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Comments (61)

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  gortok
  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!
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  mcv
  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.
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  basil
  I’ve been using graph theory for years professionally. A good example of practical uses of graph theory is any routing software. It is basically graphs all the way down.For starters the whole street network is represented as a directed graph. The most widely used algorithm is the venerable A* to find paths through the vertices of the graph, not necessarily the shortest distance but the most optimal distance given all the trade-offs you wish based on the heuristics you define. There are lots of variations of A* and today most implementations would use its faster cousin: bidirectional A* which attacks the point-to-point calculation from both ends at the same time.Then you have Dijkstra which is used for flood searches to e.g. give the best cost back home from every vertex so you know when to turn back the search if you have a search budget.Menger’s theorem I’ve used in order to determine whether we can create a loop back. Basically search outwards, then search back without visiting those same edges.Tarjan to ensure we identify all subnetworks so we don’t get stuck in a disconnected island of vertices with no way out to join the wider network.A lot of these algorithms were conceived decades ago and are still the backbone of modern routing software.One thing that’s constantly been in the back of my mind is, since routing is a highly deterministic problem space, it doesn't seem plausible that LLMs can take this over. It seems to me that it's a good example of a tool that LLMs would call out to rather than implement themselves.In fact, see this convo I had with @simonw wherein he had Astra generate a jogging route. It setup a whole GIS stack and took about half an hour. That seems like a boil the ocean kind of approach and I’m not sure if that’s ever going to be optimal. https://x.com/baz_shkara/status/2099118620647305630
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  hackerbrother
  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 :)
• satnhak
  Looks like an excellent book, and the author is right that graph theory is a very useful and practical branch of mathematics. If only I could persuade my son to read it.
• armcat
  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
  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!
• jmspring
  Oh this was a descent into past memories. I had the pleasure to take Graph Theory at UC Santa Cruz with Gerhard Ringel [1] way back when. Excellent instructor with some great stories.[1] - https://en.wikipedia.org/wiki/Gerhard_Ringel
• the__alchemist
  Hah Ok, added to Zenodo. I historically struggle with disciplines which have "Theory" in the name. The materials feel to me as an easy intro, then rapid cliff. We'll see! (I think my brain is genetically or otherwise not good at this level of abstracting)
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  vorobeez
  It's unfortunate that the book doesn't have solutions for practice problems. Which makes it hard to use for self-learning.
• matt_daemon
  If you like graph theory Dijkstra’s in Disguise is a great read: https://blog.evjang.com/2018/08/dijkstras.htmlRelated HN thread: https://news.ycombinator.com/item?id=17745779
• GL26
  comment section looks like it's filled with bots, a lot of commenters looking like they are giving their opinion as if they had read the whole pages, sometimes irrelevant
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  throwaw12
  that background is so annoying to my eyes when scrolling the content, would be great if author can fix it
• dominicrose
  It seems the "Web server is down" for this link.
• offmutegame
  This is so cool! love it
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  ultimaterr
  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
• ImHereToVote
  I prefer to do matrices. Thanks though.
• learntoplaypitc
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• anaszewail1
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• patrick_rtk
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• rdevilla
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  cedarbyte482
  This is great, graphs is also the answer to autonomous coding :D
• Krea8ly
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