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29 votes
3 answers
2k views

Exceptional books on real world applications of graph theory.

What are some exceptional graph theory books geared explicitly towards real-world applications? I would be interested in both general books on the subject (essentially surveys of applied graph theory ...
Alexander Gruber's user avatar
  • 27.2k
11 votes
1 answer
732 views

What precisely is the Friendship Paradox (and is Wikipedia wrong?)

Friendship paradox is the somewhat well-known statement that "statistically speaking, your friends have more friends than you do". To my mind, which is surely ignorant of any complexities of social ...
Jakub Konieczny's user avatar
10 votes
1 answer
1k views

Application of Combinatorics/Graph Theory to Organic Chemistry?

Recently, I have been self-teaching graph theory and having an organic chemistry course at school. When I was learning isomer enumeration I found great resemblance between organic molecules and ...
Yuxiao Xie's user avatar
  • 8,656
8 votes
3 answers
4k views

Uses of the incidence matrix of a graph

The incidence matrix of a graph is a way to represent the graph. Why go through the trouble of creating this representation of a graph? In other words what are the applications of the incidence matrix ...
Asinomás's user avatar
  • 106k
8 votes
2 answers
453 views

The Mathematics of Symbol Recognition.

I wonder what Mathematics is behind handwriting and symbol recognition. I was using Detexify just now and it struck me that a distinction could be made between $\varsigma$ (a variant of the Greek ...
Shaun's user avatar
  • 45.8k
8 votes
2 answers
605 views

Longest Path in Path of Exile

Background: In the popular online video game Path of Exile, there is a skill tree that players can allocate points to as they gain levels. The skill tree is essentially a connected graph where a node ...
Mark B's user avatar
  • 2,014
8 votes
0 answers
724 views

How is graph theory used to solve problems in number theory?

What are some applications of graph theory in number theory? How can a graph theory approach be useful to solving number theory problems? In general, is graph theory ever useful in making number ...
okarin's user avatar
  • 2,231
6 votes
0 answers
44 views

Extending a common-neighbor statistic to more than two nodes

first time poster here (happy to edit if I am violating any guidelines, please just let me know) :) I am curious whether the following formula from this paper by Li and Liang for the probability of an ...
Gabe Simmons's user avatar
5 votes
3 answers
2k views

Does "Big Data" Have a Ramsey Theory Problem?

I'm erring on the side of conservatism asking here rather than MO, as it is possible this is a complex question. "Big Data" is the Silicon Valley term for the issues surrounding the huge amounts of ...
user avatar
5 votes
1 answer
171 views

How to draw Congressional districts to mirror the Popular Vote

Let me preface this by saying that I'm not sure whether this is fundamentally a mathematical question or not, but I think it is. In the United States, the House of Representatives is elected roughly ...
Keshav Srinivasan's user avatar
4 votes
1 answer
537 views

Graph theory application of homology

I am struggling with the idea of local homology groups and would like to see an example of how to go about finding them in general. I'm thinking of the most trivial case to apply the theory of local ...
user123's user avatar
  • 291
4 votes
0 answers
719 views

Applications of Prüfer sequence

Reading a book about a graph theory I found out about Prüfer's sequences which converts a labeled tree of $n$ vertices into an array of $n-2$ numbers. I was actually pretty surprised by this and was ...
Salvador Dali's user avatar
3 votes
1 answer
1k views

Graph (or Group) in Astronomy

Is there an application of graph theory (or group theory) in astronomy. If there is, refer me some references.
H. Shabani's user avatar
3 votes
0 answers
30 views

Projection of sparse weighted graph into $\mathbb{Z}$

Problem statement in the title is simplified and this question is actually quite open-ended: I have a sparse undirected simple weighted graph $G$ and need to find an injective function $G \rightarrow \...
Joshua Gensler's user avatar
3 votes
0 answers
779 views

Importance of graph planarity for applications

What is the real-life motivation for studying (or inventing) effective algorithms to check whether or not a graph is planar (which seems to have garnered interest in recent years)? Why is planarity an ...
Stan's user avatar
  • 361

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