Stability of graph communities across time scales

@article{Delvenne2008StabilityOG,
  title={Stability of graph communities across time scales},
  author={Jean-Charles Delvenne and Sophia N. Yaliraki and Mauricio Barahona},
  journal={Proceedings of the National Academy of Sciences},
  year={2008},
  volume={107},
  pages={12755 - 12760}
}
The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters (or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We introduce here the stability of a partition, a measure of its quality as a community structure based on… 
View on NAS
europepmc.org
429 Citations
Highly Influential Citations
27
Background Citations
162
Methods Citations
103
Results Citations
5

Figures from this paper

429 Citations

Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks

This dynamic framework creates a systematic link between different stochastic dynamics and their corresponding notions of optimal communities under distinct (node and edge) centralities and shows that the Markov Stability can be computed efficiently to find multi-scale community structure in large networks.

Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms…

Gauss’s law for networks directly reveals community boundaries

It is shown that identifying community boundaries rather than communities results in a more accurate decomposition of the network into informative components, which forms the basis of the “Laplacian modularity” quality function for community detection that is applicable to general network types.

The interplay between dynamics and networks: centrality, communities, and cheeger inequality

This work introduces an umbrella framework for defining and characterizing an ensemble of dynamic processes on a network and defines a function that measures the quality of every subset of nodes as a potential cluster (or community) with respect to this process on a given network.

Detecting hierarchical organization of pervasive communities by modular decomposition of Markov chain

This work proposes a mathematical formulation to decompose a random walk spreading over the entire network into localized random walks as a proxy for pervasive communities, and applies this formulation to biological and social as well as synthetic networks to demonstrate that it can properly detect communities as pervasively structured objects.

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

A generalized framework of network quality functions was developed that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices.

Finding and Testing Network Communities by Lumped Markov Chains

A sharp definition of communities is proposed that is based on a quality threshold and can disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.

Multi-scale modularity in complex networks

  • R. Lambiotte
  • Mathematics
    8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
  • 2010
It is argued for the use of more flexible quality functions incorporating a resolution parameter that allows us to reveal the natural scales of the system.

The stability of a graph partition: A dynamics-based framework for community detection

By considering a network perspective, it is hoped to gain a deepened understanding of system-level properties beyond what could be achieved by focussing solely on the constituent units.

Coding of Markov dynamics for multiscale community detection in complex networks

A simple dynamic approach is proposed that introduces time explicitly into the Map coding procedure through the analysis of the time-evolving multistep transition matrix of the Markov process.
...

55 References

Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms…

Resolution limit in community detection

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.

Finding community structure in networks using the eigenvectors of matrices.

  • M. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
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.

Finding and evaluating community structure in networks.

  • M. NewmanM. Girvan
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
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.

Analysis of the structure of complex networks at different resolution levels

The proposed method allows for multiple resolution screening of the modular structure, and its application to two real social networks allows us to find the exact splits reported in the literature, as well as the substructure beyond the actual split.

Modularity and community structure in networks.

  • M. Newman
  • Computer Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 2006
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.

Community Structure in Graphs

Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members…

Statistical mechanics of community detection.

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.

Multiresolution community detection for megascale networks by information-based replica correlations.

  • P. RonhovdeZ. Nussinov
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
A Potts model community detection algorithm is used to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph and has an accuracy that ranks among the best of currently available methods.

Detecting the overlapping and hierarchical community structure in complex networks

The first algorithm that finds both overlapping communities and the hierarchical structure is presented, based on the local optimization of a fitness function, enabling different hierarchical levels of organization to be investigated.
...