gives the graph with weighted adjacency matrix wmat.

gives the graph with vertices vi and weighted adjacency matrix wmat.

# Details and Options • WeightedAdjacencyGraph[wmat] is equivalent to WeightedAdjacencyGraph[{1,2,,n},wmat], where wmat has dimensions × .
• WeightedAdjacencyGraph takes the same options as Graph.
• The option DirectedEdges can be used to control whether an undirected or directed graph is constructed.
• The following settings for DirectedEdges can be used in WeightedAdjacencyGraph:
•  Automatic undirected graph if wmat is symmetric True construct a directed graph False construct an undirected graph

# Examples

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## Basic Examples(2)

Construct a graph from a weighted adjacency matrix:

A symmetric weighted adjacency matrix results in an undirected graph:

## Scope(7)

Symmetric matrices are interpreted as undirected graphs:

Unsymmetric matrices are interpreted as directed graphs:

Use DirectedEdges to control whether an undirected or directed graph should be constructed:

Matrices with diagonal entries create self-loops:

Use a SparseArray object to specify the adjacency matrix:

By default, the vertices are taken to be the integers 1 through :

Use an explicit vertex list to give vertex names:

## Options(83)

### AnnotationRules(3)

Specify a property for vertices:

Edges:

Graph itself:

### DirectedEdges(3)

By default, a symmetric matrix generates an undirected graph:

Use to generate a directed graph:

By default, an unsymmetric matrix generates a directed graph:

### EdgeLabels(8)

Label the edge 12:

Label all edges individually:

Use any expression as a label:

Use Placed with symbolic locations to control label placement along an edge:

Use explicit coordinates to place labels:

Vary positions within the label:

Place multiple labels using EdgeLabels:

Any number of labels can be used:

Use automatic labeling by values through Tooltip and StatusArea:

Use edge weights as labels:

### EdgeShapeFunction(6)

Get a list of built-in settings for EdgeShapeFunction:

Undirected edges including the basic line:

Lines with different glyphs on the edges:

Directed edges including solid arrows:

Line arrows:

Open arrows:

Specify an edge function for an individual edge:

Combine with a different default edge function:

Draw edges by running a program:

EdgeShapeFunction can be combined with EdgeStyle:

EdgeShapeFunction has higher priority than EdgeStyle:

### EdgeStyle(2)

Style all edges:

Style individual edges:

### EdgeWeight(1)

Specify a weight for all edges:

### GraphHighlight(3)

Highlight the vertex 1:

Highlight the edge 23:

Highlight vertices and edges:

### GraphHighlightStyle(2)

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

### GraphLayout(5)

By default, the layout is chosen automatically:

Specify layouts on special curves:

Specify layouts that satisfy optimality criteria:

VertexCoordinates overrides GraphLayout coordinates:

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

### PlotTheme(4)

#### Base Themes(2)

Use a common base theme:

Use a monochrome theme:

#### Feature Themes(2)

Use a large graph theme:

Use a classic diagram theme:

### VertexCoordinates(3)

By default, any vertex coordinates are computed automatically:

Extract the resulting vertex coordinates using AbsoluteOptions:

Specify a layout function along an ellipse:

Use it to generate vertex coordinates for a graph:

VertexCoordinates has higher priority than GraphLayout:

### VertexLabels(13)

Use vertex names as labels:

Label individual vertices:

Label all vertices:

Use any expression as a label:

Use Placed with symbolic locations to control label placement, including outside positions:

Symbolic outside corner positions:

Symbolic inside positions:

Symbolic inside corner positions:

Use explicit coordinates to place the center of labels:

Place all labels at the upper-right corner of the vertex and vary the coordinates within the label:

Place multiple labels using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using VertexLabels:

Use the argument to Placed to control formatting including Tooltip:

Or StatusArea:

Use more elaborate formatting functions:

### VertexShape(5)

Use any Graphics, Image, or Graphics3D as a vertex shape:

Specify vertex shapes for individual vertices:

VertexShape can be combined with VertexSize:

VertexShape is not affected by VertexStyle:

VertexShapeFunction has higher priority than VertexShape:

### VertexShapeFunction(10)

Get a list of built-in collections for VertexShapeFunction:

Use built-in settings for VertexShapeFunction in the "Basic" collection:

Simple basic shapes:

Common basic shapes:

Use built-in settings for VertexShapeFunction in the "Rounded" collection:

Use built-in settings for VertexShapeFunction in the "Concave" collection:

Draw individual vertices:

Combine with a default vertex function:

Draw vertices using a predefined graphic:

Draw vertices by running a program:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexShapeFunction can be combined with VertexSize:

VertexShapeFunction has higher priority than VertexShape:

### VertexSize(8)

By default the size of vertices is computed automatically:

Specify the size of all vertices using symbolic vertex size:

Use a fraction of the minimum distance between vertex coordinates:

Use a fraction of the overall diagonal for all vertex coordinates:

Specify size in both the and directions:

Specify the size for individual vertices:

VertexSize can be combined with VertexShapeFunction:

VertexSize can be combined with VertexShape:

### VertexStyle(5)

Style all vertices:

Style individual vertices:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexStyle can be combined with BaseStyle:

VertexStyle has higher priority than BaseStyle:

VertexShape is not affected by VertexStyle:

### VertexWeight(2)

Set the weight for all vertices:

Use any numeric expression as a weight:

## Properties & Relations(4)

Use VertexCount and EdgeCount to count vertices and edges:

Use VertexList and EdgeList to enumerate vertices and edges in standard order:

Compute the WeightedAdjacencyMatrix from a graph:

An adjacency matrix with all infinity entries in the diagonal constructs a graph without self-loops: