The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
A note on the metric properties of trees
Open accessOverview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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?
In the citing paper
“a metric space is of the form M (Γ) if and only if it satisfies the so-called four-point condition”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Buneman (1974)
Citations
Cites
Harary, F. (1969) · Cited by 10,739
Mathematics in the Archaeological and Historical Sciences
(1970) · Bulletin of the London Mathematical Society · doi:10.1112/blms/2.2.252 · Cited by 388
Mathematics in the Archaeological and Historical Sciences.
Sneath, P. H. A., Hodson, F. R., Kendall, D. G., & Tautu, P. (1972) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344692 · Cited by 313
The structure and construction of taxonomic hierarchies
JARDINE, C. J., Jardine, N., & Sibson, R. (1967) · Mathematical Biosciences · doi:10.1016/0025-5564(67)90032-6 · Cited by 123
A note on the tree realizability of a distance matrix
Pereira, J. M. S. S. (1969) · Journal of Combinatorial Theory · doi:10.1016/s0021-9800(69)80092-x · Cited by 103
Cited by
Sorted by citations
Sattath, S., & Tversky, A. (1977) · Psychometrika · doi:10.1007/bf02293654 · Cited by 594
A Statistical Test for Host–Parasite Coevolution
Legendre, P., Desdevises, Y., & Bazin, É. (2002) · Systematic Biology · doi:10.1080/10635150252899734 · Cited by 501
On Metric Generators of Graphs
Sebö, A., & Tannier, É. (2004) · Mathematics of Operations Research · doi:10.1287/moor.1030.0070 · Cited by 499
Bandelt, H., & Mulder, H. M. (1986) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(86)90043-2 · Cited by 460
Speyer, D. E., & Sturmfels, B. (2004) · Advances in Geometry · doi:10.1515/advg.2004.023 · Cited by 450
A canonical decomposition theory for metrics on a finite set
Bandelt, H., & Dress, A. (1992) · Advances in Mathematics · doi:10.1016/0001-8708(92)90061-o · Cited by 361
Dress, A. (1984) · Advances in Mathematics · doi:10.1016/0001-8708(84)90029-x · Cited by 314
Distance spectra of graphs: A survey
Aouchiche, M., & Hansen, P. (2014) · Linear Algebra and its Applications · doi:10.1016/j.laa.2014.06.010 · Cited by 301
Admixture, Population Structure, and F -Statistics
Peter, B. M. (2016) · Genetics · doi:10.1534/genetics.115.183913 · Cited by 265
Estimating Species Trees from Unrooted Gene Trees
Liu, L., & Yu, L. (2011) · Systematic Biology · doi:10.1093/sysbio/syr027 · Cited by 255
Reconstructing the shape of a tree from observed dissimilarity data
Bandelt, H., & Dress, A. (1986) · Advances in Applied Mathematics · doi:10.1016/0196-8858(86)90038-2 · Cited by 254
Topological pattern recognition for point cloud data
Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230
Spanning trees and optimization problems
(2004) · Choice Reviews Online · doi:10.5860/choice.42-1619a · Cited by 231
Comparing Numerical Taxonomic Studies
Rohlf, F. J., & Sokal, R. R. (1981) · Systematic Biology · doi:10.1093/sysbio/30.4.459 · Cited by 186
Develin, M., & Sturmfels, B. (2004) · Documenta Mathematica · doi:10.4171/dm/154 · Cited by 185
Inferring the Mutational History of a Tumor Using Multi-state Perfect Phylogeny Mixtures
El-Kebir, M., Satas, G., Oesper, L., & Raphael, B. J. (2016) · Cell Systems · doi:10.1016/j.cels.2016.07.004 · Cited by 150
Evans, S. N. (2007) · Lecture notes in mathematics · doi:10.1007/978-3-540-74798-7 · Cited by 136
Basic Phylogenetic Combinatorics
Dress, A., Huber, K. T., Koolen, J. H., Moulton, V., & Spillner, A. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9781139019767 · Cited by 119
Topological Data Analysis with Applications
Carlsson, G., & Vejdemo‐Johansson, M. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108975704 · Cited by 122
