Yes, simple graphs and symmetric digraphs are equivalent; their categories are even isomorphic!
But, I prefer the 2-cycles over undirected edges. 
#mathematics #graphtheory #categorytheory #hottake
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Yes, simple graphs and symmetric digraphs are equivalent; their categories are even isomorphic!
But, I prefer the 2-cycles over undirected edges. #mathematics #graphtheory #categorytheory #hottake
#git can be hard, like anything if you want to understand it
So are DAGs
Then again of you want to start with git and get to #graphtheory , which is fun in my view. It ll be after months of accidents
No employer wants that on their payroll and no team or authority wants to be responsible for it or accepts it and it ll be a nightmare for the person after fun.
So the society, the institution and the market collectively orient workforce not to have fun in learning things, including cubicles.
Oh yes move fast and break thing , but at your expense, which clearly is hoarded.
That explains a lot , including the rise of #ai
#git
https://ohshitgit.com/
Replied in thread
@paysmaths
Lowell Beineke, still attending graph theory talks in April 2025 (seated on the right) 
#math #GraphTheory #PurdueFortWayne
Ok, someone more familiar with graph theory tell me how to compute a minimum weight perfect matching on a complete graph with even-number of vertices? Or at least point me to a resource?
It's all either left as an exercise to the reader, extremely complex algorithms (Blossom or something?), or weird libraries, where apparently if I use it on complex graphs it's not necessary, but they then point me to even more complex papers.
Thought I had it solved but now it's returning a matching that's too small.
#graphtheory #computerscience #academia
A free book about Graph Theory and Additive Combinatorics.
Yufei ZhaoGraph Theory and Additive CombinatoricsGraph Theory and Additive Combinatorics (book project) by Prof. Yufei Zhao
Minimum spanning tree of a dithered image, 4096 vertices. Model: Swetlana
Without formal training, the way I modeled physical distribution system #Infrastructure for utilities districts in my #Django app evolved significantly over time.
As I learned more about graph theory and simulation, I figured out how to model for both the physical structure and the logical aspects of their interconnection and behavior in various scenarios.
#GraphTheory #WaterInfrastructure #Modeling
1/6
For various (mathematical, meteorological, alimentary) reasons, I usually prefer 2π day.
Nevertheless, today I make the following offering:
http://arxiv.org/abs/2503.10002
Pjotr Buys, @Janvadehe and I used Shearer's induction to address the question:
How few independent sets can a triangle-free graph of average degree d have?
The answer is close to how many a random graph has.
What is perhaps surprising is just *how* close it comes.
(I queried the combinatorial hive mind about this last week.)
arXiv.orgTriangle-free graphs with the fewest independent setsGiven $d>0$ and a positive integer $n$, let $G$ be a triangle-free graph on $n$ vertices with average degree $d$. With an elegant induction, Shearer (1983) tightened a seminal result of Ajtai, Komlós and Szemerédi (1980/1981) by proving that $G$ contains an independent set of size at least $(1+o(1))\frac{\log d}{d}n$ as $d\to\infty$.
By a generalisation of Shearer's method, we prove that the number of independent sets in $G$ must be at least $\exp\left((1+o(1))\frac{(\log d)^2}{2d}n\right)$ as $d\to\infty$. This improves upon results of Cooper and Mubayi (2014) and Davies, Jenssen, Perkins, and Roberts (2018). Our method also provides good lower bounds on the independence polynomial of $G$, one of which implies Shearer's result itself. As certified by a classic probabilistic construction, our bound on the number of independent sets is sharp to several leading terms as $d\to\infty$.
This video is a really pretty visualization of the A* pathfinding algorithm using #OpenStreetMap road network data for #Chicago and #Rome as examples.
youtu.be- YouTubeEnjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
Calling all #igraph enthusiasts!
We've identified and fixed a bug in {ig.degree.betweenness} related to the cluster_edge_betweenness() function.
The issue stemmed from a grep() action used for subgraph identification.
A fix has been implemented, and an update has been pushed to CRAN—it will be available in the coming days.
In the meantime, you can reinstall from the main branch here: https://github.com/benyamindsmith/ig.degree.betweenness
Continued thread
Cactus Language • Overview 3.2
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/
Given a body of conceivable propositions we need a way to follow the threads of their indications from their object domain to their values for the mind and a way to follow those same threads back again. Moreover, we need to implement both ways of proceeding in computational form. Thus we need programs for tracing the clues sentences provide from the universe of their objects to the signs of their values and, in turn, from signs to objects. Ultimately, we need to render propositions so functional as indicators of sets and so essential for examining the equality of sets as to give a rule for the practical conceivability of sets. Tackling that task requires us to introduce a number of new definitions and a collection of additional notational devices, to which we now turn.
Resources —
Cactus Language • Overview
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory
Inquiry Into Inquiry · Cactus Language • Overview 3
More from 
Inquiry Into Inquiry
Continued thread
Cactus Language • Overview 3.1
• https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/
In the development of Cactus Language to date the following two species of graphs have been instrumental.
• Painted And Rooted Cacti (PARCAI).
• Painted And Rooted Conifers (PARCOI).
It suffices to begin with the first class of data structures, developing their properties and uses in full, leaving discussion of the latter class to a part of the project where their distinctive features are key to developments at that stage. Partly because the two species are so closely related and partly for the sake of brevity, we'll always use the genus name “PARC” to denote the corresponding cacti.
To provide a computational middle ground between sentences seen as syntactic strings and propositions seen as indicator functions the language designer must not only supply a medium for the expression of propositions but also link the assertion of sentences to a means for inverting the indicator functions, that is, for computing the “fibers” or “inverse images” of the propositions.
#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#AutomataTheory #FormalLanguages #FormalGrammars #GraphTheory
Inquiry Into Inquiry · Cactus Language • Overview 3
More from Inquiry Into Inquiry
Continued thread
Cactus Language • Overview 1.2
• https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/
Resource —
For readers interested and intrepid enough to read ahead, here’s an outline of my work in progress on the OEIS Wiki, which I’ll be revising and serializing to my Inquiry blog.
Part 1
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1
Cactus Language • Syntax
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Syntax
Part 2
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2
Generalities About Formal Grammars
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2#Generalities
Part 3
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3
Cactus Language • Stylistics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stylistics
Cactus Language • Mechanics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Mechanics
Cactus Language • Semantics
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Semantics
Stretching Exercises
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stretching_Exercises
References
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_References
Document History
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Document_History
#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#Automata #FormalLanguages #FormalGrammars #GraphTheory
Inquiry Into Inquiry · Cactus Language • Overview 1
More from Inquiry Into Inquiry
Cactus Language • Overview 1.1
• https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/
❝Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually no knowledge in immediately adjacent areas. If our intellectual gaze could shift slightly, it would alter each quill’s direction, and suddenly our entire reality would change.❞
— Herbert J. Bernstein • “Idols of Modern Science”
The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions. In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called “painted cacti”.
Painted cacti are a specialization of what graph‑theorists refer to as “cacti”, which are in turn a generalization of what they call “trees”. The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint. The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.
#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#Automata #FormalLanguages #FormalGrammars #GraphTheory
Inquiry Into Inquiry · Cactus Language • Overview 1
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A question for the (combinatorial) hive mind.
There are a lot of extremal results that are matched asymptotically by some probabilistic construction, but with some gap, often quite substantial. I'm thinking about the Ramsey numbers R(k,k) or R(3,k), but examples of this phenomenon are prevalent.
I'm curious, does someone out there know of good examples of (extremal) results where some probabilistic construction (e.g. via a random graph) is matched asymptotically, and very precisely?
Visualizing Interconnected Networks with Matplotlib and NetworkX
Learn to visualize complex networks using Network Visualization Matplotlib & NetworkX in Python. Create insightful visualizations & communicate complex data clearly! #NetworkVisualization #Python #Matplotlib #NetworkX #DataVisualization #GraphTheory
https://tech-champion.com/programming/python-programming/visualizing-interconnected-networks-with-matplotlib-and-networkx/
Efficiently Creating and Visualizing Symmetric Adjacency Matrices in Python
Master Python Adjacency Matrix techniques! Learn efficient creation, NetworkX visualization, & handling of large datasets. Represent & analyze complex relationships in your data. #PythonAdjacencyMatrix #GraphTheory #NetworkX #DataVisualization #DataScience #GraphAlgorithms
https://tech-champion.com/programming/python-programming/efficiently-creating-and-visualizing-symmetric-adjacency-matrices-in-python/
Network Graph Visualization: Improving Clarity in Dense Clusters with NetworkX
Improve Network Graph Visualization with NetworkX & Matplotlib! Learn simple yet effective strategies to enhance clarity, especially in dense clusters. Explore alternative layout algorithms & parameter adjustments for insightful data representation. #NetworkGraphVisualization #NetworkX #Matplotlib #DataVisualization #GraphTheory #Python
https://tech-champion.com/programming/python-programming/network-graph-visualization-improving-clarity-in-dense-clusters-with-networkx/