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Graph Theory Notes

Graph Theory graphs nodes edges algorithms networks

Introduction to Graph Theory

Definition 1 (Simple Graph)

A simple graph is a graph with no self-loops and no multiple edges between the same pair of vertices.

\[G = (V, E)\]

Where:

  1. $V$ is a non-empty set of vertices (nodes)
  2. $E$ is a set of unordered pairs of distinct vertices, i.e. \(E \subseteq \{\{u, v\} \mid u, v \in V,\; u \neq v\}\)