Explorations

This section walks through each family of Dynkin diagrams, showing their adjacency matrices, root systems, mutation graphs, and Cartan spectra.

Simply-Laced (Simple Graphs)

The ADE families correspond to simple undirected graphs (symmetric adjacency matrices with 0/1 entries).

• Type A – Path Graphs
• Type D – Forked Graphs
• Type E – Exceptional Diagrams

Non-Simply-Laced (Directed Multigraphs)

The BCFG families correspond to directed multigraphs with edge multiplicities greater than 1. Their adjacency matrices are non-symmetric.

• Type B – Odd Orthogonal
• Type C – Symplectic
• Types F and G – Exceptional Multigraphs