Start Doing Graph Theory

(vertex.degree)

188 points | by ibobev 4 days ago

11 comments

  • mcv 54 minutes ago
    I've been doing a lot with graphs over the past couple of years. Basically since I started using neo4j, although not everything involves neo4j directly. I've developed a number of really interesting graph algorithms, but I'm always a bit disappointed by how little use I get out of my graph theory knowledge. I've never needed a Hamilton path or do something with the degrees of my vertices. It's all just logic and intuition.

    But maybe I should read this to see if there's anything that applies to my current work.

    • throw-qqqqq 6 minutes ago
      My personal experience has been that the simpler undergrad algorithms are the most applicable. That’s probably also why you learn them first.

      IMO, it’s much more practical to thoroughly learn and understand the simpler techniques. There is often more depth to it, than you’d think.

      Analogy: Many (most?) MMA matches are won with techniques you learn in the first year.

      Aside: I’ve gotten much more mileage out of simple statistics in the 16 years since I graduated, than advanced algorithms.

  • gortok 27 minutes ago
    A problem I didn’t even conceive of a year ago was whether or not a book was written by a human.

    This author has done nothing to deserve that scrutiny, but I can’t escape the feeling now of having to be guarded when I see a new book online with a relatively short history (spring 2026 is the earliest version of this text), as I can’t be sure it’s either “AI-enhanced” or AI-written.

    I don’t like this feeling and it dampers any enthusiasm I once had for being excited about stuff like this.

    That aside, if the author did write this themselves without AI, kudos to them and their acheivement!

    • layer8 19 minutes ago
      I spot-checked a few random chapters, and it looks clearly human-written to me. But I share your general worry.
  • hackerbrother 1 hour ago
    Cool. I am applying to jobs and it seems graph theory is popular in the "Leet Code" questions pace. So very timely, thank you! And clever domain name :)
  • armcat 54 minutes ago
    Graphs are fantastic - PageRank [1] that powered Google Search (still does to some extent), TextRank for extractive text summarisation [2], Louvain for neighbourhood detection [3] all use graphs, as well as tonnes of others like belief propagation, Markov clustering, A*, and so on. So yeah, learn it.

    [1] https://en.wikipedia.org/wiki/PageRank

    [2] https://aclanthology.org/W04-3252.pdf

    [3] https://en.wikipedia.org/wiki/Louvain_method

  • igleria 2 hours ago
    not super fond of my memories of having to come up with a graph demonstration on a fixed time on a paper exam, but at least I can say I was once a person that could do that!
  • matt_daemon 39 minutes ago
    If you like graph theory Dijkstra’s in Disguise is a great read: https://blog.evjang.com/2018/08/dijkstras.html

    Related HN thread: https://news.ycombinator.com/item?id=17745779

  • ultimaterr 36 minutes ago
    what applications is this useful for? node topology is already a solved problem for decentralized networks since most validators are on aws. unless this is for fun? theres finite space to order nodes topologically speaking tbh
  • vorobeez 2 hours ago
    It's unfortunate that the book doesn't have solutions for practice problems. Which makes it hard to use for self-learning.
    • OgsyedIE 1 hour ago
      The book you want in this case is Gross, Yellen & Anderson, Graph Theory and its Applications, 3rd Edition.

      There are plenty of ways to get a copy.

    • eru 1 hour ago
      You can ask Claude for the solutions?
      • vorobeez 1 hour ago
        Sure I can. But from my experience solutions in math books usually continue learning process and can provide even more insight to a problem. Solutions from ChatGPT or Claude barely can replace that.

        (Edit) But I understand that goal of a book can be completely different. So it's just problem of my expectations.

        • karmakurtisaani 54 minutes ago
          For elaborating something unclear they're great tho.
      • Gormo 1 hour ago
        If you don't have the solutions, how do you verify Claude's work?
        • DecoPerson 1 hour ago
          Everything, except the bleeding edge and situations requiring the context window to be more than 60% filled, are elementary to Opus 5.5 . If you provide the questions completely, you can be very sure that Claude’s solutions will be correct. The world has changed; AI is reliable; we need to adapt.
          • adamddev1 23 minutes ago
            > The world has changed; AI is reliable; we need to adapt.

            Yes, but I think it's important to state that it's only reliable for things that are very well known and extensively written about.

        • deredede 1 hour ago
          According to current practices, you ask ChatGPT or DeepSeek to verify it.
          • Gormo 28 minutes ago
            Turtles all the way down, I guess.
  • throwaw12 2 hours ago
    that background is so annoying to my eyes when scrolling the content, would be great if author can fix it
  • rdevilla 2 hours ago
    [dead]
  • cedarbyte482 2 hours ago
    This is great, graphs is also the answer to autonomous coding :D
    • roarcher 2 hours ago
      How so?
      • cedarbyte482 2 hours ago
        We have experienced that adverserial review cycles is the only way to really guarantee good outputs from coding agents - best modelled as a cyclic graph.
        • sandos 1 hour ago
          I am even more confused after this answer: Are the nodes actual reviews or something else?
        • eru 1 hour ago
          I don't think modelling this as a graph adds anything that you wouldn't get from the phrase 'adversarial review cycles' already. So graph theory is pretty much useless for this application.

          Please prove me wrong.

          • ultimaterr 28 minutes ago
            what does neuron topology have to do with autonomous coding? MLP problem? doesn't make any sense