Deterministic Modularity Optimization
Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)Published 1 January 2007
Sune Lehmann, Lars Kai Hansen
Citations46
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
We study community structure of networks. We have developed a scheme for maximizing the modularity Q [Newman and Girvan, Phys. Rev. E 69, 026113 (2004)] based on mean field methods. Further, we have defined a simple family of random networks with community structure; we understand the behavior of these networks analytically. Using these networks, we show how the mean field methods display better performance than previously known deterministic methods for optimization of Q.
Keywords
Computer ScienceBiochemistry, Genetics and Molecular BiologyPhysics and Astronomy
ScienceOptimization by Simulated Annealing
44,600 Citations1983Scott Kirkpatrick, C. D. Gelatt +1 more
A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems.
Reviews of Modern PhysicsStatistical mechanics of complex networks
20,607 Citations2002Réka Albert, Albert-Ĺaszló Barabási
A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
SIAM ReviewThe Structure and Function of Complex Networks
18,742 Citations2003Michael Newman
Developments in this field are reviewed, 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.
Physical Review EFinding and evaluating community structure in networks
13,892 Citations2004Michelle G. Newman, Michelle Girvan
It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.
Proceedings of the National Academy of SciencesModularity and community structure in networks
12,281 Citations2006M. E. J. Newman
It is shown that the modularity of a network can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which is called modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times.
Nature Reviews GeneticsNetwork biology: understanding the cell's functional organization
7,878 Citations2004Albert-Ĺaszló Barabási, Zoltán N. Oltvai
This work states that rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize the view of biology and disease pathologies in the twenty-first century.
Physical Review EFast algorithm for detecting community structure in networks
5,491 Citations2004M. E. J. Newman
An algorithm is described which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster, than previous algorithms.
NatureUncovering the overlapping community structure of complex networks in nature and society
5,435 Citations2005Gergely Palla, Imre Derényi +2 more
After defining a set of new characteristic quantities for the statistics of communities, this work applies an efficient technique for exploring overlapping communities on a large scale and finds that overlaps are significant, and the distributions introduced reveal universal features of networks.
Physical Review EFinding community structure in networks using the eigenvectors of matrices
4,801 Citations2006M. E. J. Newman
A modularity matrix plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations, and a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong are proposed.
NatureFunctional cartography of complex metabolic networks
4,013 Citations2005Roger Guimerà, Luı́s A. Nunes Amaral
A methodology is proposed that can find functional modules in complex networks, and classify nodes into universal roles according to their pattern of intra- and inter-module connections, which yields a ‘cartographic representation’ of complex networks.
Advances In PhysicsEvolution of networks
3,140 Citations2002S. N. Dorogovt︠s︡ev, J. F. F. Mendes
The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.
Proceedings of the National Academy of SciencesResolution limit in community detection
3,045 Citations2006Santo Fortunato, Marc Barthélemy
It is found that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined.
Journal of Statistical Mechanics Theory and ExperimentComparing community structure identification
2,877 Citations2005León Danon, Albert Dı́az-Guilera +2 more
It is found that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes.
Physical Review EStatistical mechanics of community detection
2,119 Citations2006Jörg Reichardt, Stefan Bornholdt
The properties of the ground state configuration are elucidated to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study.
The European Physical Journal BDetecting community structure in networks
2,022 Citations2004M. E. J. Newman
A number of more recent algorithms that appear to work well with real-world network data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks are described.
SIAM Journal on Matrix Analysis and ApplicationsPartitioning Sparse Matrices with Eigenvectors of Graphs
1,692 Citations1990Alex Pothen, Horst D. Simon +1 more
It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph, which can be used to compute good separators in grid graphs.
Physical Review EModularity from fluctuations in random graphs and complex networks
905 Citations2004Roger Guimerà, Marta Sales‐Pardo +1 more
It is shown both numerically and analytically that random graphs and scale-free networks have modularity and it is argued that this fact must be taken into consideration to define statistically significant modularity in complex networks.
International Journal of Neural SystemsA NEW METHOD FOR MAPPING OPTIMIZATION PROBLEMS ONTO NEURAL NETWORKS
452 Citations1989Carsten Peterson, Bo Söderberg
A novel modified method for obtaining approximate solutions to difficult optimization problems within the neural network paradigm is presented, which considers the graph partition and the travelling salesman problems and exhibits an impressive level of parameter insensitivity.
Nature PhysicsClasses of complex networks defined by role-to-role connectivity profiles
432 Citations2006Roger Guimerà, Marta Sales‐Pardo +1 more
It is reported that networks with different functions, including the Internet, metabolic, air transportation and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes on the basis of their link type frequency.
Polynomial algorithm for the k-cut problem
192 Citations1988Olivier Goldschmidt, Dorit S. Hochbaum
A polynomial algorithm for the case of a fixed k, to find a partition of an edge weighted graph into k nonempty components, such that the total edge weight between components is minimum.
Library Hi TechE‐prints and the Open Archives Initiative
38 Citations2003Simeon Warner
A brief survey of OAI e-print repositories, and of services using metadata harvested from e‐print repositories using the OAI protocol for metadata harvesting (OAI‐PMH), and several situations where metadata harvesting may be used to further improve the utility of e‐ print archives as a component of the scholarly communication infrastructure are presented.
