<p>Linear algebra is very useful for certain areas of graph theory (including some fairly advanced linear algebra). It can also be very useful in practice -- linear algebra and graph theory are two of the things which make Google work. And elementary linear algebra is used in enough places that you might want to learn it in any case. </p>

CC BY-SA 2.5
2011-01-25T14:19:20.917Z
2011-01-25T14:19:20.917Z
Peter Shor 
<p>There are plenty of good books on graph theory. Start with something introductory like <a href="http://www.amazon.co.uk/Graph-Theory-Modeling-Applications-Algorithms/dp/0131565362/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1295946098&amp;sr=1-1" rel="nofollow noreferrer">Graph Theory: Modeling, Applications and Algorithms</a>, or one of the many more or less equivalent books at that level. Then move onto something more advanced, such as </p>

<ul>
<li><a href="http://www.amazon.co.uk/Graph-Theory-Advanced-Graduate-Mathematics/dp/1846289696/ref=sr_1_7?ie=UTF8&amp;qid=1295945927&amp;sr=8-7" rel="nofollow noreferrer">Graph Theory: An Advanced Course (Graduate Texts in Mathematics) by Adrian Bondy and U.S.R. Murty</a>, </li>
<li><a href="http://www.amazon.co.uk/Modern-Graph-Theory-Graduate-Mathematics/dp/0387984887/ref=sr_1_5?ie=UTF8&amp;qid=1295945927&amp;sr=8-5" rel="nofollow noreferrer">Modern Graph Theory (Graduate Texts in Mathematics) by B. Bollobás</a> or </li>
<li><a href="http://www.amazon.co.uk/Graph-Theory-Graduate-Texts-Mathematics/dp/3642142788/ref=sr_1_10?ie=UTF8&amp;qid=1295945927&amp;sr=8-10" rel="nofollow noreferrer">Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel</a>. </li>
</ul>

<p>Also building on your background in discrete mathematics is invaluable. A book such as </p>

<ul>
<li><a href="http://www.amazon.co.uk/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=sr_1_1?ie=UTF8&amp;qid=1295947660&amp;sr=8-1" rel="nofollow noreferrer">Concrete Mathematics: Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth, Oren Patashnik</a></li>
</ul>

<p>would be provide you will a solid grounding.</p>

<p>Most of these books would then serve as references for life.</p>

<p>See also this question <a href="https://cstheory.stackexchange.com/questions/2571/what-kind-of-mathematical-background-is-needed-for-complexity-theory">What kind of mathematical background is needed for complexity theory?</a>, as much of the background will overlap, in particular wrt combinatorics and stochastics (probability and statistics).</p>

CC BY-SA 2.5
2011-01-26T00:49:48.190Z
Also Introduction Graph Theory by D.B. West.
Kaveh
CC BY-SA 2.5
2011-01-25T09:02:30.150Z
2011-01-25T09:40:37.170Z
2017-04-13T12:32:28.080Z
Dave Clarke
<p>I don't think you really need too much.</p>

<p>You should have some experience proving proofs of theorems (<em>mathematical induction</em>) and understand what <em>recurrences</em> are.</p>

<p>You will find some good Discrete Mathematics courses containing Graph Theory ;)</p>

CC BY-SA 2.5
2011-01-25T08:48:31.797Z
2011-01-25T08:48:31.797Z
Oscar Mederos
<p>It is going to be the first time for me to learn graph theory. What kind of mathematical background do I need to prepare master theses about this subject in following years?
Which subjects should be reviewed and is there any book that covers all of them?</p>

CC BY-SA 2.5
2011-01-26T00:51:25.410Z
The nice thing about Graph theory is that you really don't need much background to start it and that background is usually given in an introductory chapter or appendix of some books (e.g.  West's Graph Theory book).
Kaveh
<graph-theory><co.combinatorics><soft-question><advice-request>
What kind of mathematical background is needed for graph theory?
user3439
# What kind of mathematical background is needed for graph theory?

(Asked by: username_0 on 2011-01-25)

It is going to be the first time for me to learn graph theory. What kind of mathematical background do I need to prepare master theses about this subject in following years?
Which subjects should be reviewed and is there any book that covers all of them?

**Tags:** graph-theory, co.combinatorics, soft-question, advice-request

> **Comments:**
> **username_1**: The nice thing about Graph theory is that you really don't need much background to start it and that background is usually given in an introductory chapter or appendix of some books (e.g.  West's Graph Theory book).  

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## 3 answers

### Answer by username_3 on 2011-01-25. Score: 15

There are plenty of good books on graph theory. Start with something introductory like [Graph Theory: Modeling, Applications and Algorithms](http://www.amazon.co.uk/Graph-Theory-Modeling-Applications-Algorithms/dp/0131565362/ref=sr_1_1?s=books&ie=UTF8&qid=1295946098&sr=1-1), or one of the many more or less equivalent books at that level. Then move onto something more advanced, such as

* [Graph Theory: An Advanced Course (Graduate Texts in Mathematics) by Adrian Bondy and U.S.R. Murty](http://www.amazon.co.uk/Graph-Theory-Advanced-Graduate-Mathematics/dp/1846289696/ref=sr_1_7?ie=UTF8&qid=1295945927&sr=8-7),
* [Modern Graph Theory (Graduate Texts in Mathematics) by B. Bollobás](http://www.amazon.co.uk/Modern-Graph-Theory-Graduate-Mathematics/dp/0387984887/ref=sr_1_5?ie=UTF8&qid=1295945927&sr=8-5) or
* [Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel](http://www.amazon.co.uk/Graph-Theory-Graduate-Texts-Mathematics/dp/3642142788/ref=sr_1_10?ie=UTF8&qid=1295945927&sr=8-10).

Also building on your background in discrete mathematics is invaluable. A book such as

* [Concrete Mathematics: Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth, Oren Patashnik](http://www.amazon.co.uk/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=sr_1_1?ie=UTF8&qid=1295947660&sr=8-1)

would be provide you will a solid grounding.

Most of these books would then serve as references for life.

See also this question [What kind of mathematical background is needed for complexity theory?](https://cstheory.stackexchange.com/questions/2571/what-kind-of-mathematical-background-is-needed-for-complexity-theory), as much of the background will overlap, in particular wrt combinatorics and stochastics (probability and statistics).

> **Comments:**
> **username_1**: Also Introduction Graph Theory by D.B. West.  

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### Answer by username_2 on 2011-01-25. Score: 12

Linear algebra is very useful for certain areas of graph theory (including some fairly advanced linear algebra). It can also be very useful in practice -- linear algebra and graph theory are two of the things which make Google work. And elementary linear algebra is used in enough places that you might want to learn it in any case.


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### Answer by username_4 on 2011-01-25. Score: 5

I don't think you really need too much.

You should have some experience proving proofs of theorems (*mathematical induction*) and understand what *recurrences* are.

You will find some good Discrete Mathematics courses containing Graph Theory ;)


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