### Buchbeiträge

**On Finding Graph Clusterings with Maximum Modularity**.

In:
A. Brandstädt, D. Kratsch und H. Müller (Herausgeber):

*Graph-Theoretic Concepts in Computer Science*, Seiten 121-132.
Springer, Berlin / Heidelberg, 2007.

Ulrik Brandes, Daniel Delling, Marco Gaertler, Robert Görke, Martin Hoefer, Zoran Nikoloski und Dorothea Wagner.

[doi]
[Kurzfassung]
[BibTeX]
Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts, and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomaration approach.

### Artikel in Tagungsbänden

**Content Aggregation on Knowledge Bases using Graph Clustering**.

In: Y. Sure und J. Domingue
(Herausgeber):

*The Semantic Web: Research and Applications*, Band 4011, Reihe LNAI, Seiten 530-544.
Springer, Heidelberg, 2006.

Christoph Schmitz, Andreas Hotho, Robert Jäschke und Gerd Stumme.

[doi]
[Kurzfassung]
[BibTeX]
Recently, research projects such as PADLR and SWAP
have developed tools like Edutella or Bibster, which are targeted at
establishing peer-to-peer knowledge management (P2PKM) systems. In
such a system, it is necessary to obtain provide brief semantic
descriptions of peers, so that routing algorithms or matchmaking
processes can make decisions about which communities peers should
belong to, or to which peers a given query should be forwarded.
This paper provides a graph clustering technique on
knowledge bases for that purpose. Using this clustering, we can show
that our strategy requires up to 58% fewer queries than the
baselines to yield full recall in a bibliographic P2PKM scenario.

**Content Aggregation on Knowledge Bases using Graph Clustering**.

In:

*Proceedings of the 3rd European Semantic Web Conference*, Band 4011, Reihe LNCS, Seiten 530-544.
Springer, Budva, Montenegro, 2006.

Christoph Schmitz, Andreas Hotho, Robert Jäschke und Gerd Stumme.

[doi]
[BibTeX]

**Content Aggregation on Knowledge Bases using Graph Clustering**.

In: Y. Sure und J. Domingue
(Herausgeber):

*The Semantic Web: Research and Applications*, Band 4011, Reihe LNAI, Seiten 530-544.
Springer, Heidelberg, 2006.

Christoph Schmitz, Andreas Hotho, Robert Jäschke und Gerd Stumme.

[doi]
[Kurzfassung]
[BibTeX]
Recently, research projects such as PADLR and SWAP have developed tools like Edutella or Bibster, which are targeted at establishing peer-to-peer knowledge management (P2PKM) systems. In such a system, it is necessary to obtain provide brief semantic descriptions of peers, so that routing algorithms or matchmaking processes can make decisions about which communities peers should belong to, or to which peers a given query should be forwarded. This paper provides a graph clustering technique on knowledge bases for that purpose. Using this clustering, we can show that our strategy requires up to 58% fewer queries than the baselines to yield full recall in a bibliographic P2PKM scenario.

**Information-Theoretic Co-Clustering**.

In:

*Proceedings of The Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining(KDD-2003)*, Seiten 89-98.
2003.

I. S. Dhillon, S. Mallela und D. S. Modha.

[doi]
[BibTeX]

### Sonstiges

**The structure and function of complex networks**.

2003.

M. E. J. Newman.

[doi]
[Kurzfassung]
[BibTeX]
Inspired by empirical studies of networked systems such as the Internet,
social networks, and biological networks, researchers have in recent years
developed a variety of techniques and models to help us understand or predict
the behavior of these systems. Here we review developments in this field,
including such concepts as the small-world effect, degree distributions,
clustering, network correlations, random graph models, models of network growth
and preferential attachment, and dynamical processes taking place on networks.

### Artikel in Tagungsbänden

**On spectral clustering: Analysis and an algorithm**.

In:

*Advances in Neural Information Processing Systems 14*, Seiten 849-856.
MIT Press, 2001.

Andrew Y. Ng, Michael I. Jordan und Yair Weiss.

[Kurzfassung]
[BibTeX]
Despite many empirical successes of spectral clustering methods| algorithms that cluster points using eigenvectors of matrices derived from the data|there are several unresolved issues. First, there are a wide variety of algorithms that use the eigenvectors in slightly dierent ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems. 1

### Sonstiges

**Some uses of spectral methods**.

2000.

A.G. Ranade.

[BibTeX]

### Technische Berichte

**Spectral Partitioning Works: Planar Graphs and Finite Element Meshes**.

1996.

Daniel A. Spielman und Shang Teng.

[BibTeX]

### Artikel in Zeitschriften

**Partitioning Sparse Matrices with Eigenvectors of Graphs**.

*SIAM J. MATRIX ANAL. APPLIC.*, 11(3):430-452, 1990.

A. Pothen, H.D. Simon und K.P. Liou.

[doi]
[BibTeX]

**Lower bounds for the partitioning of graphs**.

*IBM Journal of Research and Development*, 17(5):420-425, 1973.

W.E. Donath und A.J. Hoffman.

[BibTeX]