What are higher-order networks?

Bick, Christian; Gross, Elizabeth; Harrington, Heather A.; Schaub, Michael T.

doi:10.1137/21m1414024

Cited by 426Complex Network Analysis TechniquesGraph Theory and AlgorithmsTopological and Geometric Data Analysis

What are higher-order networks?

Open access

Bick, Christian, Gross, Elizabeth, Harrington, Heather A., Schaub, Michael T.·2023·SIAM Review

DOI 10.1137/21m1414024

Open this paper in CoChat — free account

Abstract

Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships between pairs of such vertices. This simple combinatorial structure makes graphs interpretable and flexible modeling tools. The simplicity of graphs as system models, however, has been scrutinized in the literature recently. Specifically, it has been argued from a variety of different angles that there is a need for higher-order networks, which go beyond the paradigm of modeling pairwise relationships, as encapsulated by graphs. In this survey article we take stock of these recent developments. Our goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

Integrity signals

Registry

Crossref · 10.1137/21m1414024

Cites

304 of 304 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Interactions in air transport are typically not pairwise but form higher-order relationships.
“Additional complexity stems from the fact that those interactions are typically not of a pairwise nature, but rather form higher-order relationships -the simplest example being a passenger connecting multiple flights, thus creating a relation between many elements simultaneously. This could be tackled by the recent concept of higher-order networks ( Bianconi, 2021; Bick et al., 2023 ).”
From Status quo and challenges in air transport management research (2024) · cites this paper as Bick et al., 2023