Inferring evolutionary trees with strong combinatorial evidence
Berry, V., & Gascuel, O. (2000) · Theoretical Computer Science · doi:10.1016/s0304-3975(99)00235-2 · Cited by 106
Tree structures for proximity data
Colonius, H., & Schulze, H.-H. (1981) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1981.tb00626.x · Cited by 103
Metrics on partially ordered sets—A survey
Monjardet, B. (1981) · Discrete Mathematics · doi:10.1016/0012-365x(81)90206-5 · Cited by 102
Formation of the Arabidopsis Pentatricopeptide Repeat Family
Rivals, É., Bruyère, C., Toffano‐Nioche, C., & Lecharny, A. (2006) · PLANT PHYSIOLOGY · doi:10.1104/pp.106.077826 · Cited by 106
Train, C.-M., Glover, N. M., Gonnet, G. H., Altenhoff, A. M., & Dessimoz, C. (2017) · Bioinformatics · doi:10.1093/bioinformatics/btx229 · Cited by 96
Makarenkov, V., & Legendre, P. (2001) · Journal of Classification · doi:10.1007/s00357-001-0018-x · Cited by 100
The performance of coalescent-based species tree estimation methods under models of missing data
Nute, M., Chou, J., Molloy, E. K., & Warnow, T. J. (2018) · BMC Genomics · doi:10.1186/s12864-018-4619-8 · Cited by 86
Quantifying Homologous Replacement of Loci between Haloarchaeal Species
Williams, D. F., Gogarten, J. P., & Papke, R. T. (2012) · Genome Biology and Evolution · doi:10.1093/gbe/evs098 · Cited by 85
From a Phylogenetic Tree to a Reticulated Network
Makarenkov, V., & Legendre, P. (2004) · Journal of Computational Biology · doi:10.1089/106652704773416966 · Cited by 82
The Nonlinear Geometry of Banach Spaces
Kalton, N. J. (2008) · Revista Matemática Complutense · doi:10.5209/rev_rema.2008.v21.n1.16426 · Cited by 79
On the treeness of internet latency and bandwidth
Ramasubramanian, V., Malkhi, D., Kühn, F., Balakrishnan, M., Gupta, A., & Akella, A. (2009) · ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS) · doi:10.1145/1555349.1555357 · Cited by 74
Cyclic permutations and evolutionary trees
Semple, C., & Steel, M. (2003) · Advances in Applied Mathematics · doi:10.1016/s0196-8858(03)00098-8 · Cited by 72
Real Time Classification of Viruses in 12 Dimensions
Yu, C., Hernandez, T., Zheng, H., Yau, S.-C., Huang, H.-H., He, R. L., Yang, J., & Yau, S. S. ‐. (2013) · PLoS ONE · doi:10.1371/journal.pone.0064328 · Cited by 70
Tree metrics and their Lipschitz-free spaces
Godard, A. (2010) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-2010-10421-5 · Cited by 69
Recovering Symbolically Dated, Rooted Trees from Symbolic Ultrametrics
Böcker, S., & Dress, A. (1998) · Advances in Mathematics · doi:10.1006/aima.1998.1743 · Cited by 67
On metric properties of certain clique graphs
Howorka, E. (1979) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(79)90069-8 · Cited by 66
Reconstructing trees from subtree weights
Pachter, L. S., & Speyer, D. E. (2004) · Applied Mathematics Letters · doi:10.1016/s0893-9659(04)90095-x · Cited by 63
Bandelt, H. (1990) · SIAM Journal on Discrete Mathematics · doi:10.1137/0403001 · Cited by 60
Codivergence of Mycoviruses with Their Hosts
Göker, M., Scheuner, C., Klenk, H., Stielow, J. B., & Menzel, W. (2011) · PLoS ONE · doi:10.1371/journal.pone.0022252 · Cited by 56
Optimal variable weighting for hierarchical clustering: An alternating least-squares algorithm
Soete, G. D., DeSarbo, W. S., & Carroll, J. D. (1985) · Journal of Classification · doi:10.1007/bf01908074 · Cited by 54
Protein space: A natural method for realizing the nature of protein universe
Yu, C., Deng, M., Cheng, S.-Y., Yau, S.-C., He, R. L., & Yau, S. S.-T. (2012) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2012.11.005 · Cited by 53
On optimal embeddings of metrics in graphs
Imrich, W., Simões-Pereira, J. M. S., & Zamfirescu, C. M. D. (1984) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(84)90009-1 · Cited by 48
