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.
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.
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 :)
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!
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.
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.
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.
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.
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.
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
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 :)
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!
It's unfortunate that the book doesn't have solutions for practice problems. Which makes it hard to use for self-learning.
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.
You can ask Claude for the solutions?
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.
For elaborating something unclear they're great tho.
If you don't have the solutions, how do you verify Claude's work?
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.
According to current practices, you ask ChatGPT or DeepSeek to verify it.
that background is so annoying to my eyes when scrolling the content, would be great if author can fix it
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This is great, graphs is also the answer to autonomous coding :D
How so?
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.
I am even more confused after this answer: Are the nodes actual reviews or something else?
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.