Finding community structure in networks using the eigenvectors of matrices.
Physical Review E, 74(3):36104, 2006.
MEJ Newman.
[BibTeX]
Spectral Graph Theory.
1997.
F. R. K. Chung.
[BibTeX]
On Spectral Bounds for the k-Partitioning of Graphs.
2001.
B. Monien.
[BibTeX]
The Laplacian spectrum of graphs.
Graph Theory, Combinatorics, and Applications, 2:871-898, 1991.
B. Mohar.
[BibTeX]
Spectral Graph Theory and its Applications.
Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on:29-38, 2007.
D.A. Spielman.
[Kurzfassung]
[BibTeX]
Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications.
On generating all maximal independent sets.
Inf. Process. Lett., 27(3):119-123, 1988.
David S. Johnson und Christos H. Papadimitriou.
[doi]
[BibTeX]
Generating bicliques of a graph in lexicographic order.
Theoretical Computer Science, 337(1-3):240 - 248, 2005.
Vânia M.F. Dias, Celina M.H. de Figueiredo und Jayme L. Szwarcfiter.
[doi]
[Kurzfassung]
[BibTeX]
An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B=X[union or logical sum]Y, such that both X and Y are independent sets, and all vertices of X are adjacent to those of Y. If both X,Y[not equal to][empty set], then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques.
A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory.
Czechoslovak Mathematical Journal, 25(100):619-633, 1975.
M. Fiedler.
[BibTeX]
The second eigenvalue of the Google matrix.
A Stanford University Technical Report http://dbpubs. stanford. edu, 2003.
T.H. Haveliwala und S.D. Kamvar.
[BibTeX]
Co-clustering documents and words using bipartite spectral graph partitioning.
In:
KDD '01: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, Seiten 269-274.
ACM Press, New York, NY, USA, 2001.
Inderjit S. Dhillon.
[doi]
[BibTeX]
Graph Separators.
2002.
Guy Blelloch.
[BibTeX]
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]
Spectral K-way ratio-cut partitioning and clustering..
IEEE Trans. on CAD of Integrated Circuits and Systems, 13(9):1088-1096, 1994.
Pak K. Chan, Martine D. F. Schlag und Jason Y. Zien.
[doi]
[BibTeX]
Multiclass Spectral Clustering.
In:
Proc. International Conference on Computer Vision (ICCV 03).
Nice, France, 2003.
Stella X. Yu und Jianbo Shi.
[BibTeX]
New spectral methods for ratio cut partitioning and clustering..
IEEE Trans. on CAD of Integrated Circuits and Systems, 11(9):1074-1085, 1992.
Lars W. Hagen und Andrew B. Kahng.
[doi]
[BibTeX]
Tag recommendations based on tensor dimensionality reduction.
In:
RecSys '08: Proceedings of the 2008 ACM conference on Recommender systems, Seiten 43-50.
ACM, New York, NY, USA, 2008.
Panagiotis Symeonidis, Alexandros Nanopoulos und Yannis Manolopoulos.
[doi]
[BibTeX]
Some uses of spectral methods.
2000.
A.G. Ranade.
[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.
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.