IncidenceGraph
gives the graph with incidence matrix m.
IncidenceGraph[{v1,v2,…},m]
gives the graph with vertices vi and incidence matrix m.
Details and Options

- IncidenceGraph[m] gives a graph with vertices {1,2,…,n}, where m has dimensions
×
and the resulting graph has incidence matrix m.
- IncidenceGraph takes the same options as Graph.
Examples
open allclose allBasic Examples (4)
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 a 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 (78)
EdgeLabels (7)
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:
Use automatic labeling by values through Tooltip and StatusArea:
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:
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:
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)
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 any expression as a label:
Use Placed with symbolic locations to control label placement, including outside positions:
Symbolic outside corner 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:
Any number of labels can be used:
Use the argument to Placed to control formatting including Tooltip:
Or StatusArea:
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:
Use built-in settings for VertexShapeFunction in the "Rounded" collection:
Use built-in settings for VertexShapeFunction in the "Concave" collection:
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 (4)
VertexShapeFunction can be combined with VertexStyle:
VertexShapeFunction has higher priority than VertexStyle:
VertexShape is not affected by VertexStyle:
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 AdjacencyMatrix from a graph:
Text
Wolfram Research (2010), IncidenceGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/IncidenceGraph.html.
CMS
Wolfram Language. 2010. "IncidenceGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/IncidenceGraph.html.
APA
Wolfram Language. (2010). IncidenceGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IncidenceGraph.html