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Community detection in temporal multilayer networks, with an application to correlation networks
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Bazzi, Marya, Porter, Mason A., Williams, Stacy, McDonald, Mark, Fenn, Daniel J. and Howison, Sam D. (2016) Community detection in temporal multilayer networks, with an application to correlation networks. Multiscale Modeling & Simulation, 14 (1). pp. 1-41. doi:10.1137/15M1009615 ISSN 1540-3459.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1137/15M1009615
Abstract
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain “communities” of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the “modularity” quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a “null network''---is application-dependent. We differentiate between “null networks” and “null models” in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis depends only on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure persistence of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular “Louvain” heuristic faces with temporal multilayer networks and suggest ways to mitigate them.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Multiscale Modeling & Simulation | ||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||
| ISSN: | 1540-3459 | ||||||
| Official Date: | 6 January 2016 | ||||||
| Dates: |
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| Volume: | 14 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 1-41 | ||||||
| DOI: | 10.1137/15M1009615 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Open Access Version: |
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