This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# IncidenceGraph

 IncidenceGraph[m] gives the graph with incidence matrix m.
• IncidenceGraph[m] gives a graph with vertices where m has dimensions × and the resulting graph has incidence matrix m.
Construct a graph from its incidence matrix:
Construct a directed graph from its incidence matrix:
Construct a graph with a self-loop:
Construct a directed graph from its incidence matrix:
Construct a graph from its incidence matrix:
 Out[1]=
 Out[2]=

Construct a directed graph from its incidence matrix:
 Out[1]=
 Out[2]=

Construct a graph with a self-loop:
 Out[1]=
 Out[2]=

Construct a directed graph from its incidence matrix:
 Out[1]=
 Out[2]=
 Scope   (6)
Incidence matrices without negative integer entries are interpreted as undirected graphs:
Incidence matrices with negative integer entries are interpreted as directed graphs:
Incidence matrices with integer entries 2 create self-loop:
Use a SparseArray object to specify the incidence matrix:
By default the vertices are taken to be the integers 1 through :
Use an explicit vertex list to give vertex names:
IncidenceGraph works with large matrices:
 Options   (77)
Label the edge :
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 weight for all edges:
Use any numeric expression as a weight:
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:
Highlight the vertex :
Highlight the edge :
Highlight vertices and edges:
Get a list of built-in settings for GraphHighlightStyle:
Use built-in settings for GraphHighlightStyle:
Get a list of built-in settings for GraphStyle:
Use built-in settings for GraphStyle:
Specify property for vertices:
Edges:
Graph itself:
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:
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:
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 collection:
Simple basic shapes:
Common basic shapes:
Use built-in settings for VertexShapeFunction in the collection:
Use built-in settings for VertexShapeFunction in the 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:
VertexShape is not affected by VertexStyle:
Set the weight for all vertices:
Use any numeric expression as a weight:
Use VertexCount and EdgeCount to count vertices and edges:
Use VertexList and EdgeList to enumerate vertices and edges in standard order:
Compute the AdjacencyMatrix from a graph:
A graph can be reconstructed from its incidence matrix:
New in 8