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Algorithms 2017, 10(4), 112; https://doi.org/10.3390/a10040112

Mapping Higher-Order Network Flows in Memory and Multilayer Networks with Infomap

Integrated Science Lab, Department of Physics, Umeå University, SE-901 87 Umeå, Sweden
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Received: 15 June 2017 / Revised: 15 September 2017 / Accepted: 26 September 2017 / Published: 30 September 2017
(This article belongs to the Special Issue Algorithms for Community Detection in Complex Networks)
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Abstract

Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-detection algorithms to reveal important modular regularities in the flows. Here we show that various forms of higher-order network flows can be represented in a unified way with networks that distinguish physical nodes for representing a complex system’s objects from state nodes for describing flows between the objects. Moreover, these so-called sparse memory networks allow the information-theoretic community detection method known as the map equation to identify overlapping and nested flow modules in data from a range of different higher-order interactions such as multistep, multi-source, and temporal data. We derive the map equation applied to sparse memory networks and describe its search algorithm Infomap, which can exploit the flexibility of sparse memory networks. Together they provide a general solution to reveal overlapping modular patterns in higher-order flows through complex systems. View Full-Text
Keywords: community detection; Infomap; higher-order network flows; overlapping communities; multilayer networks; memory networks community detection; Infomap; higher-order network flows; overlapping communities; multilayer networks; memory networks
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Edler, D.; Bohlin, L.; Rosvall, A.M. Mapping Higher-Order Network Flows in Memory and Multilayer Networks with Infomap. Algorithms 2017, 10, 112.

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