The tidy set: a minimal simplicial set for computing homology of clique complexes

Untitled work

(2001) · Cited by 5,374 · see citing works

Three-dimensional alpha shapes

Edelsbrunner, H., & Mücke, E. P. (1994) · ACM Transactions on Graphics · doi:10.1145/174462.156635 · Cited by 2,488 · see citing works

Introduction to Algorithms, third edition

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009) · Cited by 2,309 · see citing works

Elements of Algebraic Topology

Munkres, J. R. (2018) · CRC Press eBooks · doi:10.1201/9780429493911 · Cited by 2,113 · 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

ELEMENTS OF ALGEBRAIC TOPOLOGY

Kuratowski, K. (1972) · Elsevier eBooks · doi:10.1016/b978-0-08-016160-0.50028-2 · Cited by 1,290 · see citing works

Untitled work

(1993) · Medical Entomology and Zoology · Cited by 1,116 · see citing works

Simplicial Homotopy Theory

Goerss, P. G., & Jardine, J. F. (2009) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0346-0189-4 · Cited by 1,034 · see citing works

Introduction to Algorithms

Radhakrishnan, S., Kolippakkam, D. N., & Mathura, V. S. (2008) · Springer eBooks · doi:10.1007/978-0-387-84870-9_3 · Cited by 843 · see citing works

On cliques in graphs

Moon, J. W., & Moser, L. (1965) · Israel Journal of Mathematics · doi:10.1007/bf02760024 · Cited by 839 · see citing works

Simplicial Homotopy Theory

Goerss, P. G., & Jardine, J. F. (1999) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8707-6 · Cited by 689 · see citing works

The Boost graph library : user guide and reference manual

Siek, J. G., Lee, L., & Lumsdaine, A. (2002) · CERN Document Server (European Organization for Nuclear Research) · Cited by 610 · see citing works

Combinatorial Algebraic Topology

Kozlov, D. N. (2007) · Algorithms and computation in mathematics · doi:10.1007/978-3-540-71962-5 · Cited by 535 · see citing works

On the Local Behavior of Spaces of Natural Images

Carlsson, G., Ishkhanov, T., de Silva, V., & Zomorodian, A. (2008) · International Journal of Computer Vision · doi:10.1007/s11263-007-0056-x · Cited by 477 · see citing works

Simplicial Spaces, Nuclei and m -Groups

Whitehead, J. H. C. (1939) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s2-45.1.243 · Cited by 429 · see citing works

Algorithms and theory of computation handbook

Atallah, M. J. (1999) · Choice Reviews Online · doi:10.5860/choice.37-0975 · Cited by 425 · see citing works

Computational Homology

Kaczyński, T., Mischaikow, K., & Mrożek, M. (2004) · Applied mathematical sciences · doi:10.1007/b97315 · Cited by 403 · see citing works

Topological estimation using witness complexes

Silva, V. D., & Carlsson, G. (2004) · The Eurographics Association · doi:10.2312/spbg/spbg04/157-166 · Cited by 337 · see citing works

Simplicial homotopy theory

Curtis, E. B. (1971) · Advances in Mathematics · doi:10.1016/0001-8708(71)90015-6 · Cited by 304 · see citing works

Fast construction of the Vietoris-Rips complex

Zomorodian, A. J. (2010) · Computers & Graphics · doi:10.1016/j.cag.2010.03.007 · Cited by 204 · see citing works

Semi-Simplicial Complexes and Singular Homology

Eilenberg, S., & Zilber, J. A. (1950) · Annals of Mathematics · doi:10.2307/1969364 · Cited by 186 · see citing works

Cambridge University Press 1696–1712

McKenzie, D. F. (2016) · Cambridge University Press eBooks · doi:10.1017/cbo9780511695612 · Cited by 156 · see citing works

A barcode shape descriptor for curve point cloud data

Collins, A., Zomorodian, A., Carlsson, G., & Guibas, L. J. (2004) · Computers & Graphics · doi:10.1016/j.cag.2004.08.015 · Cited by 132 · see citing works

Near optimal algorithms for computing Smith normal forms of integer matrices

Storjohann, A. (1996) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/236869.237084 · Cited by 127 · see citing works

Strong Homotopy Types, Nerves and Collapses

Barmak, J. A., & Minian, E. G. (2011) · Discrete & Computational Geometry · doi:10.1007/s00454-011-9357-5 · Cited by 105 · see citing works

