Weighted Adjacency Matrix

graph-theory

Definition

Weighted Adjacency Matrix

The weighted adjacency matrix is a special form of the adjacency matrix that, instead of using $1$ and $0$ as values, sets the value equal to the weight of an edge.

$$A=(a_{ij}{)}_{i,j}=1,\dots n\text{with}{a}_{ij}=\{\begin{array}{ll}{w}_e& \text{if}e=(v_i,v_j)\in E\\ 0& \text{else}\end{array}$$

Note that this matrix does not differentiate between $w_e=0$ and $e\notin E$.