Graph Fundamentals

Discrete Math · Axiom Academy

Understanding vertices, edges, degrees, and the multiple ways to represent graph structures in discrete mathematics. V: A set of vertices (or nodes) E: A set of edges (connections between vertices) Each edge connects two vertices. The degree of a vertex is the number of edges connected to it. Let's visualize a simple graph being built step by step. Graphs come in several varieties, each with specific properties and applications: The same graph can be represented in multiple ways. Each representation has advantages for different algorithms and analysis: Visual Diagram: Intuitive, shows structure clearly Adjacency Matrix: 2D array, fast edge lookup O(1) Adjacency List: Space-efficient, good for sparse graphs 4. Converting Between Representations Understanding how to convert between representations is crucial. Let's watch a graph transform from its visual form into both an adjacency matrix and adjacency list.

This is the written version of the interactive lesson above. See the full Discrete Math course.