Localized homology

Zomorodian, A., & Carlsson, G. (2008) · Computational Geometry · doi:10.1016/j.comgeo.2008.02.003 · Cited by 89 · see citing works

Algorithms and Theory of Computation Handbook

Charnes, C. (2009) · Cited by 85 · see citing works

The flow complex: a data structure for geometric modeling

Giesen, J., & John, M. (2003) · MPG.PuRe (Max Planck Society) · doi:10.5555/644108.644157 · Cited by 80 · see citing works

Persistent voids: a new structural metric for membrane fusion

Kasson, P. M., Zomorodian, A. J., Park, S., Singhal, N., Guibas, L. J., & Pande, V. S. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btm250 · Cited by 53 · see citing works

Homology algorithm based on acyclic subspace

Mrożek, M., Pilarczyk, P., & Żelazna, N. (2007) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2007.08.044 · Cited by 46 · see citing works

Computational Topology

Zomorodian, A. J. (2009) · Chapman & Hall/CRC applied algorithms and data structures series · doi:10.1201/9781584888215-c3 · Cited by 46 · see citing works

T. Kaczynski, K. Mischaikow, M. Mrozek, Computational Homology, Springer Verlag, NY, 2004

貴之, 坂. (2005) · 応用数理 · doi:10.11540/bjsiam.15.2_184 · Cited by 33 · see citing works

Computer assisted method for proving existence of periodic orbits

Pilarczyk, P. (1999) · Topological Methods in Nonlinear Analysis · doi:10.12775/tmna.1999.019 · Cited by 28 · see citing works

Algorithms for subset testing and finding maximal sets

Yellin, D. M. (1992) · Symposium on Discrete Algorithms · Cited by 22 · see citing works

Linear colorings of simplicial complexes and collapsing

Civan, Y., & Yalçın, E. (2007) · Journal of Combinatorial Theory Series A · doi:10.1016/j.jcta.2007.02.001 · Cited by 14 · see citing works

LC reductions yield isomorphic simplicial complexes

Matoušek, J. (2007) · Libraries and Cultural Resources (University of Calgary) · doi:10.11575/cdm.v3i2.61933.g46656 · Cited by 12 · see citing works

Reporting maximal cliques: new insights into an old problem

Cazals, F., & Karande, C. (2006) · HAL · Cited by 11 · 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

Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time

Eppstein, D., Löffler, M., & Strash, D. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-17517-6_36 · Cited by 363 · 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

Topological pattern recognition for point cloud data

Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230 · see citing works

Topological Strata of Weighted Complex Networks

Petri, G., Scolamiero, M., Donato, I., & Vaccarino, F. (2013) · PLoS ONE · doi:10.1371/journal.pone.0066506 · Cited by 214 · see citing works

Listing All Maximal Cliques in Large Sparse Real-World Graphs

Eppstein, D., Löffler, M., & Strash, D. (2013) · ACM Journal of Experimental Algorithmics · doi:10.1145/2543629 · Cited by 221 · see citing works

The Topology ToolKit

Tierny, J., Favelier, G., Levine, J. A., Gueunet, C., & Michaux, M. A. (2017) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2017.2743938 · Cited by 218 · see citing works

Fast construction of the Vietoris-Rips complex

Zomorodian, A. J. (2010) · Computers & Graphics · doi:10.1016/j.cag.2010.03.007 · Cited by 204 · see citing works

Topological data analysis in biomedicine: A review

Skaf, Y., & Laubenbacher, R. (2022) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2022.104082 · Cited by 169 · see citing works

Listing All Maximal Cliques in Large Sparse Real-World Graphs

Eppstein, D., & Strash, D. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-20662-7_31 · Cited by 152 · see citing works

Zigzag persistent homology in matrix multiplication time

Milosavljević, N., Morozov, D., & Škraba, P. (2011) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1998196.1998229 · Cited by 136 · see citing works

Persistent-homology-based machine learning: a survey and a comparative study

Pun, C. S., Lee, S. X., & Xia, K. (2022) · Artificial Intelligence Review · doi:10.1007/s10462-022-10146-z · Cited by 223 · see citing works

Persistent-Homology-Based Machine Learning and Its Applications -- A SurveyPreprint

Pun, C. S., Xia, K., & Lee, S. X. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3275996 · Cited by 89 · see citing works

