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Everything about Graphon
Function type in graph theory
In graph theory and statistics, a graphon is a symmetric measurable function, that is important in the study of dense graphs. Graphons arise both as a natural notion for the limit of a sequence of dense graphs, and as the fundamental defining objects of exchangeable random graph models. Graphons are tied to dense graphs by the following pair of observations: the random graph models defined by graphons give rise to dense graphs almost surely, and, by the regularity lemma, graphons capture the structure of arbitrary large dense graphs. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: GraphonA 5-minute orientation
- Skim a recent paper: Graphon Games: A Statistical Framework for Network Games and InterventionsInfluential work since 2022
- Pick up a classic book: GRAPHON CORP DEThe most-reprinted book on the subject
- Read the landmark paper: Raman spectra of Graphon carbon blackCited 157 times
- Go sideways: Counting lemmaA closely related topic
- Go sideways: Pseudorandom graphA closely related topic
📖 Definitions
Noun The completion of the metric space of the set of finite graphs endowed with the cut metric.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Raman spectra of Graphon carbon black
Rate-optimal graphon estimation
Adsorption of non-ionic surface-active agents at the Graphon/solution interface
Calculation of Thermodynamic Functions of Adsorbed Molecules from Adsorption Isotherm Measurements: Nitrogen on Graphon1,2
Graphon Mean Field Games and Their Equations
Thermodynamics of the Adsorption of Water on Graphon from Heats of Immersion and Adsorption Data
Graphon Control of Large-Scale Networks of Linear Systems
Hydrophilic oxygen complexes on activated graphon
🆕 Influential since 2022
📚 Books worth reading
- 📕GRAPHON CORP DEICON Group Ltd. · 2000
- 📕Esōterikai enargeiai tēs empneuseōs Tōn Graphōn ...Thomas Hartwell Horne · 1834
- 📕Ho graphōn paragraphei, metagraphete hōs einaiNikolaos V. Tōmadakēs · 1973
- 📕Apanthisma tōn Hierōn GraphōnGrēgorios Kalaganēs · 1851
- 📕Esōterikai enargeiai tēs empneuseōs tōn GraphōnNeophytos Vamvas · 1837
- 📕Plēres enkyklopaidikon lexikon tōn Hagiōn Graphōn · 1983
- 📕A Graphon-based Framework for Modeling Large NetworksRan He · 2015
- 📕Lexikon tōn Hagiōn GraphōnG. Kōnstantinou · 1888
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Counting lemma The counting lemmas this article discusses are statements in combinatorics and graph theory. The first one extracts information from ϵ-regular pairs of…
- Pseudorandom graph In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete…
- Szemerédi regularity lemma In extremal graph theory, Szemerédi's regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between…
- Erdős–Stone theorem In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph…
- Expander code In coding theory, expander codes form a class of error-correcting codes that are constructed from bipartite expander graphs. Along with Justesen codes…
- Phase-field models on graphs Phase-field models on graphs are a discrete analogue to phase-field models, defined on a graph. They are used in image analysis (for feature identification)…
- Grothendieck inequality In mathematics, the Grothendieck inequality states that there is a universal constant K G {\displaystyle K_{G}} with the following property. If Mij is…
- Johnson–Lindenstrauss lemma In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings…