MeshConnectivityGraph
MeshConnectivityGraph[mr,0]
gives a graph of points connected by lines.
MeshConnectivityGraph[mr,d]
gives a graph between cells of dimension d that share a cell of dimension d-1.
MeshConnectivityGraph[mr,{d,e},r]
gives a graph from cells of dimension d to cells of dimension e that share a cell of dimension r.
Details and Options


- MeshConnectivityGraph is also known as mesh adjacency graph and mesh incidence graph.
- Typical uses include getting cell adjacencies and topological information in a mesh.
- A vertex {d,i} in the connectivity graph corresponds to the cell cd,i with dimension d and index i in the mesh mr.
- An undirected edge in MeshConnectivityGraph[mr,d]connects two vertices {d,i} and {d,j} whenever the cells cd,i and cd,j both have a common subcell of dimension d-1. For d=0, the common subcell has dimension 1.
- Common cases for d are:
-
0 points that share a line 1 lines that share a point 2 polygons that share an edge 3 polyhedra that share a polygon - In MeshConnectivityGraph[mr,{d,e},r], a directed edge connects the vertex {d,i} to the vertex {e,j} whenever the cells cd,i and ce,j have a common cell of dimension r that is either a subset or a superset of cd,i and ce,j.
- MeshConnectivityGraph[mr] is effectively equivalent to MeshConnectivityGraph[mr,0].
- MeshConnectivityGraph[mr,d,r] is equivalent to the undirected graph of the graph MeshConnectivityGraph[mr,{d,d},r].
- MeshConnectivityGraph takes the same options as Graph with the following changes:
-
AnnotationRules Inherited

Examples
open allclose allBasic Examples (2)
Scope (4)
MeshConnectivityGraph works on MeshRegion:
MeshConnectivityGraph works on all dimensions:
Construct a connectivity graph between cells of dimension 0 in a mesh:
Between cells of dimension 0 and 1:
Between cells of dimension 0 and 0 sharing the same face:
By default, AnnotationRulesInherited annotations are preserved:
With the setting AnnotationRulesNone, annotations are not preserved and the graph is indexed:
Options (81)
AnnotationRules (4)
Specify an annotation for vertices:
With the setting AnnotationRulesNone, annotations are not preserved and the graph is indexed:
DirectedEdges (1)
By default, a directed path is generated when computing connectivity between cells of different dimensions:
Use DirectedEdges->False to interpret rules as undirected edges:
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:
GraphHighlight (3)
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 (2)
By default, any vertex coordinates are computed automatically:
Extract the resulting vertex coordinates using AbsoluteOptions:
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 (5)
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:
Applications (10)
Basic Applications (5)
Adjacency Queries (1)
Polyhedra Operations (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:
Topological Operations (3)
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:
Properties & Relations (3)
The cell of index {d,k} corresponds to the vertex :
MeshConnectivityGraph between cells of different dimensions is a directed bipartite graph:
The AdjacencyMatrix of a mesh connectivity graph between cells of the same dimension is symmetric:
Text
Wolfram Research (2020), MeshConnectivityGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/MeshConnectivityGraph.html.
CMS
Wolfram Language. 2020. "MeshConnectivityGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeshConnectivityGraph.html.
APA
Wolfram Language. (2020). MeshConnectivityGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeshConnectivityGraph.html