Equations for Chow and Hilbert quotients
Gibney, A., & Maclagan, D. (2010) · Algebra & Number Theory · doi:10.2140/ant.2010.4.855 · Cited by 46
The representation of three-way proximity data by single and multiple tree structure models
Carroll, J. D., Clark, L. A., & DeSarbo, W. S. (1984) · Journal of Classification · doi:10.1007/bf01890116 · Cited by 44
A Statistical Framework to Test the Consensus Among Additive Trees (Cladograms)
Lapointe, F., & Legendre, P. (1992) · Systematic Biology · doi:10.1093/sysbio/41.2.158 · Cited by 44
DEPP: Deep Learning Enables Extending Species Trees using Single Genes
Jiang, Y., Balaban, M., Zhu, Q., & Mirarab, S. (2022) · Systematic Biology · doi:10.1093/sysbio/syac031 · Cited by 45
Critchley, F., & Fichet, B. (1994) · Lecture notes in statistics · doi:10.1007/978-1-4612-2686-4_2 · Cited by 44
A selection theorem in metric trees
Aksoy, A., & Khamsi, M. A. (2006) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-06-08555-8 · Cited by 41
On optimal realizations of finite metric spaces by graphs
Althöfer, I. (1988) · Discrete & Computational Geometry · doi:10.1007/bf02187901 · Cited by 40
Free Spaces Over Some Proper Metric Spaces
Dalet, A. (2014) · Mediterranean Journal of Mathematics · doi:10.1007/s00009-014-0455-5 · Cited by 38
Reconstructing approximate tree metrics
Abraham, I., Balakrishnan, M., Kühn, F., Malkhi, D., Ramasubramanian, V., & Talwar, K. (2007) · ACM Symposium on Principles of Distributed Computing (PODC) · doi:10.1145/1281100.1281110 · Cited by 34
Hyperconvexity and tight-span theory for diversities
Bryant, D., & Tupper, P. F. (2012) · Advances in Mathematics · doi:10.1016/j.aim.2012.08.008 · Cited by 36
DeSarbo, W. S., Manrai, A. K., & Manrai, L. A. (1993) · Handbooks in operations research and management science · doi:10.1016/s0927-0507(05)80028-3 · Cited by 36
A Stochastic Local Search Algorithm for Distance-Based Phylogeny Reconstruction
Tria, F., Caglioti, E., Loreto, V., & Pagnani, A. (2010) · Molecular Biology and Evolution · doi:10.1093/molbev/msq154 · Cited by 35
A geometric relationship of F 2, F 3 and F 4-statistics with principal component analysis
Peter, B. M. (2022) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2020.0413 · Cited by 36
l∞-Approximation via Subdominants
Chepoi, V. D., & Fichet, B. (2000) · Journal of Mathematical Psychology · doi:10.1006/jmps.1999.1270 · Cited by 33
The choice of optimal distance measure in genome-wide datasets
Glazko, G. V., Gordon, A. Y., & Mushegian, A. R. (2005) · Bioinformatics · doi:10.1093/bioinformatics/bti1201 · Cited by 33
Submatrices of non-tree-realizable distance matrices
Simões-Pereira, J. M. S., & Zamfirescu, C. M. D. (1982) · Linear Algebra and its Applications · doi:10.1016/0024-3795(82)90001-5 · Cited by 33
Symmetric Matrices Representable by Weighted Trees over a Cancellative Abelian Monoid
Bandelt, H., & Steel, M. A. (1995) · SIAM Journal on Discrete Mathematics · doi:10.1137/s0895480191201759 · Cited by 32
Virus classification in 60-dimensional protein space
Li, Y., Tian, K., Yin, C., He, R. L., & Yau, S. S. ‐. (2016) · Molecular Phylogenetics and Evolution · doi:10.1016/j.ympev.2016.03.009 · Cited by 32
Implicit inequality constraints in a binary tree model
Zwiernik, P., & Smith, J. Q. (2011) · Electronic Journal of Statistics · doi:10.1214/11-ejs640 · Cited by 31
Abdi, H. (1990) · Lecture notes in biomathematics · doi:10.1007/978-3-662-10619-8_3 · Cited by 30
The Balanced Minimum Evolution Problem
Catanzaro, D., Labbé, M., Pesenti, R., & Salazar‐González, J. (2011) · INFORMS journal on computing · doi:10.1287/ijoc.1110.0455 · Cited by 29
Characterization of the Distance between Subtrees of a Tree by the Associated Tight Span
