-, graph partitioning [1], k-means clustering [23], particle swarm optimization [3], and bee colony optimization [18]. Subsequently, novel methods for detecting community structures were proposed. For ... |

2 |
Greedy discrete particle swarm optimization for large-scale social network clustering
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- 2015
(Show Context)
Citation Context ... on conventional graph clustering methods have been proposed, including the hierarchical clustering algorithm [12, 8, 25], graph partitioning [1], k-means clustering [23], particle swarm optimization =-=[3]-=-, and bee colony optimization [18]. Subsequently, novel methods for detecting community structures were proposed. For example, [43] proposed an IP method that applied a community capacity limit and mi... |

2 |
Structural inference of hierarchies
- Clauset, Moore, et al.
- 2007
(Show Context)
Citation Context ...t hierarchical levels to assist in identifying the inner structure of a network. Hence, hierarchical community structures have been detected in many complex networks. As well, numerous studies (e.g., =-=[32, 36, 4, 34, 14]-=-) have proposed approaches to detect hierarchical structures in complex networks, and applied their approaches to real social networks. Notably, [32] improved the agglomerative algorithm and objective... |

2 |
A new approach for discovering and quantifying hierarchical structure of complex networks
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- 2008
(Show Context)
Citation Context .... Each community may have subcommunities based on the strong similarities among individuals, such that the hierarchical relationship forms a nested structure called a hierarchical community structure =-=[5, 11, 35]-=- (Figure 1(a)), and the hierarchical relationship is represented by a tree-like dendrogram (Figure 1(b)), in which each community is represented by a node and the hierarchical relationship is represen... |

1 |
community detection model using particle swarm optimization
- Duan, Wang, et al.
(Show Context)
Citation Context ...thod with supervised learning mechanism was proposed to incorporate prior information into community structure detection. Metaheuristics have been recently employed to detect community structures. In =-=[9]-=-, particle swarm optimization was applied to detect community structures, and experimental results showed that the isolated nodes can be detected with increased ease. A genetic algorithm (GA) develope... |

1 |
Detecting community structure in complex networks based on k-means clustering and data field theory
- Gao, Jin
- 2008
(Show Context)
Citation Context ... detecting community structures were proposed. For example, [43] proposed an IP method that applied a community capacity limit and minimal difference for numbers of nodes in different communities. In =-=[13]-=-, a weight was assigned to each node in a network, and then the conventional k-means clustering method was applied to classify nodes into k communities. A nonlinear programming model was established i... |

1 |
Fahmy, Genetic algorithms for community detection in social networks
- Hafez, Ghali, et al.
- 2012
(Show Context)
Citation Context ...em with a single-objective function based on community score; the quality of the detected community structures was better than that of the previous GA approaches. A GA approach was 5 also proposed in =-=[15]-=- to solve the community structure detection problem with a multi-objective function, improving the single-objective function designed in [31]. The k-means algorithm was first adopted by [22] to find a... |

1 |
Ant colony optimization for community detection in large-scale complex networks
- He, Liu, et al.
- 2011
(Show Context)
Citation Context ...ealing algorithm to detect community structures. Experimental results showed that aside from visualizing the detected community structure, the most important node in each community was also found. In =-=[16]-=-, ant colony optimization algorithm was applied to detect community structures, in which each ant represented a network node; each ant then iteratively selected whether to join a community; and finall... |

1 |
Automatic kernel clustering with bee colony optimization algorithm, Information Sciences 283
- Kuo, Huang, et al.
- 2014
(Show Context)
Citation Context ... methods have been proposed, including the hierarchical clustering algorithm [12, 8, 25], graph partitioning [1], k-means clustering [23], particle swarm optimization [3], and bee colony optimization =-=[18]-=-. Subsequently, novel methods for detecting community structures were proposed. For example, [43] proposed an IP method that applied a community capacity limit and minimal difference for numbers of no... |

1 |
Uncovering overlapping cluster structures via stochastic competitive learning, Information Sciences 247
- Li, Zhao
- 2013
(Show Context)
Citation Context ...n which the nodes within each cluster are strongly connected with each other (i.e., interactions within the same cluster are strong), and the links between two different clusters are connected weakly =-=[10, 20, 47]-=-. Extended from cluster analysis, the individuals with similar backgrounds or interests interact frequently and generally gather together to form one or several communities. A structure with multiple ... |

1 |
Revealing network communities with a nonlinear programming method, Information Sciences 229
- Li
- 2013
(Show Context)
Citation Context ...etection in social or complex networks [11, 32, 33, 36, 37, 45]. Although those approaches are computationally efficient, they cannot guarantee that exact optimal solutions will be obtained. Notably, =-=[21, 43]-=- developed the mathematical programming methods for detecting community structures without any hierarchy. Second, most previous works (e.g., [32, 36, 37]) did not apply flexible community capacity lim... |

1 |
Two-stage algorithm using influence coefficient for detecting the hierarchical, non-overlapping and overlapping community structure, Physica A: Statistical Mechanics and its Applications 408
- Mu, Liu, et al.
- 2014
(Show Context)
Citation Context ...cted hierarchical community structure for Zachary’s karate club network. (b) Drawing of our detected structure. (c) Drawing of the structure detected by [17]. (d) Drawing of the structure detected by =-=[24]-=-. Nodes in the two super communities at level 2 are connected strongly with nodes 1 and 34, respectively (Figures 4(a) and 4(b)). In the real Zachary’s karate club, node 1 is the coach of the club, an... |

1 | Community detection in networks via a spectral heuristic based on the clustering coefficient, Discrete Applied Mathematics 176 - Nascimento - 2014 |