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Topic · Discrete Mathematics and Combinatorics

Limits and Structures in Graph Theory

Limits and Structures in Graph Theory is a research topic within Discrete Mathematics and Combinatorics. Science Explorer counts 13k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores limits, structures, and extremal problems in graph theory, focusing on topics such as graph limits, Szemerédi's theorem, hypergraphs, regularity lemma, Erdos-Rényi random graphs, Ramsey numbers, the sum-product phenomenon, quasirandomness, random regular graphs, and Dirac's theorem.

  • Graph Limits
  • Szemerédi's Theorem
  • Hypergraphs
  • Regularity Lemma
  • Erdos-Rényi Random Graphs
  • Ramsey Numbers
  • Sum-Product Phenomenon
  • Quasirandomness
  • Random Regular Graphs
  • Dirac's Theorem
Research works
13k
fractional, since 1950
In the world top 10%
1.3k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+26%
the tick is no change
Largest producer
China
31% of the 10 largest, 2022-now
Limits and Structures in Graph Theory

Which countries lead Limits and Structures in Graph Theory research?

By volume, China and the United States publish the most (542 and 461 works in 2022-now).

By volume, 2022-now

  1. 1 China 542 works
  2. 2 United States 461 works
  3. 3 United Kingdom 148 works
  4. 4 India 105 works
  5. 5 Canada 99 works
  6. 6 France 98 works
  7. 7 Germany 91 works
  8. 8 Russia 82 works
  9. 9 Hungary 77 works
  10. 10 Israel 66 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 30.6%United States: 26.0%United Kingdom: 8.4%India: 6.0%6 others listed: 29.0%31%largest
China542 · 30.6%United States461 · 26.0%United Kingdom148 · 8.4%India105 · 6.0%6 others listed514 · 29.0%

Shares of the rows listed above, not of the whole node.

Which institutions lead Limits and Structures in Graph Theory research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Limits and Structures in Graph Theory research, followed by Hungarian Academy of Sciences and ETH Zurich.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 47 works
  2. 2 Hungarian Academy of SciencesHungary 46 works
  3. 3 ETH ZurichSwitzerland 32 works
  4. 4 University of OxfordUnited Kingdom 28 works
  5. 5 Russian Academy of SciencesRussia 25 works
  6. 6 University of Science and Technology of ChinaChina 20 works
  7. 7 Tel Aviv UniversityIsrael 20 works
  8. 8 University of WarwickUnited Kingdom 19 works
  9. 9 Nankai UniversityChina 19 works
  10. 10 University of Illinois Urbana-ChampaignUnited States 19 works

Who are the leading researchers in Limits and Structures in Graph Theory?

The most-cited researchers publishing on Limits and Structures in Graph Theory include David H. Haussler, R. W. L. Jones and Claude E. Shannon.

  1. 1 David H. Haussler United States 209k citations
  2. 2 R. W. L. Jones United Kingdom 189k citations
  3. 3 Claude E. Shannon United States 138k citations
  4. 4 Mark E. J. Newman United States 138k citations
  5. 5 Susan Holmes United States 124k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Limits and Structures in Graph Theory?

The most cited paper in Limits and Structures in Graph Theory is "Spectral Graph Theory" (Fan Chung, 1996), with 5,771 citations. Next come "A critical point for random graphs with a given degree sequence" (2,427) and "On the Shannon capacity of a graph" (1,675).

Most cited papers
#PaperReleasedCitations
1 Spectral Graph Theory Fan Chung · Regional conference series in mathematics Conference paper 3 Dec 1996 5,771
2 A critical point for random graphs with a given degree sequence Michael S. O. Molloy, Bruce A. Reed · Random Structures and Algorithms Mar 1995 2,427
3 On the Shannon capacity of a graph László Lovász · IEEE Transactions on Information Theory 1979 1,675
4 The strong perfect graph theorem Maria Chudnovsky, Neil R. Robertson, Paul D. Seymour et al. · Annals of Mathematics Open access Jul 2006 1,300
5 A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs Béla Bollobás · European Journal of Combinatorics Open access Dec 1980 1,208
All 100 most cited papers, with filters and sorting

Where is Limits and Structures in Graph Theory research done?

The largest centres of Limits and Structures in Graph Theory research in 2022-now are Budapest (Hungary), Shanghai (China), Beijing (China) and Moscow (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Princeton, Budapest and Tel Aviv.

Largest cities, 2022-now

  1. 1 BudapestHungary 70 works
  2. 2 ShanghaiChina 54 works
  3. 3 BeijingChina 52 works
  4. 4 MoscowRussia 44 works
  5. 5 NanjingChina 39 works
  6. 6 ParisFrance 36 works
  7. 7 ZurichSwitzerland 34 works
  8. 8 TianjinChina 32 works
  9. 9 PragueCzechia 29 works
  10. 10 Xi'anChina 29 works

Where it is the local speciality

  1. PrincetonUS · 22.5 works16×
  2. BudapestHU · 70.5 works15×
  3. Tel AvivIL · 23.7 works13×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Limits and Structures in Graph Theory than the world average.

See Limits and Structures in Graph Theory on the map

Where is the best place to study Limits and Structures in Graph Theory?

Among universities, judged by research, Princeton University, Georgia Institute of Technology and University of Oxford score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 17.61%fractional works in this field (log) →share of work in the world top 10% →Georgia Institute of…Princeton UniversityUniversity of OxfordETH Zurich
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Princeton UniversityUnited States 73.421.4%19.7×18 +182.1%
2Georgia Institute of TechnologyUnited States 72.026.4%12.3×16 +189.6%
3University of OxfordUnited Kingdom 71.911.5%9.7×28 +34.9%
4ETH ZurichSwitzerland 71.58.3%22.7×32 +84.2%
5University of WarwickUnited Kingdom 68.818.7%20.3×19 +133.9%
6Massachusetts Institute of TechnologyUnited States 68.516.6%12.9×19 +47.6%
7University of CambridgeUnited Kingdom 67.417.0%7.2×18 +19.2%
8Hunan UniversityChina 67.129.6%7.4×11 +213.0%
9University of BirminghamUnited Kingdom 66.716.8%10.6×14 +32.0%
10Tel Aviv UniversityIsrael 63.89.8%12.3×20 +74.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Limits and Structures in Graph Theory, country by country

Is Limits and Structures in Graph Theory research growing?

Output in 2022-2025 was 26% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Limits and Structures in Graph Theory.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Limits and Structures in Graph Theory as a percentage of every work published that year, 0.0083% in 2024.

still counting0.010%0.020%0.030%Limits and Structures in Graph Theory0.0085% in 202519801990200020102020

Fractional works of Limits and Structures in Graph Theory over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Limits and Structures in Graph Theory10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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