An Introduction to Graph Theory: The Mathematics of Networks

Graph theory is a fascinating branch of mathematics that underpins everything from social networks to logistics, biology, and even internet search engines. Whether you’re a computer scientist, a mathematician, or just curious about the world of connections, understanding graph theory opens up a world of possibilities.

What Is Graph Theory?

At its core, graph theory is the study of graphs – mathematical structures used to model pairwise relationships between objects.

A graph consists of:

• Vertices (Nodes): Represent entities (e.g., people, cities, websites).

• Edges (Links): Represent connections between entities.

Graphs can be directed (with arrows indicating direction) or undirected (where connections have no direction).

Real-World Examples

• Social Networks: Users (vertices) connected by friendships or follows (edges).

• Road Networks: Cities (nodes) connected by highways (edges).

• Biology: Neural connections in the brain.

• Computer Science: Web pages linked through hyperlinks.

Basic Types of Graphs

1. Simple Graph: A graph with no loops (edges that connect a vertex to itself) or multiple edges between two nodes.