A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585 · see citing works
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010 · see citing works
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,562 · see citing works
Chemical Oscillations, Waves, and Turbulence
Kuramoto, Y. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-69689-3 · Cited by 7,242 · see citing works
Spectral Graph Theory
Chung, F. (1996) · Regional conference series in mathematics · doi:10.1090/cbms/092 · Cited by 5,918 · see citing works
Untitled work
(2001) · Cited by 5,374 · see citing works
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2235192 · Cited by 4,421 · see citing works
The Kuramoto model: A simple paradigm for synchronization phenomena
Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F., & Spigler, R. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.137 · Cited by 3,470 · see citing works
Multilayer networks
Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014) · Journal of Complex Networks · doi:10.1093/comnet/cnu016 · Cited by 3,235 · see citing works
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
Strogatz, S. H. (2000) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(00)00094-4 · Cited by 3,094 · see citing works
Graphs and Hypergraphs
(1973) · North-Holland mathematical library · doi:10.1016/s0924-6509(09)x7013-3 · Cited by 3,006 · see citing works
Master Stability Functions for Synchronized Coupled Systems
Pecora, L. M., & Carroll, T. L. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2109 · Cited by 2,662 · see citing works
Network neuroscience
Bassett, D. S., & Sporns, O. (2017) · Nature Neuroscience · doi:10.1038/nn.4502 · Cited by 2,398 · see citing works
Diffusion maps
Coifman, R. R., & Lafon, S. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.006 · Cited by 2,380 · see citing works
Networks
Newman, M. E. J. (2018) · doi:10.1093/oso/9780198805090.001.0001 · Cited by 2,317 · see citing works
Topology and data
Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302 · cited 3× · see citing works
“When data is given as a point cloud, one needs to determine what is the appropriate filtration parameter and corresponding complex to build [51, 87, 88, 110].”
Background
Elements of Algebraic Topology
Munkres, J. R. (2018) · CRC Press eBooks · doi:10.1201/9780429493911 · Cited by 2,113 · see citing works
Community detection in networks: a user guide
Fortunato, S., & Hric, D. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.09.002 · Cited by 2,086 · see citing works
Graph Signal Processing: Overview, Challenges, and Applications
Ortega, A., Pascal Frossard, B., Kovačević, J., Moura, J. M. F., & Vandergheynst, P. (2018) · Proceedings of the IEEE · doi:10.1109/jproc.2018.2820126 · Cited by 1,803 · see citing works
Networks beyond pairwise interactions: Structure and dynamics
Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G., & Petri, G. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.05.004 · Cited by 1,739 · see citing works
Computational topology an introduction
Edelsbrunner, H., & Harer, J. (2010) · Cited by 1,718 · see citing works
Computing Persistent Homology
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591 · see citing works
Sync: The Emerging Science of Spontaneous Order
Goldenfeld, N. D. (2004) · Physics Today · doi:10.1063/1.1784276 · Cited by 1,528 · see citing works
Network Science
Barabรกsi, A.-L. (2016) · Cited by 1,375 · see citing works
ergm : A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks
Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M., & Morris, M. (2008) · Journal of Statistical Software · doi:10.18637/jss.v024.i03 · Cited by 1,302 · see citing works
Sync: The Emerging Science of Spontaneous Order
Strogatz, S. H. (2003) · Cited by 1,297 · see citing works
Stability of Persistence Diagrams
Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2007) · Discrete & Computational Geometry · doi:10.1007/s00454-006-1276-5 · Cited by 1,280 · see citing works
Barcodes: the persistent topology of data
Ghrist, R. (2007) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-07-01191-3 · Cited by 1,236 · cited 1× · see citing works
“Thus, for an appropriate choice of basis [282] of the homology groups Hn, a barcode summarizes the information carried by the homology groups and the maps f i,j [51, 109], its persistent homology.”
Background
Networks beyond pairwise interactions: Structure and dynamics
Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J., & Petri, G. (2020) · UCL Discovery (University College London) · Cited by 1,179 · see citing works
Persistence and Smoothness of Invariant Manifolds for Flows
Fenichel, N. (1971) · Indiana University Mathematics Journal · doi:10.1512/iumj.1972.21.21017 · Cited by 1,113 · see citing works
The Kuramoto model in complex networks
Rodrigues, F. A., Peron, T., Ji, P., & Kurths, J. (2015) · Physics Reports · doi:10.1016/j.physrep.2015.10.008 · Cited by 1,026 · see citing works
Simplicial models of social contagion
Iacopini, I., Petri, G., Barrat, A., & Latora, V. (2019) · Nature Communications · doi:10.1038/s41467-019-10431-6 · Cited by 899 · see citing works
Persistent homology—a survey
Edelsbrunner, H., & Harer, J. (2008) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/453/08802 · Cited by 875 · see citing works
Structural Properties of the Caenorhabditis elegans Neuronal Network
Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., & Chklovskii, D. B. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1001066 · Cited by 867 · see citing works
A roadmap for the computation of persistent homology
Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0109-5 · Cited by 769 · see citing works
Self-citation
Beyond pairwise mechanisms of species coexistence in complex communities
Levine, J. M., Bascompte, J., Adler, P. B., & Allesina, S. (2017) · Nature · doi:10.1038/nature22898 · Cited by 737 · see citing works
Theoretical Foundations for Centrality Measures
Friedkin, N. E. (1991) · American Journal of Sociology · doi:10.1086/229694 · Cited by 699 · see citing works
Random walks and diffusion on networks
Masuda, N., Porter, M. A., & Lambiotte, R. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.07.007 · Cited by 661 · see citing works
PageRank Beyond the Web
Gleich, D. F. (2015) · SIAM Review · doi:10.1137/140976649 · Cited by 656 · see citing works
Higher-order interactions stabilize dynamics in competitive network models
Grilli, J., Barabás, G., Smith, M. J., & Allesina, S. (2017) · Nature · doi:10.1038/nature23273 · Cited by 645 · see citing works
Statistical topological data analysis using persistence landscapesPreprint
Bubenik, P. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1207.6437 · Cited by 628 · see citing works
Evolutionary dynamics of higher-order interactions in social networks
Alvarez-Rodriguez, U., Battiston, F., de Arruda, G. F., Moreno, Y., Perc, M., & Latora, V. (2021) · Nature Human Behaviour · doi:10.1038/s41562-020-01024-1 · Cited by 593 · see citing works
Simplicial closure and higher-order link prediction
Benson, A. R., Abebe, R., Schaub, M. T., Jadbabaie, A., & Kleinberg, J. M. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1800683115 · Cited by 548 · see citing works
Self-citation
polymake: a Framework for Analyzing Convex Polytopes
Gawrilow, E., & Joswig, M. (2000) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8438-9_2 · Cited by 548 · see citing works
Topological Data Analysis
Wasserman, L. (2017) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-031017-100045 · Cited by 519 · see citing works
Persistence Images: A Stable Vector Representation of Persistent HomologyPreprint
Adams, H., Chepushtanova, S., Emerson, T., Hanson, E., Kirby, M. J. L., Motta, F. C., Neville, R., Peterson, C., Shipman, P. D., & Ziegelmeier, L. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1507.06217 · Cited by 517 · see citing works
Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival
Nicolau, M. M., Levine, A. J., & Carlsson, G. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1102826108 · Cited by 516 · see citing works
From networks to optimal higher-order models of complex systems
Lambiotte, R., Rosvall, M., & Scholtes, I. (2019) · Nature Physics · doi:10.1038/s41567-019-0459-y · Cited by 487 · see citing works
Hypergraphs and Cellular Networks
Klamt, S., Haus, U., & Theis, F. J. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000385 · Cited by 473 · see citing works
Computing global structural balance in large-scale signed social networks
Facchetti, G., Iacono, G., & Altafini, C. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1109521108 · Cited by 433 · see citing works
Hierarchical structures of amorphous solids characterized by persistent homology
Hiraoka, Y., Nakamura, T., Hirata, A., Escolar, E. G., Matsue, K., & Nishiura, Y. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1520877113 · Cited by 415 · see citing works
An Introduction to Morse Theory
Matsumoto, Y. (2001) · Translations of mathematical monographs · doi:10.1090/mmono/208 · Cited by 408 · see citing works
Evolutionary dynamics of higher-order interactions in social networks
Alvarez-Rodriguez, U., Battiston, F., de Arruda, G. F., Moreno, Y., Perc, M., & Latora, V. (2021) · Zurich Open Repository and Archive (University of Zurich) · doi:10.5167/uzh-214990 · Cited by 402 · see citing works
Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
