On Modularity Clustering

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maxi...

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Bibliographic Details
Published in:IEEE transactions on knowledge and data engineering Vol. 20; no. 2; pp. 172 - 188
Main Authors: Brandes, U., Delling, D., Gaertler, M., Gorke, R., Hoefer, M., Nikoloski, Z., Wagner, D.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.02.2008
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Agglomeration
Applied sciences
Clustering
Clustering algorithms
Combinatorial algorithms
Complex systems
Computations on discrete structures
Computer science; control theory; systems
Data processing. List processing. Character string processing
Exact sciences and technology
Foundations
G.1.6.a Constrained optimization
Graph Theory
Graphs
Graphs and networks
Greedy algorithms
Hardness
Heuristic algorithms
Integer linear programming
Inter programming
Knowledge and data engineering tools and techniques
Mathematics and statistics
Memory organisation. Data processing
Modularity
Partitioning algorithms
Simulated annealing
Software
Surface hardness
Knowledge and data engineering tools and techniques
G.1.6.a Constrained optimization
Combinatorial algorithms
Graph Theory
Computations on discrete structures
Inter programming
Clustering
Graphs and networks
Mathematics and statistics
Cluster analysis
Graph clustering
Complex system
Modular system
Linear programming
Graph theory
Integer programming
Graph decomposition
modularity
community structure
Classification
Quality control
Greedy algorithm
graph partitioning
ISSN:1041-4347, 1558-2191
Online Access:Get full text
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Summary:Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly 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 agglomerative approach.
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ISSN:1041-4347
1558-2191
DOI:10.1109/TKDE.2007.190689