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Multiplex measures for higher-order networks (2402.16782v3)
Published 26 Feb 2024 in physics.soc-ph and cs.SI
Abstract: A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order interactions among a collection of units. In this work, we introduce a comprehensive set of measures to describe structural connectivity patterns in multiplex hypergraphs, considering scales from node and hyperedge levels to the system's mesoscale. We validate our measures with three real-world datasets: scientific co-authorship in physics, movie collaborations, and high school interactions. This validation reveals new collaboration patterns, identifies trends within and across movie subfields, and provides insights into daily interaction dynamics. Our framework aims to offer a more nuanced characterization of real-world systems marked by both multiplex and higher-order interactions.
- F. Battiston and G. Petri, Higher-Order Systems (Springer, 2022).
- A. Patania, G. Petri, and F. Vaccarino, The shape of collaborations, EPJ Data Science 6, 1 (2017).
- G. Ghoshal, V. Zlatić, and G. Caldarelli, Random hypergraphs and their applications, Physical Review E 79, 066118 (2009).
- A. R. Benson, Three hypergraph eigenvector centralities, SIAM Journal on Mathematics of Data Science 1, 293 (2019).
- F. Tudisco and D. J. Higham, Node and edge nonlinear eigenvector centrality for hypergraphs, Communications Physics 4, 1 (2021).
- F. Musciotto, F. Battiston, and R. N. Mantegna, Detecting informative higher-order interactions in statistically validated hypergraphs, Communications Physics 4, 1 (2021).
- F. Musciotto, F. Battiston, and R. N. Mantegna, Identifying maximal sets of significantly interacting nodes in higher-order networks, arXiv preprint arXiv:2209.12712 (2022).
- J.-G. Young, G. Petri, and T. P. Peixoto, Hypergraph reconstruction from network data, Communications Physics 4, 1 (2021).
- M. M. Wolf, A. M. Klinvex, and D. M. Dunlavy, Advantages to modeling relational data using hypergraphs versus graphs, in 2016 IEEE High Performance Extreme Computing Conference (HPEC) (IEEE, 2016) pp. 1–7.
- A. Vazquez, Finding hypergraph communities: a bayesian approach and variational solution, Journal of Statistical Mechanics: Theory and Experiment 2009, P07006 (2009).
- T. Carletti, D. Fanelli, and R. Lambiotte, Random walks and community detection in hypergraphs, Journal of Physics: Complexity 2, 015011 (2021).
- P. S. Chodrow, N. Veldt, and A. R. Benson, Generative hypergraph clustering: From blockmodels to modularity, Science Advances 7, eabh1303 (2021).
- M. Contisciani, F. Battiston, and C. De Bacco, Inference of hyperedges and overlapping communities in hypergraphs, Nature communications 13, 1 (2022).
- P. Chodrow, N. Eikmeier, and J. Haddock, Nonbacktracking spectral clustering of nonuniform hypergraphs, SIAM Journal on Mathematics of Data Science 5, 251 (2023).
- P. S. Skardal and A. Arenas, Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching, Communications Physics 3, 1 (2020).
- A. P. Millán, J. J. Torres, and G. Bianconi, Explosive higher-order kuramoto dynamics on simplicial complexes, Physical Review Letters 124, 218301 (2020).
- M. Lucas, G. Cencetti, and F. Battiston, Multiorder laplacian for synchronization in higher-order networks, Physical Review Research 2, 033410 (2020).
- Y. Zhang, M. Lucas, and F. Battiston, Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes, Nature Communications 14, 1605 (2023).
- L. Neuhäuser, A. Mellor, and R. Lambiotte, Multibody interactions and nonlinear consensus dynamics on networked systems, Physical Review E 101, 032310 (2020).
- F. Battiston, V. Nicosia, and V. Latora, Structural measures for multiplex networks, Physical Review E 89, 032804 (2014).
- H. Sun and G. Bianconi, Higher-order percolation processes on multiplex hypergraphs, Physical Review E 104, 034306 (2021).
- https://journals.aps.org/datasets (2021).
- V. Nicosia and V. Latora, Measuring and modeling correlations in multiplex networks, Phys. Rev. E 92, 032805 (2015).
- S. P. Borgatti and M. G. Everett, Models of core/periphery structures, Social Networks 21, 375 (2000).
- F. Tudisco and D. J. Higham, Core-periphery detection in hypergraphs, SIAM Journal on Mathematics of Data Science 5, 1 (2023).
- A. Ceria and H. Wang, Temporal-topological properties of higher-order evolving networks, Scientific Reports 13, 5885 (2023).
- I. Iacopini, M. Karsai, and A. Barrat, The temporal dynamics of group interactions in higher-order social networks, arXiv preprint arXiv:2306.09967 (2023).
- L. Di Gaetano, F. Battiston, and M. Starnini, Percolation and topological properties of temporal higher-order networks, Physical Review Letters 132, 037401 (2024).