---
id: intro-graphs
title: Introduction to Graphs
author: Darren Yao, Benjamin Qi
---

<module-excerpt>

**Graph theory** is one of the most important topics at the Silver level and above, although some basic problems occasionally appear in Bronze. 

</module-excerpt>

Graphs can be used to represent many things, from images to wireless signals, but one of the simplest analogies is to a map. Consider a map with several cities and highways connecting the cities. Some problems relating to graphsare:

 - If we have a map with some cities and roads, what's the shortest distance I have to travel to get from point A to point B?
 - Consider a map of cities and roads. Is city A connected to city B? Consider a region to be a group of cities such that each city in the group can reach any other city in said group, but no other cities. How many regions are in this map, and which cities are in which region?

Both of these will be covered in Silver. For now, it suffices to learn how graphs are represented.

## Tutorial

 - Recommended
   - CPH 11
   - Intro to USACO 10.1 - 10.3
   - [CSAcademy Graph Intro](https://csacademy.com/lesson/introduction_to_graphs)
   - [CSAcademy Graph Representations](https://csacademy.com/lesson/graph_representation)
     - Usually, adjacency lists are used.
 - Other
   - [Topcoder Graphs Pt 1](https://www.topcoder.com/community/data-science/data-science-tutorials/introduction-to-graphs-and-their-data-structures-section-1/)

## Trees?


## USACO Bronze Problems

(add some more)

 - Tree
   - [Factory](http://usaco.org/index.php?page=viewproblem2&cpid=940)
   - [Family Tree](http://usaco.org/index.php?page=viewproblem2&cpid=833)
   - [Grass Planting (Silver)](http://usaco.org/index.php?page=viewproblem2&cpid=894)
 - Permutation
   - [Swapity Swap](http://usaco.org/index.php?page=viewproblem2&cpid=1013)
 - General Graph
   - [The Great Revegetation](http://usaco.org/index.php?page=viewproblem2&cpid=916)