## Communities in Graphs (2002)

Venue: | of Lecture Notes in Computer Science |

Citations: | 8 - 1 self |

### BibTeX

@TECHREPORT{Brinkmeier02communitiesin,

author = {Michael Brinkmeier},

title = {Communities in Graphs},

institution = {of Lecture Notes in Computer Science},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

Many applications, like the retrieval of information from the WWW, require or are improved by the detection of sets of closely related vertices in graphs. Depending on the application, many approaches are possible. In this paper we present a purely graph-theoretical approach, independent of the represented data. Based on the edge-connectivity of subgraphs, a tree of subgraphs is constructed, such that the children of a node are pairwise disjoint and contained in their parent. We describe a polynomial algorithm for the construction of the tree and present two heuristics, constructing the correct result in signi cantly decreased time. Furthermore we give a short description of possible applications in the elds of information retrieval, clustering and graph drawing. 1.

### Citations

3024 | Authoritative Sources in a Hyperlinked Environment
- Kleinberg
- 1999
(Show Context)
Citation Context ...be interesting to examine. The main task we had in mind, was the detection of communities in the WWW. In combination with ranking algorithms based on link-analysis, like PageRank ([PBMW98]) and HITS (=-=[Kle98]-=-), the results of purely text-based searches may be structured more eciently and precise by the covered topic and the relation between them. Especially the problem of the results tending to a tightly ... |

2496 | Emergence of scaling in random networks - Barabási, Albert - 1999 |

2434 | The PageRank citation ranking: bringing order to the Web
- Page, Brin, et al.
- 1998
(Show Context)
Citation Context ...estions which might be interesting to examine. The main task we had in mind, was the detection of communities in the WWW. In combination with ranking algorithms based on link-analysis, like PageRank (=-=[PBMW98]-=-) and HITS ([Kle98]), the results of purely text-based searches may be structured more eciently and precise by the covered topic and the relation between them. Especially the problem of the results te... |

432 | Improved Algorithms for Topic Distillation in a Hyperlinked Environment
- Bharat, Henzinger
- 1998
(Show Context)
Citation Context ...recise by the covered topic and the relation between them. Especially the problem of the results tending to a tightly knit community (TKC) and the drift to more general topics, as observed with HITS (=-=[BH98]-=-, [BRRT01], [CDK + 99], [Kle98], [Lit]) may be compensated 1 . Anotherseld of application is clustering in general. Since we use weighted graphs, nearly every clustering problem may be treated with co... |

259 | Scale-free characteristics of random networks: the topology of the WWW - Albert, Jeong, et al. - 2000 |

115 | A clustering algorithm based on graph connectivity
- Hartuv, Shamir
- 2000
(Show Context)
Citation Context ...nd their algorithm requires the knowledge two vertices in dierent communities, both having a larger degree than the edge-connectivity of the whole graph. Hartuv and Shamir describe in [HSL + 99] and [=-=HS00]-=- an algorithm which - similar to ours - determines minimal cuts recursively. If one of the resulting two parts has an edge-connectivity larger than half the number of its vertices, then it is interpre... |

61 | Identifying aggregates in hypertext structures
- Butafogo, Schneiderman
- 1991
(Show Context)
Citation Context ... parts are examined. Unfortunately the resulting clustering is not uniquely determined. In [Bot93] R. Botafogo extended his former work on the clustering of Hypertexts by biconnected components (cmp. =-=[BS91]-=-) to k-components in the sense of Matula. His aggregates can be constructed from our communities, by removing all subcommunities. The resulting connected components are Botafogo's clusters. In his pap... |

50 |
Planarity for clustered graphs
- Feng, Cohen, et al.
- 1995
(Show Context)
Citation Context ...ompletely determined by the communities of vertices and edges. Furthermore we are going to see that the communities in a graph G can be partially ordered, resulting in a natural clustering of G (cmp. =-=[FCE95]-=-, [Fen97]). More detailled, we obtain a tree of subgraphs whose leaves are the vertices of G, whose inner node represent the communities. Furthermore the children of a node are disjoint and completely... |

40 |
Cluster analysis for hypertext systems
- Botafogo
- 1993
(Show Context)
Citation Context ...n half the number of its vertices, then it is interpreted as a cluster. Otherwise it is cut again and its two parts are examined. Unfortunately the resulting clustering is not uniquely determined. In =-=[Bot93]-=- R. Botafogo extended his former work on the clustering of Hypertexts by biconnected components (cmp. [BS91]) to k-components in the sense of Matula. His aggregates can be constructed from our communi... |

31 |
k-components, clusters and slicing in graphs
- Matula
- 1972
(Show Context)
Citation Context ...runtime. Related Work. As the author realized after the theoretical part of this paper wassnished, our communities are very closely related to the k-components introduced by D.W.Matula in [Mat69] and =-=[Mat72]-=-. In fact the community of an edge or vertex x is the k-component with maximal k, containing x. Our k-communities are precisely the k-components. But our approach seems more algorithmic and the Key wo... |

25 | Algorithms for drawing clustered graphs
- Feng
- 1997
(Show Context)
Citation Context ... determined by the communities of vertices and edges. Furthermore we are going to see that the communities in a graph G can be partially ordered, resulting in a natural clustering of G (cmp. [FCE95], =-=[Fen97]-=-). More detailled, we obtain a tree of subgraphs whose leaves are the vertices of G, whose inner node represent the communities. Furthermore the children of a node are disjoint and completely containe... |

22 |
Panayiotis Tsaparas. Finding authorities and hubs from link structures on the world wide web
- Borodin, Robers, et al.
- 2001
(Show Context)
Citation Context ...y the covered topic and the relation between them. Especially the problem of the results tending to a tightly knit community (TKC) and the drift to more general topics, as observed with HITS ([BH98], =-=[BRRT01]-=-, [CDK + 99], [Kle98], [Lit]) may be compensated 1 . Anotherseld of application is clustering in general. Since we use weighted graphs, nearly every clustering problem may be treated with communities.... |

14 | Diameter of the world-wide web, Nature - Albert, Jenog, et al. - 1999 |

9 |
Ecient identi of web communities
- Flake, Lawrence, et al.
- 2000
(Show Context)
Citation Context ...y general, the techniques presented here can be applied for many dierent problems involving the clustering of data. In fact similar approaches are already presented in the literature. For example in [=-=FLG00]-=- Flake et al. use minimal cuts - our main tool - for the detection of sets of vertices, which have at least as many edges inside the set, than outside. But their communities are not unique, and their ... |

4 |
The cohesive strength of graphs
- Matula
- 1969
(Show Context)
Citation Context ...decrease in runtime. Related Work. As the author realized after the theoretical part of this paper wassnished, our communities are very closely related to the k-components introduced by D.W.Matula in =-=[Mat69]-=- and [Mat72]. In fact the community of an edge or vertex x is the k-component with maximal k, containing x. Our k-communities are precisely the k-components. But our approach seems more algorithmic an... |

1 |
A review of world wide web searching techniques, focusing on hits and related algorithms that utilise the link topology of the world wide web to provide the basis for a structure based search technology. 26
- Litow
(Show Context)
Citation Context ...ation between them. Especially the problem of the results tending to a tightly knit community (TKC) and the drift to more general topics, as observed with HITS ([BH98], [BRRT01], [CDK + 99], [Kle98], =-=[Lit]-=-) may be compensated 1 . Anotherseld of application is clustering in general. Since we use weighted graphs, nearly every clustering problem may be treated with communities. Unfortunately, the communit... |