Graph Theory and Network Algorithms

An 8x8 knights tour graph with an illustrated tour. A scale-free graph with randomized vertex coloring exemplifying opinion distribution.

Graph Theory is the study of discrete mathematical structures composed of vertices (nodes) represented by dots and edges (links) represented by lines connecting the dots. Generally speaking, Graph Theory is a branch of Combinatorics but it is closely connected to Applied Mathematics, Optimization Theory and Computer Science. In its applied form, Graph Theory is used every day by Google and Microsoft in feeding you web information. It plays a major role in the functioning of your Facebook account and can be used to help analyze Twitter relationships. Graph Theory can also help track down criminals and makes your GPS function.