Modularity and community structure in networks.
@article{Newman2006ModularityAC,
title={Modularity and community structure in networks.},
author={Mark E. J. Newman},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={2006},
volume={103 23},
pages={
8577-82
}
}Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. [] Key Method Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods…
9,131 Citations
Finding community structure in networks using the eigenvectors of matrices.
- Computer SciencePhysical 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.
Z-Score-Based Modularity for Community Detection in Networks
- Computer SciencePloS one
- 2016
A new quality function for community detection called Z-modularity is obtained that measures the Z-score of a given partition with respect to the fraction of the number of edges within communities and mitigates the resolution limit of the original modularity in certain cases.
Graph spectra and the detectability of community structure in networks
- Computer SciencePhysical review letters
- 2012
Using methods from random matrix theory, the spectra of networks that display community structure are calculated, and it is shown that spectral modularity maximization is an optimal detection method in the sense that no other method will succeed in the regime where the modularity method fails.
Community identification in networks with unbalanced structure.
- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012
This paper introduces a metric to characterize the community structure better than other metrics in this situation, and proposes a method to infer the number of communities, which may solve the resolution limit problem.
The Importance of Community
- Computer Science
- 2014
The role of modularity in organizing the collective dynamics of social networks is explored, which may have important implications for understanding the process of consensus formation through individuals affecting the opinions of their neighbours via interactions through the links of the social network.
Asymptotic distribution of modularity in networks
- Computer ScienceMetrika
- 2019
For a specific partition of a given network, it is shown that the distribution of modularity under a null hypothesis of free labeling is asymptotically normal when the size of the network gets large.
Walk-modularity and community structure in networks
- Computer ScienceNetwork Science
- 2015
A natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which is referred to as walk-modularity, is explored and returns significantly improved results compared to traditional modularity maximization.
Modularity-based community detection in large networks: An empirical evaluation
- Computer Science2014 IEEE International Conference on Information and Automation (ICIA)
- 2014
This work applied a constrained power method for modularity optimization for large-scale networks and was able to find the community structures on a desktop computer with a single CPU in less than one hour yet with high accuracy, the first result reported in literature by conventional computing approaches.
Finding network communities using modularity density
- Computer ScienceArXiv
- 2016
A detailed analysis of a recently proposed function, namely modularity density, is presented, showing that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs.
A Comparison of Methods for Community Detection in Large Scale Networks
- Computer ScienceCompleNet
- 2012
The main goal of this work is to show a comparative study of some of the state-of-art methods for community detection in large scale networks using modularity maximization, taking into account not just the quality of the provided partitioning, but the computational cost associated to the method.
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