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Mapping Higher-Order Network Flows in Memory and Multilayer Networks with Infomap
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2017 (English)In: Algorithms, ISSN 1999-4893, E-ISSN 1999-4893, Vol. 10, no 4, article id 112Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 10, no 4, article id 112
Keyword [en]
community detection, Infomap, higher-order network flows, overlapping communities, multilayer tworks, memory networks
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-144114DOI: 10.3390/a10040112ISI: 000419169400004OAI: oai:DiVA.org:umu-144114DiVA, id: diva2:1177770
Available from: 2018-01-26 Created: 2018-01-26 Last updated: 2018-05-14Bibliographically approved
In thesis
1. Toward higher-order network models
Open this publication in new window or tab >>Toward higher-order network models
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complex systems play an essential role in our daily lives. These systems consist of many connected components that interact with each other. Consider, for example, society with billions of collaborating individuals, the stock market with numerous buyers and sellers that trade equities, or communication infrastructures with billions of phones, computers and satellites.

The key to understanding complex systems is to understand the interaction patterns between their components - their networks. To create the network, we need data from the system and a model that organizes the given data in a network representation. Today's increasing availability of data and improved computational capacity for analyzing networks have created great opportunities for the network approach to further prosper. However, increasingly rich data also gives rise to new challenges that question the effectiveness of the conventional approach to modeling data as a network. In this thesis, we explore those challenges and provide methods for simplifying and highlighting important interaction patterns in network models that make use of richer data.

Using data from real-world complex systems, we first show that conventional network modeling can provide valuable insights about the function of the underlying system. To explore the impact of using richer data in the network representation, we then expand the analysis for higher-order models of networks and show why we need to go beyond conventional models when there is data that allows us to do so. In addition, we also present a new framework for higher-order network modeling and analysis. We find that network models that capture richer data can provide more accurate representations of many real-world complex systems.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2018. p. 89
Keyword
network science, complex systems, complex networks, network analysis, higher-order networks, community detection, citation networks, network modeling
National Category
Physical Sciences Other Computer and Information Science
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-147673 (URN)978-91-7601-892-7 (ISBN)
Public defence
2018-06-08, Sal N420, Naturvetarhuset, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2018-05-18 Created: 2018-05-14 Last updated: 2018-05-15Bibliographically approved

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Edler, DanielBohlin, LudvigRosvall, Martin
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