gives the adjacency matrix of edge weights of the graph g.

uses rules vw to specify the graph g.

# Details and Options

• WeightedAdjacencyMatrix returns a SparseArray object, which can be converted to an ordinary matrix using Normal.
• An entry wij of the weighted adjacency matrix is the weight of a directed edge from vertex νi to vertex νj. If there is no edge the weight is taken to be 0.
• An edge without explicit EdgeWeight specified is taken to have weight 1.
• An undirected edge is interpreted as two directed edges with opposite directions and the same weight.
• The vertices vi are assumed to be in the order given by VertexList[g].
• The weighted adjacency matrix for a graph will have dimensions ×, where is the number of vertices.

# Examples

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## Basic Examples(2)

The weighted adjacency matrix of an undirected graph:

The weighted adjacency matrix of a directed graph:

## Scope(5)

The weighted adjacency matrix of an undirected graph is symmetric:

The weighted adjacency matrix of a directed graph can be unsymmetric:

Use rules to specify the graph:

The weighted adjacency matrix of the graph with self-loops has diagonal entries:

Use MatrixPlot to visualize the matrix:

## Properties & Relations(4)

Rows and columns of the weighted adjacency matrix follow the order given by VertexList:

The number of rows or columns is equal to the number of vertices:

The main diagonals for a loop-free graph are all zeros: