Hi, I was wondering if there was a glossary somewhere of all the various terms/names that people have for various theories? As a relatively new FNAF theorist I've got a lot to catch up, and when I'm reading old posts and seeing people use these shorthand names like everyone already knows what they mean, it can be a pain to have to stop and figure out what that theory actually is and how it related to what they're talking about.

Which characteristics (or set of characteristics) of an undirected graph, other than nodes and edges, come close to uniquely defining a graph?

For example, I can say I have a graph of one component with n nodes, n-1 and I can further give you the degree distribution, then you'll have a pretty good idea what the graph might look like.

As a bonus, how about weighted graphs?

As of Today the following leagues have achieved complete circles of suck (meaning every team has a transitive win (including OT Wins but not SO Wins) vs every other team in the conference)

[Hockey East] (https://imgur.com/a/Wvn1dwV) : Providence > New Hampshire > Vermont > Boston College > Connecticut > Mass.-Lowell > Northeastern > Maine > Merrimack > Boston University > UMass > Providence

[CCHA] (https://imgur.com/a/E8twXMd) : Lake Superior > Michigan Tech > Northern Michigan > St. Thomas > Ferris State > Minnesota State > Bowling Green > Bemidji State > Lake Superior

[Big Ten] (https://imgur.com/svSrJyq) : Michigan > Michigan State > Ohio State > Penn State > Minnesota > Notre Dame > Wisconsin > Michigan

[Atlantic Hockey] (https://imgur.com/3phMQvz): Sacred Heart > Air Force > Bentley > Holy Cross > Mercyhurst > Canisius > RIT > American Int'l > Army > Niagara > Sacred Heart

ECAC and NCHC do not have a full circle at this time

Largest ECAC Circle of Suck:

Harvard > Cornell > Dartmouth > St. Lawrence > RPI > Union > Clarkson > Harvard

Largest [NCHC] (https://imgur.com/a/MClUx5u): Circle of Suck: Western Michigan > Minnesota-Duluth > North Dakota > Denver > Western Michigan

The largest Circle of Suck is at least 52 (I say at least because I was only able to iterate over 6 million cycles):

I've heard that Graph Theory and Algebra can be applied to develop statistical theory. However, I'm having a difficult time finding a text which might work well for me as an undergraduate. My background is one semester of Abstract Algebra, Real Analysis, Combinatorics, Graph Theory, Combinatorics of Finite Sets, Differential Equations, all the Calculus, Mathematical Logic, Set Theory, Number Theory, Probability, Mathematical Statistics, and Mathematical Cryptography. I can elaborate on what I learned in these classes if that will help give a better suggestion.

Does anyone have text suggestions that are accessible to an undergraduate with this background and draw the lines between what are traditionally areas of "pure" mathematics with statistics?

hi, after seeing this recent post of a 'skew go' board i have been thinking about how to properly formalize what exactly differentiates these boards in terms of graph theory. i understand they can be described as containing polygons with different numbers of edges but im looking for something a little more rigorous than that. anybody here who has gone down this rabbit trail??

I found this video very interesting as it introduced me to the concept of graph limit and the challenge of defining a limit for sparse graphs.

What is the limit of a sequence of graphs?? | Benjamini-Schramm Convergence

Looking for more content like this about the theory and applications of graph limit. If you know of any article or video please post in the comments.

Every so often I see people asking for PMD fanfic recommendations. Despite spending entirely too much time reading fanfiction, I always hesitate to give any...I just like too many. Listing a couple off the top of my head feels like an injustice, and picking my subjective "best few" feels like a commitment. I'm not a writer; what right do I have to make subjective statements about quality?

But there's an obvious solution to this dilemma: if I aggregate many different opinions and do MATH to it, it becomes less subjective, right? And if these opinions happen to come from other authors within the community, then they might actually hold some legitimacy, right?

So, I scraped FanFiction.net and analyzed 2804 PMD fanfics (sourced from various collections and search results) so that you don't have to. This includes the various stats provided by FFnet, the 2122 authors who wrote these fics, and the 10750 reviews they wrote. This dataset is surprisingly rich, so this post will only cover the first half of my analysis (Edit: Part 2 here), and that is...

Rankings and recommendations! Extensive ones.

Here's how this post is organized, so you can skip to the parts that most interest you:

1. The main list of "most recommended" fics is first, in case you just want the results.
2. An explanation of the graph theory backing the rankings.
3. Lists for specific categories, including best up-and-coming fics, "most popular" fics, best oneshots, and longest fics.

Notes:

• I've tried to mark dead stories with an "(x)", but I might have messed up some (especially since authors sometimes mark discontinued stories as "complete"). The line is also just inherently fuzzy. I considered incomplete stories that haven't been updated in more than a couple years as "dead". This won't necessarily reflect whether a fic is maybe dead (or on "hiatus", wink-wink-nudge-nudge), or if an ongoing rewrite exists.
• I've tried to filter stories with content that's...strictly adult-only, without blanket filtering all M-rated stories (different authors interpret ratings differently). But do pay attention to the rating if that's something you care about. (Also if I clearly messed up, please let me know.)

1. Top 50 PMD fanfics, according to PMD writers

For fresh recommendations that aren't 40% dead, also see the "up-and-coming" list further down.

|Rank|Fanfic|Auth

I suspect we can use Konig's theorem for this: I find the minimum vertex cover and show that it is larger than E(G)/D, which will tell me that the maximum matching is larger than E(G)/D. The problem is that I don't know how to practically use the number of edges in G while trying to construct a vertex cover.

I'm honestly not even sure where to begin so I don't have any work that I can show. Maybe I'm completely off the mark. Any hints would be greatly appreciated.

I have a problem that I just can't figure it out: Let be an undirected graph, whose vertices represent the first n natural numbers {1,2,...n}, and two vertices are adjacent, if and only if the numbers x and y are mutually prime. Write the adjacency matrix of the graphs: G5,G6,G7. What is the structure of the Gn graph adjacency matrix?

I want to make a program that will allow you to add nodes and connections between them, and after that visualize the chosen algorithm (Dijkstra's, Bellman-Ford, Ford-Fulkerson, etc.) by coloring the nodes or edges step by step. For example, I want the user to be able to click on the canvas to add a node, and similar for the edges. I also want to be able to access the nodes, so I can change their color and keep track of them while running the algorithms. Which programming languages would be best for this use?

Hey. I'm not sure if I need a programming sub or a math sub, but I'm hoping to make something like a simplified sigmajs. I'm not sure where to get started so I'll be happy to accept an answer whether that's a graphing library like sigmajs if this will be impossible without a lot of foundational maths or just confirmation that if I study some specific part of graph theory I'll find my answer.

I've got 2 sets of data - nodes and links. Nodes contain some text and an id, links are a set of a and b, so a link of a:1 b:2 would be a link from a to b. Is graph theory or something more specific within it what I'm looking for? I would like to organize the nodes without too much overlap, don't care too much about whether the links are direct straight lines or curves.

--edit: here's a random example of how I would like to visualize some nodes:

sample

sample

sample

That last one is from neo4j. Visualizations from graph databases also seem to resemble what I'm looking for and suggest to me dynamically modeling this is very possible :)

Hi,

As the question states, in an undirected weighted graph, given up to three vertices as inputs, I would like to find the shortest cycle that starts in vertice v, goes through each of the input vertices, and return to v. The order of the input vertices does not matter, since the priority is finding the shortest cycle.

Are there any algorithms I can check to solve the problem? I know Dijkstra's but would like to know other ones as well.

Thank you very much and have a wonderful day!

I have a graph theory problem that's quite tricky to solve. Suppose you have an undirected graph with N nodes and some edges between these nodes. Now, an 'action' consists of picking a random node and deleting all its edges, and connecting it with all the nodes that it previously had no connections with. The question is to devise an algorithm that, given the number of nodes N and the initial state of the graph, can decide if it is possible, after an arbitrary number of steps, for the graph to end up being complete.

Thomson Reuters Final Round: Reverse a string.

They really sent 2 senior engineers to watch me reverse a string LMAO

if im interested in contacting a local professor regarding graph theory, would i have better luck asking in a cs or math department?

I am trying to learn Graph theory , and have found two playlists, anyone who is experienced in graph theory , can u please review them a little for me coz i don't know which one is better and covers things...

https://www.youtube.com/playlist?list=PL612CE2AB6F38DF9A

https://www.youtube.com/watch?v=E40r8DWgG40&list=PLEAYkSg4uSQ2fXcfrTGZdPuTmv98bnFY5

would be highly thankful for ur suggestions...