Hirai, H. (2006) · Annals of Combinatorics · doi:10.1007/s00026-006-0277-7 · Cited by 29
Counting distance permutations
Skala, M. (2008) · Journal of Discrete Algorithms · doi:10.1016/j.jda.2008.09.011 · Cited by 28
New Efficient Algorithm for Detection of Horizontal Gene Transfer Events
Boc, A., & Makarenkov, V. (2003) · Lecture notes in computer science · doi:10.1007/978-3-540-39763-2_15 · Cited by 28
M-convex functions and tree metrics
Hira, H., & Murota, K. (2004) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/bf03167590 · Cited by 28
Kelly, J. B. (1975) · Lecture notes in mathematics · doi:10.1007/bfb0081128 · Cited by 28
Conservation genetics of the wood turtle (Glyptemys insculpta) in Quebec, Canada
Tessier, N., Paquette, S. R., & Lapointe, F. (2005) · Canadian Journal of Zoology · doi:10.1139/z05-065 · Cited by 27
Anchoring quartet-based phylogenetic distances and applications to species tree reconstruction
Sayyari, E., & Mirarab, S. (2016) · BMC Genomics · doi:10.1186/s12864-016-3098-z · Cited by 26
Sequence Alignment, Mutual Information, and Dissimilarity Measures for Constructing Phylogenies
Penner, O., Grassberger, P., & Paczuski, M. (2011) · PLoS ONE · doi:10.1371/journal.pone.0014373 · Cited by 26
Everything You always wanted to Know about the Average Consensus, and More
Lapointe, F., & Levasseur, C. (2004) · Computational biology · doi:10.1007/978-1-4020-2330-9_5 · Cited by 26
On the Hyperbolicity of Large-Scale NetworksPreprint
Kennedy, W. S., Narayan, O., & Saniee, I. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1307.0031 · Cited by 36
Богатый, С. А. (2002) · Russian Mathematical Surveys · doi:10.1070/rm2002v057n02abeh000495 · Cited by 20
Quasi-ultrametrics and their 2-ball hypergraphs
Diatta, J., & Fichet, B. (1998) · Discrete Mathematics · doi:10.1016/s0012-365x(98)00067-3 · Cited by 23
On the consistency of the minimum evolution principle of phylogenetic inference
Denis, F., & Gascuel, O. (2003) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(02)00285-8 · Cited by 23
A reduction algorithm for approximating a (nonmetric) dissimilarity by a tree distance
Gascuel, O., & Levy, D. (1996) · Journal of Classification · doi:10.1007/bf01202585 · Cited by 23
Inferring evolutionary trees with strong combinatorial evidence
Berry, V., & Gascuel, O. (1997) · Lecture notes in computer science · doi:10.1007/bfb0045078 · Cited by 23
A SURVEY ON ALGORITHMIC ASPECTS OF TANDEM REPEATS EVOLUTION
Rivals, É. (2004) · International Journal of Foundations of Computer Science · doi:10.1142/s012905410400239x · Cited by 21
Spectral Unsupervised Parsing with Additive Tree Metrics
Parikh, A. P., Cohen, S. B., & Xing, E. P. (2014) · Proceedings of the conference - Association for Computational Linguistics. Meeting · doi:10.3115/v1/p14-1100 · Cited by 21
Maximum likelihood estimates of pairwise rearrangement distances
Serdoz, S., Egri-Nagy, A., Sumner, J. G., Holland, B. R., Jarvis, P., Tanaka, M. M., & Francis, A. R. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.04.015 · Cited by 20
Mathematics and the Lifeway of Mesopithecus
Escarguel, G. (2005) · International Journal of Primatology · doi:10.1007/s10764-005-5324-4 · Cited by 20
Faithful tropicalization of the Grassmannian of planes
Cueto, M. A., Häbich, M., & Werner, A. (2014) · Mathematische Annalen · doi:10.1007/s00208-014-1037-3 · Cited by 18
Fast Parallel Recognition of Ultrametrics and Tree Metrics
Dahlhaus, E. (1993) · SIAM Journal on Discrete Mathematics · doi:10.1137/0406041 · Cited by 19
The Complexity of Metric Realization
Winkler, P. M. (1988) · SIAM Journal on Discrete Mathematics · doi:10.1137/0401051 · Cited by 19
PEOPLE’S INTUITIONS ABOUT RANDOMNESS AND PROBABILITY: AN EMPIRICAL STUDY
Lecoutre, M., Rovira, K., Lecoutre, B., & Poitevineau, J. (2006) · Statistics Education Research Journal · doi:10.52041/serj.v5i1.507 · Cited by 18