Linear-Size Approximations to the Vietoris–Rips Filtration

Sheehy, D. R. (2013) · Discrete & Computational Geometry · doi:10.1007/s00454-013-9513-1 · Cited by 84 · see citing works

The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

Boissonnat, J.-D., & Maria, C. (2014) · Algorithmica · doi:10.1007/s00453-014-9887-3 · Cited by 72 · see citing works

Vietoris–Rips complexes also provide topologically correct reconstructions of sampled shapes

Attali, D., Lieutier, A., & Salinas, D. (2012) · Computational Geometry · doi:10.1016/j.comgeo.2012.02.009 · Cited by 63 · see citing works

Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

Hajij, M., Wang, B., Scheidegger, C., & Rosen, P. (2018) · IEEE Pacific Visualization Symposium · doi:10.1109/pacificvis.2018.00024 · Cited by 57 · see citing works

The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

Boissonnat, J., & Maria, C. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33090-2_63 · Cited by 44 · see citing works

An output-sensitive algorithm for persistent homology

Chen, C., & Kerber, M. (2012) · Computational Geometry · doi:10.1016/j.comgeo.2012.02.010 · Cited by 38 · see citing works

Approximate Čech Complex in Low and High Dimensions

Kerber, M., & Sharathkumar, R. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-45030-3_62 · Cited by 32 · see citing works

Approximating persistent homology in Euclidean space through collapses

Botnan, M. B., & Spreemann, G. (2015) · Applicable Algebra in Engineering Communication and Computing · doi:10.1007/s00200-014-0247-y · Cited by 27 · see citing works

Listing All Maximal Cliques in Large Sparse Real-World GraphsPreprint

Eppstein, D., & Strash, D. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1103.0318 · Cited by 27 · see citing works

Topological Anomaly Detection in Dynamic Multilayer Blockchain Networks

Ofori-Boateng, D., Segovia-Domínguez, I., Akçora, C. G., Kantarcioglu, M., & Gel, Y. R. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-86486-6_48 · Cited by 25 · see citing works

Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes

Attali, D., Lieutier, A., & Salinas, D. (2011) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1998196.1998276 · Cited by 24 · see citing works

Linear-size approximations to the vietoris-rips filtration

Sheehy, D. R. (2012) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/2261250.2261286 · Cited by 22 · see citing works

Efficient data structure for representing and simplifying simplicial complexes in high dimensions

Attali, D., Lieutier, A., & Salinas, D. (2011) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1998196.1998277 · Cited by 21 · see citing works

Persistent Homology: a Step-by-step Introduction for Newcomers

Fugacci, U., Scaramuccia, S., Iuricich, F., & Floriani, L. D. (2016) · PORTO@Iris · doi:10.2312/stag.20161358 · Cited by 21 · see citing works

An output-sensitive algorithm for persistent homology

Chen, C., & Kerber, M. (2011) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1998196.1998228 · Cited by 15 · see citing works

Delaunay Triangulations of Closed Euclidean d-Orbifolds

Caroli, M., & Teillaud, M. (2016) · Discrete & Computational Geometry · doi:10.1007/s00454-016-9782-6 · Cited by 13 · see citing works

Computational Tools in Weighted Persistent Homology

Ren, S., Wu, C., & Wu, J. (2021) · Chinese Annals of Mathematics Series B · doi:10.1007/s11401-021-0255-8 · Cited by 13 · see citing works

Quantitative Simplification of Filtered Simplicial Complexes

Mémoli, F., & Okutan, O. B. (2019) · Discrete & Computational Geometry · doi:10.1007/s00454-019-00104-y · Cited by 12 · see citing works

A Survey on the High Performance Computation of Persistent Homology

Malott, N. O., Chen, S., & Wilsey, P. A. (2022) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2022.3147070 · Cited by 12 · see citing works

Computing discrete Morse complexes from simplicial complexes

Fugacci, U., Iuricich, F., & Floriani, L. D. (2019) · Graphical Models · doi:10.1016/j.gmod.2019.101023 · Cited by 11 · see citing works

Persistence Cycles for Visual Exploration of Persistent Homology

Iuricich, F. (2021) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2021.3110663 · Cited by 11 · see citing works

Efficient Computation of Simplicial Homology through Acyclic Matching

Fugacci, U., Iuricich, F., & Floriani, L. D. (2014) · International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) · doi:10.1109/synasc.2014.84 · Cited by 10 · see citing works

