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Topic · Geometry and Topology

Graph theory and applications

Graph theory and applications is a research topic within Geometry and Topology. Science Explorer counts 18k 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 focuses on the study of graph spectra, topological indices, Laplacian energy, resistance distance, and their applications in analyzing molecular structures and networks.

  • Graph Spectra
  • Topological Indices
  • Laplacian Energy
  • Resistance Distance
  • Molecular Structure
  • Eccentric Connectivity Index
  • Spectral Radius
  • Distance Spectra
  • Eigenvalues
  • Networks
Research works
18k
fractional, since 1950
In the world top 10%
1.9k
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
36% of the 10 largest, 2022-now
Graph theory and applications

Which countries lead Graph theory and applications research?

By volume, China and India publish the most (976 and 581 works in 2022-now).

By volume, 2022-now

  1. 1 China 976 works
  2. 2 India 581 works
  3. 3 United States 384 works
  4. 4 Pakistan 172 works
  5. 5 Russia 108 works
  6. 6 Iran 106 works
  7. 7 United Kingdom 90 works
  8. 8 Türkiye 88 works
  9. 9 Germany 87 works
  10. 10 Saudi Arabia 86 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: 36.4%India: 21.7%United States: 14.3%Pakistan: 6.4%6 others listed: 21.1%36%largest
China976 · 36.4%India581 · 21.7%United States384 · 14.3%Pakistan172 · 6.4%6 others listed565 · 21.1%

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

Which institutions lead Graph theory and applications research?

By volume in 2022-now, Vellore Institute of Technology University publishes the most Graph theory and applications research, followed by Centre National de la Recherche Scientifique and Xinjiang University.

By volume, 2022-now

  1. 1 Vellore Institute of Technology UniversityIndia 48 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 39 works
  3. 3 Xinjiang UniversityChina 35 works
  4. 4 Russian Academy of SciencesRussia 35 works
  5. 5 COMSATS University IslamabadPakistan 29 works
  6. 6 East China University of Science and TechnologyChina 25 works
  7. 7 South China Normal UniversityChina 24 works
  8. 8 Qinghai Normal UniversityChina 24 works
  9. 9 Nankai UniversityChina 22 works
  10. 10 Northwestern Polytechnical UniversityChina 22 works

Who are the leading researchers in Graph theory and applications?

The most-cited researchers publishing on Graph theory and applications include Kenji Watanabe, Takashi Taniguchi and Albert-Ĺaszló Barabási.

  1. 1 Kenji Watanabe Japan 237k citations
  2. 2 Takashi Taniguchi Japan 227k citations
  3. 3 Albert-Ĺaszló Barabási United States 223k citations
  4. 4 Harry Eugene Stanley United States 198k 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 Graph theory and applications?

The most cited paper in Graph theory and applications is "A tutorial on spectral clustering" (Ulrike von Luxburg, 2007), with 10,505 citations. Next come "A Set of Measures of Centrality Based on Betweenness" (10,473) and "Spectral Graph Theory" (5,771).

Most cited papers
#PaperReleasedCitations
1 A tutorial on spectral clustering Ulrike von Luxburg · Statistics and Computing Open access 21 Aug 2007 10,505
2 A Set of Measures of Centrality Based on Betweenness Linton C. Freeman · Sociometry Mar 1977 10,473
3 Spectral Graph Theory Fan Chung · Regional conference series in mathematics Conference paper 3 Dec 1996 5,771
4 Inequalities: Theory of Majorization and its Applications. Barry C. Arnold, Albert W. Marshall, Ingram Olkin · Journal of the American Statistical Association Jun 1981 5,007
5 Finding community structure in networks using the eigenvectors of matrices Mark E. J. Newman · Physical Review E Open access 11 Sep 2006 4,927
All 100 most cited papers, with filters and sorting

Where is Graph theory and applications research done?

The largest centres of Graph theory and applications research in 2022-now are Shanghai (China), Beijing (China), Chennai (India) and Lahore (Pakistan). Among places with at least 20 works in it, it is an unusually large share of all research in Xining.

Largest cities, 2022-now

  1. 1 ShanghaiChina 94 works
  2. 2 BeijingChina 71 works
  3. 3 ChennaiIndia 63 works
  4. 4 LahorePakistan 51 works
  5. 5 VelloreIndia 50 works
  6. 6 GuangzhouChina 49 works
  7. 7 ÜrümqiChina 47 works
  8. 8 Xi'anChina 45 works
  9. 9 IslamabadPakistan 45 works
  10. 10 MoscowRussia 44 works

Where it is the local speciality

  1. XiningCN · 40.0 works35×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Graph theory and applications than the world average.

See Graph theory and applications on the map

Where is the best place to study Graph theory and applications?

Among universities, judged by research, Vellore Institute of Technology University, University of Sialkot and COMSATS University Islamabad 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 29.82%fractional works in this field (log) →share of work in the world top 10% →University of SialkotVellore Institute of…Riphah International…COMSATS University I…
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
1Vellore Institute of Technology UniversityIndia 67.229.1%14.6×48 +496.2%
2University of Sialkot 65.070.8%151.0×8 +349.3%
3COMSATS University IslamabadPakistan 59.424.2%37.0×29 -8.2%
4Riphah International UniversityPakistan 53.528.3%35.7×16 +184.6%
5Jazan UniversitySaudi Arabia 51.626.8%18.1×12 +109.3%
6Xinjiang UniversityChina 49.88.2%24.3×35 +83.8%
7East China University of Science and TechnologyChina 49.614.7%15.0×25 +107.4%
8Sungkyunkwan UniversitySouth Korea 49.237.3%6.5×15 +15.5%
9South China Normal UniversityChina 48.712.3%20.5×24 +34.7%
10Jiangsu University of Science and TechnologyChina 48.746.5%9.6×10 +65.2%

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 Graph theory and applications, country by country

Is Graph theory and applications research growing?

Output in 2022-2025 was 26% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Graph theory and applications.

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 Graph theory and applications as a percentage of every work published that year, 0.016% in 2024.

still counting0.010%0.020%0.030%Graph theory and applications0.016% in 202519801990200020102020

Fractional works of Graph theory and applications 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%Graph theory and applications10.0% 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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