# Graphs and cycles

One of the most widely used structures in mathematics and applications is a **graph**. Here we don’t mean the graph of a function, but rather a diagram that you can draw with points (vertices) and segments (edges). Graphs can be used to model networks such as a transit system or even social media Friends. Many of the most important algorithms used in computing operate on data stored in a graph structure. We introduced graphs and some key terminology we use to talk about them.

In the second half of the lesson we studied **cycles** in graphs, which are paths through the edges of the graph that start and end at the same vertex. An Euler cycle is one that touches every edge once, and a Hamilton cycle is one that touches every vertex once. When does a graph have an Euler cycle? When does it have a Hamilton cycle? We tried it out with a number of sample graphs, and looked for patterns in the results.