Network

graph-theory

Definition

Network

Networks are directed or undirected graphs $G=(V,E)$, where each edge $e\in E$ is assigned a value $w(e)\in \mathbb{R}$. This value can be interpreted as length, cost, capacity, weight, etc., depending on the context.

$$w:E\to \mathbb{R}$$

Instead of the usual adjacency matrix, a network uses a weighted adjacency matrix:

$$A=(w(v_i,v_j){)}_{1\le i,j\le n}$$