Listing All Maximal Cliques in Sparse Graphs in Near-optimal TimePreprint

Eppstein, D., Löffler, M., & Strash, D. (2010) · arXiv (Cornell University) · doi:10.4230/dagsemproc.10441.2 · Cited by 7 · see citing works

Efficient Homology‐Preserving Simplification of High‐Dimensional Simplicial Shapes

Fellegara, R., Iuricich, F., Floriani, L. D., & Fugacci, U. (2019) · Computer Graphics Forum · doi:10.1111/cgf.13764 · Cited by 6 · see citing works

Persistence Homology of Proximity Hyper-Graphs for Higher Dimensional Big Data

Singh, R. P., & Wilsey, P. A. (2022) · IEEE International Conference on Big Data (BigData) · doi:10.1109/bigdata55660.2022.10020926 · Cited by 5 · see citing works

Faster Enumeration of All Maximal Cliques in Unit Disk Graphs Using Geometric Structure

Izumi, T., & SUZUKI, D. (2015) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2014fcp0018 · Cited by 3 · see citing works

The topology of representational geometry

Brown, S. R., & Farivar, R. (2025) · Frontiers in Neuroscience · doi:10.3389/fnins.2025.1597899 · Cited by 3 · see citing works

Constructing Simplicial Complexes over Topological Spaces

Doktorova, M. N. (2012) · Cited by 3 · see citing works

Approximate Cech Complexes in Low and High DimensionsPreprint

Kerber, M., & Sharathkumar, R. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1307.3272 · Cited by 3 · see citing works

Adaptive and distributed homology computation with application to large scale sensor networks

Zhang, M., Goupil, A., Colas, M., & Gellé, G. (2014) · International Conference on Wireless Communications and Signal Processing (WCSP) · doi:10.1109/wcsp.2014.6992039 · Cited by 2 · see citing works

Computational Topology and its Applications in Geometric Design

Lin, H., Dong, Z., & Chen, J. (2021) · Recent Patents on Engineering · doi:10.2174/1872212115666210901124742 · Cited by 2 · see citing works

Singular persistent homology with geometrically parallelizable computationPreprint

Goldfarb, B. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1607.01257 · Cited by 2 · see citing works

A new quantum computational set-up for algebraic topology via simplicial sets

Zucchini, R. (2025) · Journal of AppliedMath · doi:10.59400/jam3011 · Cited by 1 · see citing works

Algorithmic complexity of finding cross-cycles in flag complexes

Adamaszek, M., & Stacho, J. (2012) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/2261250.2261258 · Cited by 1 · see citing works

Stratified Formal Deformations and Intersection Homology of Data Point CloudsPreprint

Banagl, M., Mäder, T., & Sadlo, F. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.11985 · Cited by 1 · see citing works

2D-Barcode: A Visible Point Cloud Structure Descriptor Application for Mining the Enron Executives Organization Structures

Yan, Z., Yi, D., Zhao, C., Jing, C., & Kang, S. G. (2013) · International Conference on Computational and Information Sciences · doi:10.1109/iccis.2013.437

CONSTRUCTING SIMPLICIAL COMPLEXES OVER

Doktorova, M. N. (2012)

System Development at Run Time.

Landauer, C. A., & Bellman, K. L. (2015)

A spectral sequence for parallelized persistence

Lipsky, D., Skraba, P., & Vejdemo-Johansson, M. (2011) · arXiv · doi:10.48550/arxiv.1112.1245 · Cited by 22 · see citing works

The Tidy Set: A Minimal Simplicial Set for Computing Homology of Clique Complexes

Zomorodian, A. J. (2010)

The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

Boissonnat, J.-D., & Maria, C. (2014) · Algorithmica · doi:10.1007/s00453-014-9887-3 · Cited by 72 · see citing works

Fast construction of the Vietoris-Rips complex

Zomorodian, A. J. (2010) · Computers & Graphics · doi:10.1016/j.cag.2010.03.007 · Cited by 204 · see citing works

Topological estimation using witness complexes

Alexa, M., Rusinkiewicz, S., de Silva, V., & Carlsson, G. (2009)

Homotopical decompositions of simplicial and Vietoris Rips complexes

Chachólski, W., Jin, A., Scolamiero, M., & Tombari, F. (2021) · Journal of Applied and Computational Topology · doi:10.1007/s41468-021-00066-2 · Cited by 3 · see citing works