Reimann, M., Nolte, M., Scolamiero, M., Turner, K., Perin, R., Chindemi, G., Dłotko, P., Levi, R., Hess, K. P., & Markram, H. (2017) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2017.00048 · Cited by 390 · see citing works
Clique topology reveals intrinsic geometric structure in neural correlations
Giusti, C., Pastalkova, E., Curto, C., & Itskov, V. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1506407112 · Cited by 381 · see citing works
A competitive network theory of species diversity
Stefano Allesina, A., & Levine, J. M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1014428108 · Cited by 349 · see citing works
Network control principles predict neuron function in the Caenorhabditis elegans connectome
Yan, G. F., Vértes, P. E., Towlson, E. K., Chew, Y. L., Walker, D. S., Schafer, W. R., & Barabási, A.-Ĺ. (2017) · Nature · doi:10.1038/nature24056 · Cited by 349 · see citing works
Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
Stewart, I. N., Golubitsky, M., & Pivato, M. (2003) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/s1111111103419896 · Cited by 340 · see citing works
Statistical ranking and combinatorial Hodge theory
Jiang, X., Lim, L., Yao, Y., & Yinyu Ye, Y. (2010) · Mathematical Programming · doi:10.1007/s10107-010-0419-x · Cited by 335 · see citing works
Subgraph centrality and clustering in complex hyper-networks
Estrada, E., & Rodriguez-Velazquez, J. A. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.12.002 · Cited by 328 · see citing works
Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes
Millán, A. P., Torres, J. J., & Ginestra Bianconi, A. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.218301 · Cited by 327 · see citing works
Discrete Calculus
Grady, L. J., & Polimeni, J. R. (2010) · Springer eBooks · doi:10.1007/978-1-84996-290-2 · Cited by 327 · see citing works
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching
Skardal, P. S., & Arenas, A. (2020) · Communications Physics · doi:10.1038/s42005-020-00485-0 · Cited by 318 · see citing works
The Why, How, and When of Representations for Complex Systems
Torres, L., Blevins, A. S., Bassett, D. S., & Eliassi‐Rad, T. (2021) · SIAM Review · doi:10.1137/20m1355896 · Cited by 308 · see citing works
Coupling functions: Universal insights into dynamical interaction mechanisms
Stankovski, T., Pereira, T., McClintock, P. V. E., & Stefanovska, A. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.045001 · Cited by 302 · see citing works
The theory of multidimensional persistence
Carlsson, G., & Zomorodian, A. (2007) · Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07 · doi:10.1145/1247069.1247105 · Cited by 299 · see citing works
Continuous-time model of structural balance
Marvel, S. A., Kleinberg, J. M., Kleinberg, R., & Strogatz, S. H. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1013213108 · Cited by 298 · see citing works
Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes
Skardal, P. S., & Arenas, À. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.248301 · Cited by 297 · see citing works
A Concise Course in Algebraic Topology
May, J. P. (1999) · Works - Scholarship, Research, & Creative Expression (Swarthmore College) · Cited by 289 · see citing works
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
Ashwin, P., Coombes, S., & Nicks, R. (2016) · The Journal of Mathematical Neuroscience · doi:10.1186/s13408-015-0033-6 · Cited by 288 · see citing works
Phase reduction approach to synchronisation of nonlinear oscillators
Nakao, H. (2015) · Contemporary Physics · doi:10.1080/00107514.2015.1094987 · Cited by 280 · see citing works
Integrability of a globally coupled oscillator array
Watanabe, S., & Strogatz, S. H. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.2391 · Cited by 279 · see citing works
Dynamic Biological Networks: the Stomatogastric Nervous System
Sillar, K. T. (1993) · Trends in Neurosciences · doi:10.1016/0166-2236(93)90153-d · Cited by 278 · see citing works
Submillisecond Precision of the Input-Output Transformation Function Mediated by Fast Sodium Dendritic Spikes in Basal Dendrites of CA1 Pyramidal Neurons
Ariav, G., Poleg-Polsky, A., & Schiller, J. (2003) · Journal of Neuroscience · doi:10.1523/jneurosci.23-21-07750.2003 · Cited by 276 · see citing works
Random hypergraphs and their applications
Ghoshal, G., Zlatić, V., Caldarelli, G., & Newman, M. E. J. (2009) · Physical Review E · doi:10.1103/physreve.79.066118 · Cited by 273 · see citing works
Zigzag persistent homology and real-valued functions
Carlsson, G., de Silva, V., & Morozov, D. (2009) · Proceedings of the twenty-fifth annual symposium on Computational geometry · doi:10.1145/1542362.1542408 · Cited by 272 · see citing works
Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach
Gauvin, L., Panisson, A., & Cattuto, C. (2014) · PLoS ONE · doi:10.1371/journal.pone.0086028 · Cited by 272 · see citing works
The Theory of Multidimensional Persistence
Carlsson, G., & Zomorodian, A. (2009) · Discrete & Computational Geometry · doi:10.1007/s00454-009-9176-0 · Cited by 270 · see citing works
Topology of viral evolution
Chan, J. M., Carlsson, G., & Rabadan, R. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1313480110 · Cited by 269 · see citing works
Zigzag Persistence
Carlsson, G., & de Silva, V. (2010) · Foundations of Computational Mathematics · doi:10.1007/s10208-010-9066-0 · Cited by 263 · see citing works
Persistent homology analysis of brain artery trees
Bendich, P. L., Marron, J. S., Miller, E., Pieloch, A., & Skwerer, S. (2016) · The Annals of Applied Statistics · doi:10.1214/15-aoas886 · Cited by 262 · see citing works
Harmonische Funktionen und Randwertaufgaben in einem Komplex
Eckmann, B. (1944) · Commentarii Mathematici Helvetici · doi:10.1007/bf02566245 · Cited by 261 · see citing works
Social contagion models on hypergraphs
de Arruda, G. F., Petri, G., & Moreno, Y. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023032 · Cited by 260 · see citing works
Manifold Learning Theory and Applications
Ma, Y., & Fu, Y. (2011) · CRC Press eBooks · doi:10.1201/b11431 · Cited by 258 · see citing works
Homological Connectivity Of Random 2-Complexes
Linial, N., & Meshulam, R. (2006) · COMBINATORICA · doi:10.1007/s00493-006-0027-9 · Cited by 256 · see citing works
The shape of collaborations
Patania, A., Petri, G., & Vaccarino, F. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0114-8 · Cited by 254 · see citing works
Persistent homology analysis of protein structure, flexibility, and folding
Xia, K., & Wei, G. (2014) · International Journal for Numerical Methods in Biomedical Engineering · doi:10.1002/cnm.2655 · Cited by 254 · see citing works
Confidence sets for persistence diagrams
Fasy, B. T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S., & Singh, A. (2014) · The Annals of Statistics · doi:10.1214/14-aos1252 · Cited by 251 · see citing works
Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
Bick, C., Goodfellow, M., Laing, C. R., & Martens, E. A. (2020) · The Journal of Mathematical Neuroscience · doi:10.1186/s13408-020-00086-9 · Cited by 251 · see citing works
Self-citation
Configuring Random Graph Models with Fixed Degree Sequences
Fosdick, B. K., Larremore, D. B., Nishimura, J., & Ugander, J. (2018) · SIAM Review · doi:10.1137/16m1087175 · Cited by 246 · see citing works
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching
Skardal, P. S., & Arenas, À. (2020) · Rovira & Virgili repository · Cited by 243 · see citing works
A review of stochastic block models and extensions for graph clustering
Lee, C., & Wilkinson, D. J. (2019) · Applied Network Science · doi:10.1007/s41109-019-0232-2 · Cited by 235 · see citing works
Hodge Laplacians on Graphs
Lim, L. (2020) · SIAM Review · doi:10.1137/18m1223101 · Cited by 234 · see citing works
Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
Schaub, M. T., Benson, A. R., Horn, P., Lippner, G., & Jadbabaie, A. (2020) · SIAM Review · doi:10.1137/18m1201019 · Cited by 224 · see citing works
Self-citation
Topological Signal Processing Over Simplicial Complexes
Barbarossa, S., & Sardellitti, S. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.2981920 · Cited by 224 · see citing works
A review of stochastic block models and extensions for graph clustering
Lee, C. M., & Wilkinson, D. J. (2019) · Lancaster EPrints (Lancaster University) · Cited by 224 · see citing works
The dynamics ofn weakly coupled identical oscillators
Ashwin, P., & Swift, J. W. (1992) · Journal of Nonlinear Science · doi:10.1007/bf02429852 · Cited by 223 · see citing works
A concise course in algebraic topology
(1999) · Computers & Mathematics with Applications · doi:10.1016/s0898-1221(99)91199-9 · Cited by 218 · see citing works
Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
Courtney, O. T., & Ginestra Bianconi, A. (2016) · Physical review. E · doi:10.1103/physreve.93.062311 · Cited by 217 · see citing works
The importance of the whole: Topological data analysis for the network neuroscientist
Sizemore, A. E., Phillips‐Cremins, J. E., Ghrist, R., & Bassett, D. S. (2018) · Network Neuroscience · doi:10.1162/netn_a_00073 · Cited by 216 · see citing works
Spectra of combinatorial Laplace operators on simplicial complexes
Horak, D., & Jost, J. (2013) · Advances in Mathematics · doi:10.1016/j.aim.2013.05.007 · Cited by 216 · see citing works
Elementary Applied Topology
Ghrist, R. (2014) · Cited by 215 · see citing works
Topology of 3-manifolds and related topics
(1962) · Journal of the Franklin Institute · doi:10.1016/0016-0032(62)90835-9 · Cited by 215 · see citing works
Random walks on hypergraphs
Carletti, T., Battiston, F., Cencetti, G., & Fanelli, D. (2020) · Physical review. E · doi:10.1103/physreve.101.022308 · Cited by 214 · see citing works
High-order social interactions in groups of mice
Shemesh, Y., Sztainberg, Y., Forkosh, O., Shlapobersky, T., Chen, A., & Schneidman, E. (2013) · eLife · doi:10.7554/elife.00759 · Cited by 213 · see citing works
Simplicial models of social contagion
Iacopini, I., Petri, G., Barrat, A., & Latora, V. (2019) · RePEc: Research Papers in Economics · Cited by 209 · see citing works
ELEMENTARY CONCEPTS OF TOPOLOGY
Alexandroff, P. (1961) · CERN Document Server (European Organization for Nuclear Research) · Cited by 208 · see citing works
Exponential random graph () models for affiliation networks
Wang, P., Sharpe, K., Robins, G. L., & Pattison, P. E. (2008) · Social Networks · doi:10.1016/j.socnet.2008.08.002 · Cited by 204 · see citing works
Multiorder Laplacian for synchronization in higher-order networks
Lucas, M., Cencetti, G., & Battiston, F. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033410 · Cited by 198 · see citing works
The mathematics behind chimera states
Omel’chenko, O. E. (2018) · Nonlinearity · doi:10.1088/1361-6544/aaaa07 · Cited by 192 · see citing works
Revealing networks from dynamics: an introduction
Timme, M., & Casadiego, J. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/34/343001 · Cited by 190 · see citing works
Topology of random clique complexes
Kahle, M. (2008) · Discrete Mathematics · doi:10.1016/j.disc.2008.02.037 · Cited by 190 · see citing works
Dynamics of the globally coupled complex Ginzburg-Landau equation
Hakim, V., & Rappel, W. (1992) · Physical Review A · doi:10.1103/physreva.46.r7347 · Cited by 190 · see citing works
Topological Data Analysis of Biological Aggregation Models
Topaz, C. M., Ziegelmeier, L., & Halverson, T. (2015) · PLoS ONE · doi:10.1371/journal.pone.0126383 · Cited by 187 · see citing works
Exotic states in a simple network of nanoelectromechanical oscillators
Matheny, M. H., Emenheiser, J., Fon, W., Chapman, A., Salova, A., Rohden, M., Li, J., de Badyn, M. H., Pósfai, M., Dueñas‐Osorio, L., et al. (2019) · Science · doi:10.1126/science.aav7932 · Cited by 187 · see citing works
Generative hypergraph clustering: From blockmodels to modularity
Chodrow, P. S., Veldt, N., & Benson, A. R. (2021) · Science Advances · doi:10.1126/sciadv.abh1303 · Cited by 182 · see citing works
Hypermaps versus bipartite maps
Walsh, T. R. S. (1975) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(75)90042-8 · Cited by 180 · see citing works
Beyond pairwise energies: Efficient optimization for higher-order MRFs
Komodakis, N., & Nikos Paragios, A. (2009) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2009.5206846 · Cited by 180 · see citing works
A Topological Representation of Branching Neuronal Morphologies
Kanari, L., Dłotko, P., Scolamiero, M., Levi, R., Shillcock, J. C., Hess, K. P., & Markram, H. (2017) · Neuroinformatics · doi:10.1007/s12021-017-9341-1 · Cited by 179 · see citing works
The many facets of community detection in complex networks
Schaub, M. T., Delvenne, J.-C., Rosvall, M., & Lambiotte, R. (2017) · Applied Network Science · doi:10.1007/s41109-017-0023-6 · Cited by 171 · see citing works
Self-citation
Flows and Decompositions of Games: Harmonic and Potential Games
Candogan, O., Menache, I., Ozdaglar, A., & Parrilo, P. A. (2011) · Mathematics of Operations Research · doi:10.1287/moor.1110.0500 · Cited by 171 · see citing works
Arguments in Favor of Higher Order Interactions
Abrams, P. A. (1983) · The American Naturalist · doi:10.1086/284111 · Cited by 166 · see citing works
A User’s Guide to Topological Data Analysis
Munch, E. (2017) · Journal of Learning Analytics · doi:10.18608/jla.2017.42.6 · Cited by 163 · see citing works
Multibody interactions and nonlinear consensus dynamics on networked systems
Neuhäuser, L., Mellor, A., & Lambiotte, R. (2020) · Physical review. E · doi:10.1103/physreve.101.032310 · Cited by 160 · see citing works
Algebraic Statistics
Sullivant, S. (2012) · Graduate studies in mathematics · doi:10.1090/gsm/194 · Cited by 158 · see citing works
Network dynamics of coupled oscillators and phase reduction techniques
Pietras, B., & Daffertshofer, A. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.06.001 · Cited by 154 · see citing works
Dualities in persistent (co)homology
de Silva, V., Morozov, D., & Vejdemo‐Johansson, M. (2011) · Inverse Problems · doi:10.1088/0266-5611/27/12/124003 · Cited by 152 · see citing works
Random Geometric Complexes
Kahle, M. (2011) · Discrete & Computational Geometry · doi:10.1007/s00454-010-9319-3 · Cited by 150 · see citing works
Topological data analysis of contagion maps for examining spreading processes on networks
Taylor, D., Klimm, F., Harrington, H. A., Kramár, M., Mischaikow, K., Porter, M. A., & Mucha, P. J. (2015) · Nature Communications · doi:10.1038/ncomms8723 · Cited by 148 · see citing works
Self-citation
Topology of random simplicial complexes: a survey
Kahle, M. (2014) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/620/12367 · Cited by 144 · see citing works
Signal processing on higher-order networks: Livin’ on the edge... and beyond
Schaub, M. T., Zhu, Y., Seby, J.-B., Roddenberry, T. M., & Segarra, S. (2021) · Signal Processing · doi:10.1016/j.sigpro.2021.108149 · Cited by 142 · see citing works
Self-citation
Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems
Chazottes, J.-R., & Fernandez, B. (2005) · Lecture notes in physics · doi:10.1007/b103930 · Cited by 141 · see citing works
Cambridge University Press
Jefcoate, G. (2017) · Lexikon des gesamten Buchwesens Online · doi:10.1163/9789004337862_lgbo_com_030061 · Cited by 139 · see citing works
Pore configuration landscape of granular crystallization
Saadatfar, M., Takeuchi, H., Robins, V., Francois, N., & Hiraoka, Y. (2017) · Nature Communications · doi:10.1038/ncomms15082 · Cited by 134 · see citing works
Configuration models of random hypergraphs
Chodrow, P. S. (2020) · Journal of Complex Networks · doi:10.1093/comnet/cnaa018 · Cited by 134 · see citing works
Limit theorems for Betti numbers of random simplicial complexes
Kahle, M., & Meckes, E. (2013) · Homology Homotopy and Applications · doi:10.4310/hha.2013.v15.n1.a17 · Cited by 132 · see citing works
Topology of random geometric complexes: a survey
Bobrowski, O., & Kahle, M. (2018) · Journal of Applied and Computational Topology · doi:10.1007/s41468-017-0010-0 · Cited by 132 · see citing works
Component structure in the evolution of random hypergraphs
Schmidt, J. P., & Shamir, E. (1985) · COMBINATORICA · doi:10.1007/bf02579445 · Cited by 130 · see citing works
Homological connectivity of random k ‐dimensional complexes
Meshulam, R., & Wallach, N. R. (2008) · Random Structures and Algorithms · doi:10.1002/rsa.20238 · Cited by 129 · see citing works
Introduction to the R package TDAPreprint
Fasy, B. T., Kim, J., Lecci, F., & Maria, C. (2014) · arXiv (Cornell University) · doi:10.4230/lipics.socg.2020.19 · Cited by 125 · see citing works
SIS Epidemic Propagation on Hypergraphs
Bodó, Á., Katona, G. Y., & Šimon, P. (2016) · Bulletin of Mathematical Biology · doi:10.1007/s11538-016-0158-0 · Cited by 124 · see citing works
Persistent homology of time-dependent functional networks constructed from coupled time series
Stolz, B. J., Harrington, H. A., & Porter, M. A. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4978997 · Cited by 123 · see citing works
Self-citation
Coupled dynamics on hypergraphs: Master stability of steady states and synchronization
Mulas, R., Kuehn, C., & Jost, J. (2020) · Physical review. E · doi:10.1103/physreve.101.062313 · Cited by 121 · see citing works
Distributed Coverage Verification in Sensor Networks Without Location Information
Tahbaz-Salehi, A., & Jadbabaie, A. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2047541 · Cited by 117 · see citing works
What can topology tell us about the neural code?
Curto, C. (2016) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1554 · Cited by 117 · see citing works
Conley Index
Mischaikow, K., & Mrożek, M. (2002) · Handbook of dynamical systems · doi:10.1016/s1874-575x(02)80030-3 · Cited by 112 · see citing works
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
Bick, C., Ashwin, P., & Rodrigues, A. (2016) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4958928 · Cited by 111 · see citing works
Self-citation
Weisfeiler and Lehman Go Topological: Message Passing Simplicial NetworksPreprint
Bodnar, C., Frasca, F., Wang, Y. G., Otter, N., Montúfar, G., Lió, P., & Bronstein, M. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.03212 · Cited by 110 · see citing works
Multistable Attractors in a Network of Phase Oscillators with Three-Body Interactions
Tanaka, T., & Aoyagi, T. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.224101 · Cited by 109 · see citing works
Multilinear PageRank
Gleich, D. F., Lim, L., & Yu, Y. (2015) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/140985160 · Cited by 109 · see citing works
8. Logit Models for Affiliation Networks
Skvoretz, J. V., & Faust, K. (1999) · Sociological Methodology · doi:10.1111/0081-1750.00066 · Cited by 107 · see citing works
A hypergraph model of social tagging networks
Zhang, Z.-K., & Liu, C. (2010) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2010/10/p10005 · Cited by 107 · see citing works
A universal route to explosive phenomena
Kuehn, C., & Bick, C. (2021) · Science Advances · doi:10.1126/sciadv.abe3824 · Cited by 106 · see citing works
Self-citation
Topological analysis of data
Patania, A., Vaccarino, F., & Petri, G. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0104-x · Cited by 105 · see citing works
Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation
León, I., & Pazó, D. (2019) · Physical review. E · doi:10.1103/physreve.100.012211 · Cited by 105 · see citing works
Revealing Networks from Dynamics – An IntroductionPreprint
Timme, M., & Casadiego, J. (2014) · Cited by 104 · see citing works
The phase transition in a random hypergraph
Karoński, M., & Łuczak, T. (2002) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(01)00464-2 · Cited by 104 · see citing works
Sharp vanishing thresholds for cohomology of random flag complexes
Kahle, M. (2014) · Annals of Mathematics · doi:10.4007/annals.2014.179.3.5 · Cited by 103 · see citing works
Topological Data Analysis for Genomics and Evolution
Rabadán, R., & Blumberg, A. J. (2019) · Cambridge University Press eBooks · doi:10.1017/9781316671665 · Cited by 101 · see citing works
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Benson, A. R., Gleich, D. F., & Leskovec, J. (2015) · SIAM International Conference on Data Mining · doi:10.1137/1.9781611974010.14 · Cited by 100 · see citing works
Spectral Properties of Hypergraph Laplacian and Approximation Algorithms
Chan, T.-H. H., Louis, A., Tang, Z. G., & Zhang, C. (2018) · Journal of the ACM · doi:10.1145/3178123 · Cited by 98 · see citing works
Statistical and computational phase transitions in spiked tensor estimation
Lesieur, T., Miolane, L., Lelarge, M., Krząkała, F., & Zdeborová, L. (2017) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2017.8006580 · Cited by 94 · see citing works
Adaptive voter model on simplicial complexes
Horstmeyer, L., & Kuehn, C. (2020) · Physical review. E · doi:10.1103/physreve.101.022305 · Cited by 94 · see citing works
Dynamical systems on hypergraphs
Carletti, T., Fanelli, D., & Nicoletti, S. (2020) · Journal of Physics Complexity · doi:10.1088/2632-072x/aba8e1 · Cited by 94 · see citing works
Interactive Visualization of 2-D Persistence ModulesPreprint
Lesnick, M., & Wright, M. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1512.00180 · Cited by 93 · see citing works
Node and edge nonlinear eigenvector centrality for hypergraphs
Tudisco, F., & Higham, D. J. (2021) · Communications Physics · doi:10.1038/s42005-021-00704-2 · Cited by 93 · see citing works
Consistency of spectral hypergraph partitioning under planted partition model
Ghoshdastidar, D., & Dukkipati, A. (2017) · The Annals of Statistics · doi:10.1214/16-aos1453 · Cited by 91 · see citing works
Directed Algebraic Topology and Concurrency
Fajstrup, L., Goubault, É., Haucourt, E., Mimram, S., & Raußen, M. (2016) · Springer eBooks · doi:10.1007/978-3-319-15398-8 · Cited by 91 · see citing works
A Unified Dynamic Model for Learning, Replay, and Sharp-Wave/Ripples
Jahnke, S., Timme, M., & Memmesheimer, R.-M. (2015) · Journal of Neuroscience · doi:10.1523/jneurosci.3977-14.2015 · Cited by 89 · see citing works
The shape of things to come: Topological data analysis and biology, from molecules to organisms
Amézquita, E. J., Quigley, M., Ophelders, T., Munch, E., & Chitwood, D. H. (2020) · Developmental Dynamics · doi:10.1002/dvdy.175 · Cited by 87 · see citing works
37th International Symposium on Computational Geometry (SoCG 2021)
Buchin, K., & de Verdière, É. C. (2021) · HAL · Cited by 87 · see citing works
Topological data analysis of zebrafish patterns
McGuirl, M. R., Volkening, A., & Sandstede, B. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1917763117 · Cited by 86 · see citing works
Quantitative prediction of intermittent high-frequency oscillations in neural networks with supralinear dendritic interactions
Memmesheimer, R.-M. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0909615107 · Cited by 85 · see citing works
Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators
Ashwin, P., & Rodrigues, A. (2016) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2016.02.009 · Cited by 85 · see citing works
Construction of and efficient sampling from the simplicial configuration model
Young, J.-G., Petri, G., Vaccarino, F., & Patania, A. (2017) · Physical review. E · doi:10.1103/physreve.96.032312 · Cited by 84 · see citing works
Path Complexes and their Homologies
Grigor'yan, A. A., Lin, Y., Muranov, Y. V., & Yau, S. (2020) · Journal of Mathematical Sciences · doi:10.1007/s10958-020-04897-9 · Cited by 84 · see citing works
Simplicial complexes: Spectrum, homology and random walks
Parzanchevski, O., & Rosenthal, R. (2016) · Random Structures and Algorithms · doi:10.1002/rsa.20657 · Cited by 83 · see citing works
The fundamental group of random 2-complexes
Babson, E. K., Hoffman, C., & Kahle, M. (2010) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-2010-00677-7 · Cited by 80 · see citing works
Hyper-edges and multidimensional centrality
Bonacich, P., Holdren, A. C., & Johnston, M. (2004) · Social Networks · doi:10.1016/j.socnet.2004.01.001 · Cited by 80 · see citing works
Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications
Zhang, S., Ding, Z., & Cui, S. R. (2019) · IEEE Internet of Things Journal · doi:10.1109/jiot.2019.2950213 · Cited by 80 · see citing works
Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors
Vipond, O., Bull, J. A., Macklin, P. S., Tillmann, U., Pugh, C. W., Byrne, H. M., & Harrington, H. A. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2102166118 · Cited by 76 · see citing works
Self-citation
Directed hypergraphs: Introduction and fundamental algorithms—A survey
Ausiello, G., & Laura, L. (2016) · Theoretical Computer Science · doi:10.1016/j.tcs.2016.03.016 · Cited by 76 · see citing works
Isoperimetric inequalities in simplicial complexes
Parzanchevski, O., Rosenthal, R., & Tessler, R. J. (2015) · COMBINATORICA · doi:10.1007/s00493-014-3002-x · Cited by 75 · see citing works
Hypothesis testing for topological data analysis
Robinson, A. P., & Turner, K. (2017) · Journal of Applied and Computational Topology · doi:10.1007/s41468-017-0008-7 · Cited by 72 · see citing works
Spectral Gaps of Random Graphs and Applications
Hoffman, C., Kahle, M., & Paquette, E. (2019) · International Mathematics Research Notices · doi:10.1093/imrn/rnz077 · Cited by 72 · see citing works
Reconstructing effective phase connectivity of oscillator networks from observations
Kralemann, B., PIKOVSKY, A. S., & Rosenblum, M. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/8/085013 · Cited by 71 · see citing works
Persistent Path Homology of Directed Networks
Chowdhury, S., & Mémoli, F. (2018) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611975031.75 · Cited by 71 · see citing works
Subsampling Methods for Persistent HomologyPreprint
Chazal, F., Fasy, B. T., Lecci, F., Michel, B., Rinaldo, A., & Wasserman, L. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1406.1901 · Cited by 70 · see citing works
Flow-Based Network Analysis of the Caenorhabditis elegans Connectome
Bacik, K. A., Schaub, M. T., Beguerisse-Díaz, M., Billeh, Y. N., & Barahona, M. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005055 · Cited by 67 · see citing works
Self-citation
Graph-based Semi-Supervised & Active Learning for Edge Flows
Jia, J., Schaub, M. T., Segarra, S., & Benson, A. R. (2019) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3292500.3330872 · Cited by 67 · see citing works
Self-citation
Computing Multidimensional Persistence
Carlsson, G., Singh, G., & Zomorodian, A. J. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-10631-6_74 · Cited by 65 · see citing works
Maximally persistent cycles in random geometric complexes
Bobrowski, O., Kahle, M., & Škraba, P. (2017) · The Annals of Applied Probability · doi:10.1214/16-aap1232 · Cited by 65 · see citing works
Random Simplicial Complexes
Costa, A., & Färber, M. (2016) · Springer INdAM series · doi:10.1007/978-3-319-31580-5_6 · Cited by 63 · see citing works
Consistency of Spectral Partitioning of Uniform Hypergraphs under Planted Partition Model
Ghoshdastidar, D., & Dukkipati, A. (2014) · Cited by 61 · see citing works
2014 International Conference on Intelligent Networking and Collaborative Systems
(2014) · doi:10.1109/incos33065.2014 · Cited by 60 · see citing works
Generalizing the hypergraph Laplacian via a diffusion process with mediators
Chan, T.-H. H., & Liang, Z. (2019) · Theoretical Computer Science · doi:10.1016/j.tcs.2019.07.024 · Cited by 59 · see citing works
Simplicial Neural NetworksPreprint
Ebli, S., Defferrard, M., & Spreemann, G. (2020) · arXiv (Cornell University) · doi:10.5281/zenodo.4146877 · Cited by 58 · see citing works
FLOW SMOOTHING AND DENOISING: GRAPH SIGNAL PROCESSING IN THE EDGE-SPACE
Schaub, M. T., & Segarra, S. (2018) · IEEE Global Conference on Signal and Information Processing · doi:10.1109/globalsip.2018.8646701 · Cited by 57 · see citing works
Self-citation
Annotated hypergraphs: models and applications
Chodrow, P. S., & Mellor, A. (2020) · Applied Network Science · doi:10.1007/s41109-020-0252-y · Cited by 55 · see citing works
Computing Persistent Homology of Directed Flag Complexes
Lütgehetmann, D., Govc, D., Smith, J. P., & Levi, R. (2020) · Algorithms · doi:10.3390/a13010019 · Cited by 54 · see citing works

Flagged first, then by citations

12 of the 316 references couldn’t be matched to a known paper.

Sorted by citations

The physics of higher-order interactions in complex systems
Battiston, F., Amico, E., Barrat, A., Bianconi, G., de Arruda, G. F., Franceschiello, B., Iacopini, I., Kéfi, S., Latora, V., Moreno, Y., et al. (2021) · Nature Physics · doi:10.1038/s41567-021-01371-4 · Cited by 954 · see citing works
Dynamics on higher-order networks: a review
Majhi, S., Perc, M., & Ghosh, D. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0043 · Cited by 575 · see citing works
Synchronization in Hindmarsh–Rose neurons subject to higher-order interactions
Parastesh, F., Mehrabbeik, M., Rajagopal, K., Jafari, S., & Perc, M. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0079834 · Cited by 159 · see citing works
Contagion dynamics on higher-order networks
de Arruda, G. F., Aleta, A., & Moreno, Y. (2024) · Nature Reviews Physics · doi:10.1038/s42254-024-00733-0 · Cited by 109 · see citing works
Simplicial contagion in temporal higher-order networks
Chowdhary, S., Kumar, A., Cencetti, G., Iacopini, I., & Battiston, F. (2021) · Journal of Physics Complexity · doi:10.1088/2632-072x/ac12bd · Cited by 99 · see citing works
Collective dynamics of swarmalators with higher-order interactions
Anwar, M. S., Sar, G. K., Perc, M., & Ghosh, D. (2024) · Communications Physics · doi:10.1038/s42005-024-01556-2 · Cited by 83 · see citing works
Topology shapes dynamics of higher-order networks
Millán, A. P., Sun, H., Giambagli, L., Muolo, R., Carletti, T., Torres, J. J., Radicchi, F., Kurths, J., & Bianconi, G. (2025) · Nature Physics · doi:10.1038/s41567-024-02757-w · Cited by 81 · see citing works
Fast unfolding of communities in large networks: 15 years later
Blondel, V. D., Guillaume, J., & Lambiotte, R. (2024) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ad6139 · Cited by 76 · see citing works
Intralayer and interlayer synchronization in multiplex network with higher-order interactions
Anwar, M. S., & Ghosh, D. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0074641 · Cited by 74 · see citing works
The dynamic nature of percolation on networks with triadic interactions
Sun, H., Radicchi, F., Kurths, J., & Bianconi, G. (2023) · Nature Communications · doi:10.1038/s41467-023-37019-5 · Cited by 71 · see citing works
Hyperedge overlap drives explosive transitions in systems with higher-order interactions
Malizia, F., Lamata-Otín, S., Frasca, M., Latora, V., & Gómez‐Gardeñes, J. (2025) · Nature Communications · doi:10.1038/s41467-024-55506-1 · Cited by 70 · see citing works
Group interactions modulate critical mass dynamics in social convention
Iacopini, I., Petri, G., Baronchelli, A., & Barrat, A. (2022) · Communications Physics · doi:10.1038/s42005-022-00845-y · Cited by 69 · see citing works
Status quo and challenges in air transport management research
Wandelt, S., Antoniou, C., Birolini, S., Delahaye, D., Dresner, M., Fu, X., Gössling, S., Hong, S.-J., Odoni, A. R., Zanin, M., et al. (2024) · Journal of the Air Transport Research Society · doi:10.1016/j.jatrs.2024.100014 · Cited by 67 · see citing works
“This could be tackled by the recent concept of higher-order networks ( Bianconi, 2021; Bick et al., 2023 ).”
Background
Redefining Roles: A Paradigm Shift in Tryptophan–Kynurenine Metabolism for Innovative Clinical Applications
Tanaka, M., Szabó, Á., & Vécsei, L. (2024) · International Journal of Molecular Sciences · doi:10.3390/ijms252312767 · Cited by 62 · see citing works
Pattern dynamics analysis and application of West Nile virus spatiotemporal models based on higher-order network topology
Zhu, L., & Zheng, T. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01501-6 · Cited by 61 · see citing works
Optimal control of spatial diseases spreading in networked reaction–diffusion systems
Sun, G., He, R., Hou, L.-F., Luo, X., Gao, S., Chang, L., Wang, Y., & Zhang, Z. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.01.005 · Cited by 58 · see citing works
Synchronization in simplicial complexes of memristive Rulkov neurons
Mehrabbeik, M., Jafari, S., & Perc, M. (2023) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2023.1248976 · Cited by 57 · see citing works
A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs
Hickok, A., Kureh, Y. H., Brooks, H. Z., Feng, M., & Porter, M. A. (2022) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/21m1399427 · Cited by 55 · see citing works
Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
Shi, J., & Zhu, L. (2025) · Journal of Mathematical Physics · doi:10.1063/5.0211728 · Cited by 55 · see citing works
Hyper-cores promote localization and efficient seeding in higher-order processes
Mancastroppa, M., Iacopini, I., Petri, G., & Barrat, A. (2023) · Nature Communications · doi:10.1038/s41467-023-41887-2 · Cited by 51 · see citing works
A system model of three-body interactions in complex networks: consensus and conservation
Shang, Y. (2022) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2021.0564 · Cited by 50 · see citing works
The topological Dirac equation of networks and simplicial complexes
Bianconi, G. (2021) · Journal of Physics Complexity · doi:10.1088/2632-072x/ac19be · Cited by 48 · see citing works
Graph neural networks for image‐guided disease diagnosis: A review
Zhang, L., Zhao, Y., Che, T., Li, S., & Wang, X. (2023) · iRadiology · doi:10.1002/ird3.20 · Cited by 47 · see citing works
Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
Zhang, Y., Skardal, P. S., Battiston, F., Petri, G., & Lucas, M. (2024) · Science Advances · doi:10.1126/sciadv.ado8049 · Cited by 41 · see citing works
Simplicial Convolutional Filters
Yang, M., Isufi, E., Schaub, M. T., & Leus, G. J. T. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3207045 · Cited by 40 · see citing works
Self-citation
Synchronization of phase oscillators on complex hypergraphs
Adhikari, S., Restrepo, J. G., & Skardal, P. S. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0116747 · Cited by 39 · see citing works
Higher-order interactions induce anomalous transitions to synchrony
León, I., Muolo, R., Hata, S., & Nakao, H. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0176748 · Cited by 35 · see citing works
Hypergraph reconstruction from dynamics
Delabays, R., Pasquale, G. D., Dörfler, F., & Zhang, Y. (2025) · Nature Communications · doi:10.1038/s41467-025-57664-2 · Cited by 35 · see citing works
Dynamic propagation and control of a West Nile virus model based on higher-order temporal network structure
Zhu, L., & Li, Y. (2025) · Physical review. E · doi:10.1103/xwt2-f1d3 · Cited by 34 · see citing works
Dirac synchronization is rhythmic and explosive
Calmon, L., Restrepo, J. G., Torres, J. J., & Bianconi, G. (2022) · Communications Physics · doi:10.1038/s42005-022-01024-9 · Cited by 32 · see citing works
Turing patterns on discrete topologies: from networks to higher-order structures
Muolo, R., Giambagli, L., Nakao, H., Fanelli, D., & Carletti, T. (2024) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2024.0235 · Cited by 30 · see citing works
Chimeric states induced by higher-order interactions in coupled prey–predator systems
Ghosh, R., Verma, U. K., Jalan, S., & Shrimali, M. D. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0213288 · Cited by 29 · see citing works
Dirac signal processing of higher-order topological signals
Calmon, L., Schaub, M. T., & Bianconi, G. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acf33c · Cited by 29 · see citing works
Self-citation
Synchronization of multi-directed hypergraphs via adaptive pinning control
Li, K., Lin, Y., & Wang, J. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.115000 · Cited by 27 · see citing works
Chimera states in coupled pendulum with higher-order interaction
Li, X., Ghosh, D., & Lei, Y. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113325 · Cited by 27 · see citing works
When can higher‐order interactions produce stable coexistence?
Gibbs, T. L., Gellner, G., Levin, S. A., McCann, K. S., Hastings, A., & Levine, J. M. (2024) · Ecology Letters · doi:10.1111/ele.14458 · Cited by 27 · see citing works
Not your private tête-à-tête: leveraging the power of higher-order networks to study animal communication
Iacopini, I., Foote, J. R., Fefferman, N. H., Derryberry, E. P., & Silk, M. J. (2024) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2023.0190 · Cited by 26 · see citing works
Simplices-based higher-order enhancement graph neural network for multi-behavior recommendation
Hao, Q., Wang, C., Xiao, Y., & Lin, H. (2024) · Information Processing & Management · doi:10.1016/j.ipm.2024.103790 · Cited by 26 · see citing works
Toward Principles of Brain Network Organization and Function
Kulkarni, S., & Bassett, D. S. (2025) · Annual Review of Biophysics · doi:10.1146/annurev-biophys-030722-110624 · Cited by 26 · see citing works
Information theory for complex systems scientists: What, why, and how
Varley, T. F. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.09.007 · Cited by 26 · see citing works
Higher‐order functional connectivity analysis of resting‐state functional magnetic resonance imaging data using multivariate cumulants
Hindriks, R., Broeders, T. A. A., Schoonheim, M. M., Douw, L., Santos, F. A. N., van Wieringen, W. N., & Tewarie, P. K. B. (2024) · Human Brain Mapping · doi:10.1002/hbm.26663 · Cited by 26 · see citing works
On the higher-order smallest ring-star network of Chialvo neurons under diffusive couplings
Nair, A. S., Ghosh, I., Fatoyinbo, H. O., & Muni, S. S. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0217017 · Cited by 25 · see citing works
Collective dynamics on higher-order networks
Battiston, F., Bick, C., Lucas, M., Millán, A. P., Skardal, P. S., & Zhang, Y. (2026) · Nature Reviews Physics · doi:10.1038/s42254-025-00916-3 · Cited by 25 · see citing works
Self-citation
Percolation Theories for Quantum Networks
Meng, X., Hu, X., Tian, Y., Dong, G., Lambiotte, R., Gao, J., & Havlin, S. (2023) · Entropy · doi:10.3390/e25111564 · Cited by 25 · see citing works
Topology and dynamics of higher-order multiplex networks
Krishnagopal, S., & Bianconi, G. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114296 · Cited by 25 · see citing works
Hypergraph Transformer for Semi-Supervised Classification
Liu, Z., Tang, B., Ye, Z., Dong, X., Chen, S., & Wang, Y. (2024) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp48485.2024.10446248 · Cited by 25 · see citing works
Real-Time Trading System Based on Selections of Potentially Profitable, Uncorrelated, and Balanced Stocks by NP-Hard Combinatorial Optimization
Tatsumura, K., Hidaka, R., Nakayama, J., Kashimata, T., & Yamasaki, M. (2023) · IEEE Access · doi:10.1109/access.2023.3326816 · Cited by 24 · see citing works
Inheritance and protection of intangible cultural heritage in drama category based on AI human–computer interaction and digital technology
Ren, J. (2025) · Discover Artificial Intelligence · doi:10.1007/s44163-025-00268-y · Cited by 23 · see citing works
Coevolution of multipathogens on higher-order networks
Gao, Y., Li, J., Gao, F., & Wang, W. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.117588 · Cited by 23 · see citing works
Encapsulation structure and dynamics in hypergraphs
LaRock, T., & Lambiotte, R. (2023) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad0b39 · Cited by 23 · see citing works
A unified framework for simplicial Kuramoto models
Nurisso, M., Arnaudon, A., Lucas, M., Peach, R. L., Expert, P., Vaccarino, F., & Petri, G. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0169388 · Cited by 23 · see citing works
Multi-population phase oscillator networks with higher-order interactions
Bick, C., Böhle, T., & Kuehn, C. (2022) · Nonlinear Differential Equations and Applications NoDEA · doi:10.1007/s00030-022-00796-x · Cited by 23 · see citing works
Self-citation
Hyperedge overlap drives synchronizability of systems with higher-order interactions
Lamata-Otín, S., Malizia, F., Latora, V., Frasca, M., & Gómez‐Gardeñes, J. (2025) · Physical review. E · doi:10.1103/physreve.111.034302 · Cited by 22 · see citing works
Optimal Synchronization of Higher-Order Dynamical Networks
Chen, G. (2025) · Artificial Intelligence Science and Engineering · doi:10.23919/aise.2025.000003 · Cited by 22 · see citing works
Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity
Duchet, B., Bick, C., & Byrne, Á. (2023) · Neural Computation · doi:10.1162/neco_a_01601 · Cited by 22 · see citing works
Self-citation
An information-theoretic approach to build hypergraphs in psychometrics
Marinazzo, D., Roozendaal, J. V., Rosas, F. E., Stella, M., Comolatti, R., Colenbier, N., Stramaglia, S., & Rosseel, Y. (2024) · Behavior Research Methods · doi:10.3758/s13428-024-02471-8 · Cited by 22 · see citing works
Local Dirac Synchronization on networks
Calmon, L., Krishnagopal, S., & Bianconi, G. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0132468 · Cited by 21 · see citing works
Stochastic epidemic model on a simplicial complex
Palafox-Castillo, G., & Berrones, A. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128053 · Cited by 20 · see citing works
A general view on double limits in differential equations
Kuehn, C., Berglund, N., Bick, C., Engel, M., Hurth, T., Iuorio, A., & Soresina, C. (2021) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2021.133105 · Cited by 19 · see citing works
Self-citation
Correlation-Diversified Portfolio Construction by Finding Maximum Independent Set in Large-Scale Market Graph
Hidaka, R., Hamakawa, Y., Nakayama, J., & Tatsumura, K. (2023) · IEEE Access · doi:10.1109/access.2023.3341422 · Cited by 18 · see citing works
Latent Space Model for Higher-Order Networks and Generalized Tensor Decomposition
Lyu, Z., Xia, D., & Zhang, Y. (2023) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2022.2164289 · Cited by 17 · see citing works
Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude
Bick, C., Böhle, T., & Kuehn, C. (2024) · Journal of Nonlinear Science · doi:10.1007/s00332-024-10053-3 · Cited by 17 · see citing works
Self-citation
Topological signal processing and learning: Recent advances and future challenges
Isufi, E., Leus, G. J. T., Beferull‐Lozano, B., Barbarossa, S., & Lorenzo, P. D. (2025) · Signal Processing · doi:10.1016/j.sigpro.2025.109930 · Cited by 17 · see citing works
Opinion dynamics: Statistical physics and beyond
Starnini, M., Baumann, F., Galla, T., Garcia, D., Íñiguez, G., Karsai, M., Lorenz, J., & Sznajd-Weron, K. (2026) · Reviews of Modern Physics · doi:10.1103/j1zg-ddqv · Cited by 16 · see citing works
Hypergraph reconstruction from uncertain pairwise observations
Lizotte, S., Young, J.-G., & Allard, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-48081-w · Cited by 16 · see citing works
Revealing Higher-Order Interactions in High-Dimensional Complex Systems: A Data-Driven Approach
Tabar, M. R. R., Nikakhtar, F., Parkavousi, L., Akhshi, A., Feudel, U., & Lehnertz, K. (2024) · Physical Review X · doi:10.1103/physrevx.14.011050 · Cited by 16 · see citing works
Learning the effective order of a hypergraph dynamical system
Neuhäuser, L., Scholkemper, M., Tudisco, F., & Schaub, M. T. (2024) · Science Advances · doi:10.1126/sciadv.adh4053 · Cited by 16 · see citing works
Self-citation
Exploring interspecific interaction variability in microbiota: A review
Yu, Z., Gan, Z., Tawfik, A., & Meng, F. (2024) · Engineering Microbiology · doi:10.1016/j.engmic.2024.100178 · Cited by 16 · see citing works
Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony
Aguiar, M., Bick, C., & Dias, A. P. S. (2023) · Nonlinearity · doi:10.1088/1361-6544/ace39f · Cited by 15 · see citing works
Self-citation
Global topological synchronization of weighted simplicial complexes
Wang, R., Muolo, R., Carletti, T., & Bianconi, G. (2024) · Physical review. E · doi:10.1103/physreve.110.014307 · Cited by 15 · see citing works
Fractal information dissemination and clustering evolution on social hypernetwork
Luo, L., Nian, F., Cui, Y., & Li, F. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0228903 · Cited by 15 · see citing works
Higher-order Laplacian renormalization
Nurisso, M., Morandini, M., Lucas, M., Vaccarino, F., Gili, T., & Petri, G. (2025) · Nature Physics · doi:10.1038/s41567-025-02784-1 · Cited by 15 · see citing works
Unveiling the social fabric through a temporal, nation-scale social network and its characteristics
Cremers, J., Köhler, B., Maier, B. F., Eriksen, S. N., Einsiedler, J., Christensen, F. K., Lehmann, S., Lassen, D. D., Mortensen, L. H., & Bjerre-Nielsen, A. (2025) · Scientific Reports · doi:10.1038/s41598-025-98072-2 · Cited by 14 · see citing works
Insights from exact social contagion dynamics on networks with higher-order structures
Kiss, I. Z., Iacopini, I., Šimon, P., & Georgiou, N. (2023) · Journal of Complex Networks · doi:10.1093/comnet/cnad044 · Cited by 14 · see citing works
Fundamental interactions in self-organised critical dynamics on higher order networks
Tadić, B., & Melnik, R. (2024) · The European Physical Journal B · doi:10.1140/epjb/s10051-024-00705-4 · Cited by 14 · see citing works
Synchronization in spiking neural networks with short and long connections and time delays
Kusch, L., Breyton, M., Depannemaecker, D., Petkoski, S., & Jirsa, V. (2025) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0158186 · Cited by 14 · see citing works
Unveiling the role of higher-order interactions via stepwise reduction
Bian, J., Zhou, T., & Bi, Y. (2025) · Communications Physics · doi:10.1038/s42005-025-02157-3 · Cited by 13 · see citing works
The extended master stability function approach to alternating synchronization modes on networked oscillator systems
Yang, R., Wang, Y., Wang, X., Lei, Z., Zheng, Z., & Qian, Y. (2025) · New Journal of Physics · doi:10.1088/1367-2630/ae3207 · Cited by 13 · see citing works
Dynamics of competitive information propagation on hypergraphs
Yin, Q., 万一聪, Wang, Z., Guo, L., & Hong, Z. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118667 · Cited by 13 · see citing works
Effects of high-order interactions on synchronization of a fractional-order neural system
Saçu, İ. E. (2024) · Cognitive Neurodynamics · doi:10.1007/s11571-023-10055-z · Cited by 13 · see citing works
Triadic percolation induces dynamical topological patterns in higher-order networks
Millán, A. P., Sun, H., Torres, J. J., & Bianconi, G. (2024) · PNAS Nexus · doi:10.1093/pnasnexus/pgae270 · Cited by 13 · see citing works
Pattern Dynamics of a Predator–Prey Model Driven by Higher-Order Interactions
Liang, Q., & Shen, J. (2024) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127424501918 · Cited by 13 · see citing works
Entropy-based models to randomise real-world hypergraphs
Saracco, F., Petri, G., Lambiotte, R., & Squartini, T. (2025) · Communications Physics · doi:10.1038/s42005-025-02182-2 · Cited by 13 · see citing works
Quantifying gender biases towards politicians on Reddit
Marjanović, S. V., Stańczak, K., & Augenstein, I. (2022) · PLoS ONE · doi:10.1371/journal.pone.0274317 · Cited by 13 · see citing works
Pairs-Trading System Using Quantum-Inspired Combinatorial Optimization Accelerator for Optimal Path Search in Market Graphs
Tatsumura, K., Hidaka, R., Nakayama, J., Kashimata, T., & Yamasaki, M. (2023) · IEEE Access · doi:10.1109/access.2023.3316727 · Cited by 13 · see citing works
Data-Centric AI Requires Rethinking Data NotionPreprint
Hajij, M., Zamzmi, G., Ramamurthy, K. N., & Guzmán-Sáenz, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.02491 · Cited by 13 · see citing works
On Metzler Positive Systems on Hypergraphs
Cui, S., Zhang, G., Jardón-Kojakhmetov, H., & Cao, M. (2025) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2025.3548300 · Cited by 12 · see citing works
Competition between group interactions and nonlinearity in voter dynamics on hypergraphs
Kim, J., Lee, D., Min, B., Porter, M. A., Miguel, M. S., & Goh, K.-I. (2025) · Physical review. E · doi:10.1103/physreve.111.l052301 · Cited by 12 · see citing works
Higher-order connection Laplacians for directed simplicial complexes
Gong, X., Higham, D. J., Zygalakis, K. C., & Bianconi, G. (2024) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad353b · Cited by 12 · see citing works
The stability of persistent homology of hypergraphs
Ren, S., & Wu, J. (2026) · Journal of Homotopy and Related Structures · doi:10.1007/s40062-026-00400-4 · Cited by 12 · see citing works
Simplicial motif predictor method for higher-order link prediction
Yang, R., Liu, B., & Lü, L. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.126284 · Cited by 11 · see citing works
An SIS diffusion process with direct and indirect spreading on a hypergraph
Cui, S., Liu, F., Liang, L., Jardón-Kojakhmetov, H., & Cao, M. (2025) · Automatica · doi:10.1016/j.automatica.2025.112319 · Cited by 11 · see citing works
Pinning control of chimera states in systems with higher-order interactions
Muolo, R., Gambuzza, L. V., Nakao, H., & Frasca, M. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11581-7 · Cited by 11 · see citing works
Theory of phase reduction from hypergraphs to simplicial complexes: A general route to higher-order Kuramoto models
León, I., Muolo, R., Hata, S., & Nakao, H. (2025) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2025.134858 · Cited by 11 · see citing works
COMPLEX CONTAGION IN SOCIAL SYSTEMS WITH DISTRUST
de Kemmeter, J.-F., Gallo, L., Boncoraglio, F., Latora, V., & Carletti, T. (2024) · Advances in Complex Systems · doi:10.1142/s0219525924400010 · Cited by 11 · see citing works
A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs
Chu, W., & Porter, M. A. (2023) · SIAM Journal on Applied Mathematics · doi:10.1137/22m148608x · Cited by 10 · see citing works
Community detection in hypergraphs via mutual information maximization
Kritschgau, J., Kaiser, D., Rodriguez, O. A., Amburg, I., Bolkema, J., Grubb, T., Lan, F., Maleki, S., Chodrow, P. S., & Kay, B. (2024) · Scientific Reports · doi:10.1038/s41598-024-55934-5 · Cited by 10 · see citing works
Knowledge Tracing Through Enhanced Questions and Directed Learning Interaction Based on Multigraph Embeddings in Intelligent Tutoring Systems
Qiu, L., & Wang, L. (2024) · IEEE Transactions on Education · doi:10.1109/te.2024.3448532 · Cited by 10 · see citing works
Stability of twisted states: The role of phase lag, pairwise and higher-order interactions
Wang, X., Yu, D., Li, T., Li, X., Xie, Y., & Jia, Y. (2025) · Physical review. E · doi:10.1103/qmgz-h5qm · Cited by 10 · see citing works
Analysis of Higher Order Lotka–Volterra Models: Application of $\mathcal {S}$-Tensors and the Polynomial Complementarity Problem
Cui, S., Zhao, Q., Zhang, G., Jardón-Kojakhmetov, H., & Cao, M. (2025) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2025.3598785 · Cited by 10 · see citing works

Representing Higher-Order Networks: A Survey of Graph-Based FrameworksPreprint
Fujita, T., & Smarandache, F. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6347978
From networks to optimal higher-order models of complex systems
Lambiotte, R., Rosvall, M., & Scholtes, I. (2019) · Nature Physics · doi:10.1038/s41567-019-0459-y · Cited by 487 · see citing works
Higher-Order Networks Representation and Learning: A Survey
Tian, H., & Zafarani, R. (2024) · ACM SIGKDD Explorations Newsletter · doi:10.1145/3682112.3682114 · Cited by 17 · see citing works
Toward higher-order network models
Bohlin, L. (2018) · KTH Publication Database DiVA (KTH Royal Institute of Technology) · Cited by 1 · see citing works
Graphs are maximally expressive for higher-order interactionsPreprint
Peixoto, T. P., Peel, L., Gross, T., & Domenico, M. D. (2026) · arXiv (Cornell University) · doi:10.48550/arxiv.2602.16937 · Cited by 3 · see citing works

Authors: Bick, C., Gross, E., Harrington, H. A., & Schaub, M. T.
Affiliations: Vrije Universiteit Amsterdam (NL)
University of Hawaiʻi at Mānoa (US)
Centre for Human Genetics (GB)
ORCID: Bick, Christian
Gross, Elizabeth
Harrington, Heather A.
Schaub, Michael T.
Venue: SIAM Review
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Published: 2023-08
Volume: 65
Issue: 3
Pages: 686-731
ISSN: 0036-1445 (ISSN-L)
1095-7200
DOI: 10.1137/21m1414024
OpenAlex: W3158396846
Cited by: 420
References: 316
Citations by year: 2026: 133 · 2025: 141 · 2024: 82 · 2023: 34 · 2022: 16 · 2021: 12 · 2018: 1 · 2016: 1
FWCI: 38.87
Type: journal article
Language: en
Open access: hybrid
doi.org
Licence: cc-by
Locations: SIAM Review (publishedVersion, cc-by)
RWTH Publications (RWTH Aachen) (publishedVersion)
VU Research Portal (publishedVersion, other-oa)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Funders: H2020 Marie Skłodowska-Curie Actions (702410)
Technische Universitat Munchen
Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen
National Science Foundation (DMS-1945584)
Royal Society (RGFnEAn201074, UF150238)
Engineering and Physical Sciences Research Council (EP/T013613/1, EP/R018472/1, EP/R005125/1, EP/T001968/1)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
Keywords: higher-order networks, hypergraphs, pairwise relationships, graph-based modeling, complex systems, network science

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

What are higher-order networks?

Abstract

Integrity signals

Claims the paper makes

Claims other papers make about this one

Cites

Cited by

Related

Record

About these checks