@NetworkFact

Daily tweets about networks, graph theory, and related topics from @JohnDCook

johndcook.com/blog/complex-networks/
Joined July 2013
  • Tweets4.3K
  • Following19
  • Followers46.3K
223Media
Network Fact retweeted
Cliff Pickover
@pickover21 Nov 2025
Mathematics. Don't you just love the "Szekeres Snark"? In the mathematical field of graph theory, the Szekeres Snark is a snark with 50 vertices and 75 edges. It was the fifth known snark, discovered by George Szekeres in 1973. Source: tinyurl.com/2svcfhyt
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Network Fact retweeted
Cliff Pickover
@pickover8 Jul 2025
Physics. Mathematics. Reality. Universe. Stephen Wolfram's "Theory of Everything" is free online, as a 448-page PDF. Here is a sample figure, to intrigue you (p. 31). Source: arxiv.org/abs/2004.08210
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Using the pseudoinverse of a matrix to compute effective graph resistance johndcook.com/blog/2025/05/2…
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A good one
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Excited to launch my new book website featuring my new book, Dots and Lines: Hidden Networks in Social Media, AI, and Networks, coming out May 13. Check it out anthonybonato.com
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New tool to explore the social graphs of powerful people
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Match the networks
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Social network of Socrates
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A directed graph of every Chess opening
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Network Fact retweeted
Almost Sure@Almost_Sure27 Jan 2025
Random Fact: The order of a random permutation of n elements is approximately lognormal, for large n
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Mathieu
@miniapeur7 Jan 2025
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Tutte embedding is the solution of a Poisson equation. Iterative resolution is equivalent to a system of masses and springs. en.wikipedia.org/wiki/Tutte_… nbviewer.jupyter.org/github/…
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Schur’s theorem: If the integers are colored with a finite number of colors, there is always a monochrome solution to x + y = z.
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Occasionally in mathematics a statement that just has to be true turns out to be false. A paper appeared on arXiv today that disproves a well-known conjecture in probability called the bunkbed conjecture. 🧵 arxiv.org/abs/2410.02545

The bunkbed conjecture is false

We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of...

arxiv.org
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Oldies but goldies: William Thomas Tutte, How to draw a graph, 1963. Shows how to embed a planar graph in 2-D by solving a Laplacian linear system. Heavily used in mesh processing to compute surface parameterization. en.wikipedia.org/wiki/Tutte_… cs.jhu.edu/~misha/Fall07/Pap…
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Network Fact retweeted
Algebra Etc.@AlgebraFact8 Jun 2024
New post: Eigenvector centrality johndcook.com/blog/2024/06/0…
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Oldies but goldies: Paul Erdős, Alfred Renyi, On Random Graphs, 1959. Defines the basic model for random graphs and studies some of its properties. en.wikipedia.org/wiki/Erd%C5…
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Network Fact retweeted
Kirk Borne
@KirkDBorne3 Feb 2024
Introduction to Graph Theory: arxiv.org/abs/2308.04512 (422-page PDF) — edges, vertices, trees, networks, paths, and graphs (and theorems!) + Source for attached graphic: oreilly.com/library/view/gra… ————— #Mathematics #NetworkScience #DiscreteMath #GraphTheory
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