Specify an annotation for vertices:

Edges:

Graph itself:

With the setting AnnotationRulesNone, annotations are not preserved and the graph is indexed:

By default, a directed path is generated when computing connectivity between cells of different dimensions:

Use DirectedEdges->False to interpret rules as undirected edges:

Label the edge {0,1}{0,2}:

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:

Use automatic labeling by values through Tooltip and StatusArea:

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:

Style all edges:

Style individual edges:

Specify a weight for all edges:

Use any numeric expression as a weight:

Highlight the vertex 1:

Highlight the edge {0,2}{0,3}:

Highlight vertices and edges:

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

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:

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:

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:

Any number of labels can be used:

Use the argument to Placed to control formatting including Tooltip:

Or StatusArea:

Use more elaborate formatting functions:

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:

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:

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:

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:

Set the weight for all vertices:

Use any numeric expression as a weight:

Triangle connectivity graph:

Point to point:

Point to edge sharing the same face:

Cube connectivity graph:

Point to point:

Point to edge sharing the same face:

Menger mesh connectivity graph:

Point to point:

Point to edge sharing the same face:

3D boundary mesh connectivity graph:

Point to point:

Point to edge sharing the same face:

Get the face adjacency of a Voronoi mesh:

Use the mesh connectivity graph to find point-point adjacency in a mesh:

Find all the points that are connected to the point with cell index {0,1}:

Use MeshConnectivityGraph to compute the DualPolyhedron of a cuboid:

Compute the connectivity graph between points and faces:

Get the adjacent faces for each point:

Compute the coordinates of the dual:

Construct the dual of the cube:

Use MeshConnectivityGraph to test whether a mesh is connected:

Use MeshConnectivityGraph to compute ConnectedMeshComponents:

Connected components of a mesh connectivity graph:

Group the mesh cells to different mesh connected components:

Get mesh connected components:

-skeleton graph of Platonic solids: