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  • 1.
    Bassolas, Aleix
    et al.
    School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom; Departament d'Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Tarragona, Spain; Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, Palma de Mallorca, Spain.
    Holmgren, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Marot, Antoine
    RTE Réseau de Transport d'Electricité, Paris, France.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Nicosia, Vincenzo
    School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom.
    Mapping nonlocal relationships between metadata and network structure with metadata-dependent encoding of random walks2022In: Science Advances, E-ISSN 2375-2548, Vol. 8, no 43, article id eabn7558Article in journal (Refereed)
    Abstract [en]

    Integrating structural information and metadata, such as gender, social status, or interests, enriches networks and enables a better understanding of the large-scale structure of complex systems. However, existing approaches to augment networks with metadata for community detection only consider immediately adjacent nodes and cannot exploit the nonlocal relationships between metadata and large-scale network structure present in many spatial and social systems. Here, we develop a flow-based community detection framework based on the map equation that integrates network information and metadata of distant nodes and reveals more complex relationships. We analyze social and spatial networks and find that our methodology can detect functional metadata-informed communities distinct from those derived solely from network information or metadata. For example, in a mobility network of London, we identify communities that reflect the heterogeneity of income distribution, and in a European power grid network, we identify communities that capture relationships between geography and energy prices beyond country borders.

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  • 2.
    Calatayud, Joaquín
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Departamento de Biología, Geología, Física y Química inorgánica, Universidad Rey Juan Carlos, Madrid, Spain.
    Neuman, Magnus
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rojas, Alexis
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Eriksson, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Regularities in species’ niches reveal the world’s climate regions2021In: eLIFE, E-ISSN 2050-084X, Vol. 10, article id e58397Article in journal (Refereed)
    Abstract [en]

    Climate regions form the basis of many ecological, evolutionary, and conservation studies. However, our understanding of climate regions is limited to how they shape vegetation: They do not account for the distribution of animals. Here we develop a network-based framework to identify important climates worldwide based on regularities in realized niches of about 26,000 tetrapods. We show that high-energy climates, including deserts, tropical savannas, and steppes, are consistent across animal-and plant-derived classifications, indicating similar underlying climatic determinants. Conversely, temperate climates differ across all groups, suggesting that these climates allow for idiosyncratic adaptations. Finally, we show how the integration of niche classifications with geographical information enables the detection of climatic transition zones and the signal of geographic and historical processes. Our results identify the climates shaping the distribution of tetrapods and call for caution when using general climate classifications to study the ecology, evolution, or conservation of specific taxa.

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  • 3.
    Edler, Daniel
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Gothenburg Global Biodiversity Centre, University of Gothenburg, Gothenburg, Sweden; Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden.
    Holmgren, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rojas, Alexis
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Antonelli, Alexandre
    Gothenburg Global Biodiversity Centre, University of Gothenburg, Gothenburg, Sweden; Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden; Department of Biology, University of Oxford, Oxford, United Kingdom; Royal Botanical Gardens Kew, Richmond, Surrey, United Kingdom.
    Infomap Bioregions 2: exploring the interplay between biogeography and evolution2022Manuscript (preprint) (Other academic)
  • 4.
    Edler, Daniel
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Smiljanić, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics. Institute of Physics, University of Belgrade, Belgrade, Serbia.
    Holmgren, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Antonelli, Alexandre
    Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden; Gothenburg Global Biodiversity Centre, Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden; Department of Plant Sciences, University of Oxford, Oxford, United Kingdom; Royal Botanic Gardens, Kew, Richmond, Surrey, United Kingdom.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Variable Markov dynamics as a multifocal lens to map multiscale complex networksManuscript (preprint) (Other academic)
  • 5.
    Eriksson, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Carletti, Timoteo
    University of Namur, Namur, Belgium.
    Lambiotte, Renaud
    University of Oxford, Oxford, United Kingdom.
    Rojas, Alexis
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Flow-Based Community Detection in Hypergraphs2022In: Higher-Order Systems / [ed] Federico Battiston; Giovanni Petri, Springer Science+Business Media B.V., 2022, , p. 21p. 141-161Chapter in book (Refereed)
    Abstract [en]

    To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and search algorithms. But how similar are the resulting communities? We explain both methods’ machinery applied to hypergraphs and compare them on synthetic and real-world hypergraphs using various hyperedge-size biased random walks and time scales. We find that the map equation is more sensitive to time-scale changes and that Markov stability is more sensitive to hyperedge-size biases.