I’m as angry at that puzzle as everyone else, but for a different reason: I studied graph theory, and couldn’t remember how to prove it was impossible. I couldn’t see any proofs yet, or at least none that mentioned “Hamilton” or “Hamiltonian.”

So a proof. There’s a much more general proof here, but here’s an overview:

A Hamiltonian cycle includes every vertex (Spamton head) once and only once. The edges we can work with are the valid lines between Spamton heads, ie horizontal and vertical. Now you might point out that the start and end heads aren’t connected, but it wouldn’t make a difference if they were. So if we can prove there ISN’T a Hamiltonian cycle, then there isn’t a solution.

Now, here’s the trick. We’re gonna colour each Spamton head pink or yellow in a specific way. Start from the top left one. Colour it pink. The two it’s adjacent to? Yellow. The next three they’re adjacent to? Pink again. Continue alternating colours.

You’ll notice any pink head is only adjacent to yellow heads. So any valid path will have to go pink, yellow, pink, yellow, … and finally loop back to that original yellow.

But, count the number of pink and yellow Spamton heads. 1 + 3 + 5 + 3 + 1 = 13 pink, and 2 + 4 + 4 + 2 = 12 yellow. To loop all the way around, you’d need the same number of pink and yellow, since you need to transition from pink to yellow each time, and back to the first on a final yellow to pink, drawing two lines from each head to other coloured heads.

So it’s mathematically impossible! If anyone proved this elsewhere, I’ll happily link to it.

Let G be a k-regular graph without cycles of length 3. Show that G has at least 2k vertices.

I don't even know where to begin :(

Hi, I wrote a 2 part article on creating interaction networks between characters in novels and other bodies of text. The first part is a detailed literature review outlining and dissecting research papers relevant to the topic and the second part is the implementation of the thoughts and ideas presented in the first part (in python). Check it out if you're interested

Part 1 : https://towardsdatascience.com/mining-modelling-character-networks-part-i-e37e4878c467
Part 2 : https://towardsdatascience.com/mining-modelling-character-networks-part-ii-a3d77de89638

https://preview.redd.it/e4fg4bbd65h71.png?width=996&format=png&auto=webp&s=39174551e5517173481782fac9992d614a0da28e

Hello, I am trying to decide which two electives I will do alongside computer systems in my final semester of CS. I am hoping someone has done all three of these subjects and can help me out.

My current thoughts:

GRAPH THEORY:

P: loved real analysis last semester and would not mind doing another maths. Also the content seems interesting and seems applicable to CS. It is also harder to do out of uni.

N: maybe not as relevant to CS as other two (although sometimes maths subjects are better to do than cs)

AI:

P: enjoyed the algorithm subjects and the content looks fun.

ML:

P: good for industry

N: I can probably find a better course for ML online (if I can be bothered)

Let me know if you have any insights or if you really loved one of these subjects!

doi: https://doi.org/10.1167/jov.20.11.548

I am writing a lucid dreaming story, and I remember seeing 4 years ago that someone posted a bullet list of types of techniques people can use in lucid dreams. I don't remember what that link was, but it was interesting that everything had a term for it. Such as creating an object out of thin air & the limitations of everything.

I'm signed up for CSCI graph theory for next semester, and I see on quacs that there is the exact same course, with the same teacher and same time, but it's a MATH instead of CSCI, but it's full, I still need more maths credits.

Anybody know if there is there any way I can take the course as MATH instead of a CSCI?

I'd like to start getting more in depth with my music theory training in advance, but it's frustrating when I have to manually categorize everything myself.

Hi,

As the question states, in an undirected weighted graph, given up to three vertices as inputs, I would like to find the shortest cycle that starts in vertice v, goes through each of the input vertices, and return to v. The order of the input vertices does not matter, since the priority is finding the shortest cycle.

Are there any algorithms I can check to solve the problem? I know Dijkstra's but would like to know other ones as well.

Thank you very much and have a wonderful day!

Hi,

As the question states, in an undirected weighted graph, given up to three vertices as inputs, I would like to find the shortest cycle that starts in vertice v, goes through each of the input vertices, and return to v. The order of the input vertices does not matter, since the priority is finding the shortest cycle.

Are there any algorithms I can check to solve the problem? I know Dijkstra's but would like to know other ones as well.

Thank you very much and have a wonderful day!