Cognitive Geometry: An Analysis of Structure Underlying Representations of Similarity
Glazer, R., & Nakamoto, K. (1991) · Marketing Science · doi:10.1287/mksc.10.3.205 · Cited by 18
Clustering systems of phylogenetic networks
Hellmuth, M., Schaller, D., & Stadler, P. F. (2023) · Theory in Biosciences · doi:10.1007/s12064-023-00398-w · Cited by 17
Tropical Geometry of Phylogenetic Tree Space: A statistical Perspective
Monod, A., Lin, B., Yoshida, R., & Kang, Q. (2026) · Vietnam Journal of Mathematics · doi:10.1007/s10013-026-00795-w · Cited by 52
a-tint : A polymake extension for algorithmic tropical intersection theory
Hampe, S. (2013) · European Journal of Combinatorics · doi:10.1016/j.ejc.2013.10.001 · Cited by 16
Embeddings of Lipschitz-free spaces into ℓ1
Aliaga, R. J., Petitjean, C., & Procházka, A. (2020) · Journal of Functional Analysis · doi:10.1016/j.jfa.2020.108916 · Cited by 16
Isomorphism of Trees and Isometry of Ultrametric Spaces
Dovgoshey, O. A. (2020) · Theory and Applications of Graphs · doi:10.20429/tag.2020.070203 · Cited by 16
Recovering normal networks from shortest inter-taxa distance information
Bordewich, M., Huber, K. T., Moulton, V., & Semple, C. (2018) · Journal of Mathematical Biology · doi:10.1007/s00285-018-1218-x · Cited by 16
Fundamental polytopes of metric trees via parallel connections of matroids
Delucchi, E., & Hoessly, L. (2020) · European Journal of Combinatorics · doi:10.1016/j.ejc.2020.103098 · Cited by 16
ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES
Faver, T. E., Kochalski, K., Murugan, M., Verheggen, H., Wesson, E. N., & Weston, A. (2013) · Glasgow Mathematical Journal · doi:10.1017/s0017089513000438 · Cited by 15
From pairs of most similar sequences to phylogenetic best matches
Stadler, P. F., Geiß, M., Schaller, D., Sánchez, A. L., Laffitte, M. E. G., Valdivia, D. I., Hellmuth, M., & Hernández-Rosales, M. (2020) · Algorithms for Molecular Biology · doi:10.1186/s13015-020-00165-2 · Cited by 20
Using Invariants for Phylogenetic Tree Construction
Eriksson, N. (2008) · The IMA volumes in mathematics and its applications · doi:10.1007/978-0-387-09686-5_4 · Cited by 15
A priori assessment of data quality in molecular phylogenetics
Misof, B. Y., Meusemann, K., von Reumont, B. M., Kück, P., Prohaska, S. J., & Stadler, P. F. (2014) · Algorithms for Molecular Biology · doi:10.1186/s13015-014-0022-4 · Cited by 15
An Optimality Criterion for Graph Embeddings of Metrics
Simões-Pereira, J. M. S. (1988) · SIAM Journal on Discrete Mathematics · doi:10.1137/0401023 · Cited by 15
An algorithm and its role in the study of optimal graph realizations of distance matrices
Simões-Pereira, J. M. S. (1990) · Discrete Mathematics · doi:10.1016/0012-365x(90)90337-h · Cited by 15
Brandstädt, A., & Wagner, P. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-74456-6_47 · Cited by 15
Metadata
- Authors
- Buneman, P.
- Affiliations
- University of Edinburgh (GB)
- Corresponding author
- Buneman, Peter
- ORCID
- Buneman, Peter
- Venue
- Journal of Combinatorial Theory, Series B
- Publisher
- Elsevier BV
- Published
- 1974-08
- Volume
- 17
- Issue
- 1
- Pages
- 48-50
- ISSN
- 0095-8956 (ISSN-L)
- OpenAlex
- W2082445660
- Cited by
- 329
- References
- 5
- Citations by year
- 2026: 9 · 2025: 8 · 2024: 14 · 2023: 15 · 2022: 10 · 2021: 10 · 2020: 11 · 2019: 15 · 2018: 10 · 2017: 11 · 2016: 17 · 2015: 12 · 2014: 18 · 2013: 10 · 2012: 14
- FWCI
- 1.10
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Combinatorial Theory Series B (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Graph Theory Research
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- trees, measurement properties
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