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Topic · Computational Theory and Mathematics

Advanced Graph Theory Research

Advanced Graph Theory Research is a research topic within Computational Theory and Mathematics. Science Explorer counts 33k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers represents advances in graph theory and algorithms, focusing on topics such as parameterized complexity, fixed-parameter algorithms, constraint satisfaction problems, treewidth, kernelization, complexity classification, approximation algorithms, and homomorphism. The papers cover a wide range of algorithmic applications and theoretical developments in the field of graph theory.

  • Graph Theory
  • Parameterized Complexity
  • Algorithmic Applications
  • Fixed-Parameter Algorithms
  • Constraint Satisfaction Problems
  • Treewidth
  • Kernelization
  • Complexity Classification
  • Approximation Algorithms
  • Homomorphism
Research works
33k
fractional, since 1950
In the world top 10%
3.3k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+13%
the tick is no change
Largest producer
China
28% of the 10 largest, 2022-now
Advanced Graph Theory Research

Which countries lead Advanced Graph Theory Research research?

By volume, China and the United States publish the most (992 and 746 works in 2022-now).

By volume, 2022-now

  1. 1 China 992 works
  2. 2 United States 746 works
  3. 3 India 575 works
  4. 4 Germany 271 works
  5. 5 France 224 works
  6. 6 United Kingdom 187 works
  7. 7 Japan 156 works
  8. 8 Canada 154 works
  9. 9 Brazil 127 works
  10. 10 Israel 117 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: 27.9%United States: 21.0%India: 16.2%Germany: 7.6%6 others listed: 27.2%28%largest
China992 · 27.9%United States746 · 21.0%India575 · 16.2%Germany271 · 7.6%6 others listed966 · 27.2%

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

Which institutions lead Advanced Graph Theory Research research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Graph Theory Research research, followed by ETH Zurich and Mindanao State University – Iligan Institute of Technology.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 104 works
  2. 2 ETH ZurichSwitzerland 41 works
  3. 3 Mindanao State University – Iligan Institute of TechnologyPhilippines 40 works
  4. 4 Zhejiang Normal UniversityChina 37 works
  5. 5 Charles UniversityCzechia 36 works
  6. 6 Hungarian Academy of SciencesHungary 36 works
  7. 7 Xinjiang UniversityChina 35 works
  8. 8 University of WaterlooCanada 33 works
  9. 9 University of OxfordUnited Kingdom 31 works
  10. 10 Nankai UniversityChina 27 works

Who are the leading researchers in Advanced Graph Theory Research?

The most-cited researchers publishing on Advanced Graph Theory Research include Kai You Wang, Harry Eugene Stanley and Michael I. Jordan.

  1. 1 Kai You Wang China 224k citations
  2. 2 Harry Eugene Stanley United States 198k citations
  3. 3 Michael I. Jordan United States 182k citations
  4. 4 Stephen Boyd United States 142k citations
  5. 5 Philip S. Yu United States 141k citations
  6. 6 Mark E. J. Newman United States 138k 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 Advanced Graph Theory Research?

The most cited paper in Advanced Graph Theory Research is "Reducibility among Combinatorial Problems" (Richard M. Karp, 1972), with 11,108 citations. Next come "A Set of Measures of Centrality Based on Betweenness" (10,473) and "Combinatorial Optimization: Algorithms and Complexity." (6,041).

Most cited papers
#PaperReleasedCitations
1 Reducibility among Combinatorial Problems Richard M. Karp Book chapter 1972 11,108
2 A Set of Measures of Centrality Based on Betweenness Linton C. Freeman · Sociometry Mar 1977 10,473
3 Combinatorial Optimization: Algorithms and Complexity. David Johnson, Christos H. Papadimitriou, Kenneth Steiglitz · American Mathematical Monthly Mar 1984 6,041
4 Spectral Graph Theory Fan Chung · Regional conference series in mathematics Conference paper 3 Dec 1996 5,771
5 A new polynomial-time algorithm for linear programming Narendra K. Karmarkar · COMBINATORICA Dec 1984 4,858
All 98 most cited papers, with filters and sorting

Where is Advanced Graph Theory Research research done?

The largest centres of Advanced Graph Theory Research research in 2022-now are Beijing (China), Chennai (India), Shanghai (China) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Iligan City, Tirunelveli and Xining.

Largest cities, 2022-now

  1. 1 BeijingChina 103 works
  2. 2 ChennaiIndia 87 works
  3. 3 ShanghaiChina 78 works
  4. 4 ParisFrance 78 works
  5. 5 BudapestHungary 60 works
  6. 6 TokyoJapan 56 works
  7. 7 PragueCzechia 53 works
  8. 8 BengaluruIndia 49 works
  9. 9 NanjingChina 48 works
  10. 10 TianjinChina 45 works

Where it is the local speciality

  1. Iligan CityPH · 40.1 works68×
  2. TirunelveliIN · 22.6 works32×
  3. XiningCN · 31.5 works21×
  4. JinhuaCN · 37.5 works20×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Graph Theory Research than the world average.

See Advanced Graph Theory Research on the map

Where is the best place to study Advanced Graph Theory Research?

Among universities, judged by research, ETH Zurich, University of Oxford and Princeton University 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%25%50%75%mean 20.55%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityUniversity of OxfordUniversity of WaterlooETH 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
1ETH ZurichSwitzerland 68.210.5%13.3×41 +75.4%
2University of OxfordUnited Kingdom 63.117.6%5.0×31 +79.3%
3Princeton UniversityUnited States 62.223.3%11.1×22 +135.4%
4University of WaterlooCanada 61.312.7%13.6×33 +56.1%
5Mindanao State University – Iligan Institute of TechnologyPhilippines 60.49.7%219.5×40 +253.2%
6Charles UniversityCzechia 58.64.7%17.5×36 +15.5%
7Jiangsu University of Science and TechnologyChina 58.060.9%6.5×9 +5.0%
8University of WarwickUnited Kingdom 57.716.8%11.8×24 +69.0%
9Xinjiang UniversityChina 56.414.3%18.5×35 +71.3%
10East China University of Science and TechnologyChina 55.035.0%5.9×13 +104.1%

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 Advanced Graph Theory Research, country by country

Is Advanced Graph Theory Research research growing?

Output in 2022-2025 was 13% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Advanced Graph Theory Research.

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 Advanced Graph Theory Research as a percentage of every work published that year, 0.019% in 2024.

still counting0.020%0.040%0.060%Advanced Graph Theory Research0.021% in 202519801990200020102020

Fractional works of Advanced Graph Theory Research 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%Advanced Graph Theory Research9.7% 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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