  • 6.
    Eriksson, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rojas, Alexis
    Umeå University, Faculty of Science and Technology, Department of Physics.
    de Domenico, Manlio
    CoMuNe Lab, Fondazione Bruno Kessler, Povo (TN), Italy.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs2021In: Communications Physics, E-ISSN 2399-3650, Vol. 4, no 1, article id 133Article in journal (Refereed)
    Abstract [en]

    Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. Mapping the large-scale structure of those flows requires effective community detection methods applied to cogent network representations. For different hypergraph data and research questions, which combination of random-walk model and network representation is best? We define unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.

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  • 7.
    Holmgren, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping higher-order dynamics and interactions in complex networks2023Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Complex systems research seeks to explain emergent properties in social, technological, and biological systems that result from interactions between their components. As data on the intricate relationships within these systems become increasingly available, there is a growing need for more sophisticated models to describe them accurately and offer deeper insights.

    This thesis addresses challenges in incorporating higher-order interactions and dynamics into the analysis of complex systems that go beyond standard network approaches. It covers mapping changing network organizations, modeling higher-order dynamics on ordinary networks, integrating network structure and metadata, and modeling multibody interactions. The thesis offers new tools and models to enhance our understanding of how higher-order dynamics and interactions shape the organization and give rise to the function of complex systems by providing more accurate representations than traditional network models. These findings pave the way for new research in network science.

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  • 8.
    Holmgren, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bernenko, Dolores
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Lizana, Ludvig
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping robust multiscale communities in chromosome contact networks2023In: Scientific Reports, E-ISSN 2045-2322, Vol. 13, no 1, article id 12979Article in journal (Refereed)
    Abstract [en]

    To better understand DNA’s 3D folding in cell nuclei, researchers developed chromosome capture methods such as Hi-C that measure the contact frequencies between all DNA segment pairs across the genome. As Hi-C data sets often are massive, it is common to use bioinformatics methods to group DNA segments into 3D regions with correlated contact patterns, such as Topologically associated domains and A/B compartments. Recently, another research direction emerged that treats the Hi-C data as a network of 3D contacts. In this representation, one can use community detection algorithms from complex network theory that group nodes into tightly connected mesoscale communities. However, because Hi-C networks are so densely connected, several node partitions may represent feasible solutions to the community detection problem but are indistinguishable unless including other data. Because this limitation is a fundamental property of the network, this problem persists regardless of the community-finding or data-clustering method. To help remedy this problem, we developed a method that charts the solution landscape of network partitions in Hi-C data from human cells. Our approach allows us to scan seamlessly through the scales of the network and determine regimes where we can expect reliable community structures. We find that some scales are more robust than others and that strong clusters may differ significantly. Our work highlights that finding a robust community structure hinges on thoughtful algorithm design or method cross-evaluation.

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  • 9.
    Holmgren, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Blöcker, Christopher
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping biased higher-order walks reveals overlapping communitiesManuscript (preprint) (Other academic)
    Abstract [en]

    Researchers use networks to model relational data from complex systems, and tools from network science to map them and understand their function. Flow communities capture the organization of various real-world systems such as social networks, protein-protein interactions, and species distributions, and are often overlapping. However, mapping overlapping flow-based communities requires higher-order data, which is not always available. To address this issue, we take inspiration from the representation-learning algorithm node2vec, and apply higher-order biased random walks on first-order networks to obtain higher-order data. But instead of explicitly simulating the walks, we model them with sparse memory networks and control the complexity of the higher-order model with an information-theoretic approach through a tunable information-loss parameter. Using the map equation framework, we partition the resulting higher-order networks into overlapping modules. We find that our method recovers planted overlapping partitions in synthetic benchmarks and identifies overlapping communities in real-world networks.

  • 10.
    Holmgren, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping change in higher-order networks with multilevel and overlapping communitiesManuscript (preprint) (Other academic)
    Abstract [en]

    New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial generator to illustrate the effect of modeling network flows with memory in a citation network, distinguishing multidisciplinary from field-specific journals. 

  • 11.
    Holmgren, Anton
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics. Department of Biological and Environmental Sciences, Gothenburg Global Biodiversity Centre, University of Gothenburg, Gothenburg, Sweden.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping change in higher-order networks with multilevel and overlapping communities2023In: Applied Network Science, E-ISSN 2364-8228, Vol. 8, no 1, article id 42Article in journal (Refereed)
    Abstract [en]

    New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial diagram generator in three case studies to illustrate significant changes in the organization of science, the effect of modeling network flows with memory in a citation network and distinguishing multidisciplinary from field-specific journals, and the effects of multilayer representation of a collaboration hypergraph.

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