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CompleteGraph—Wolfram Language Documentation

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• See Also
  • Graph
  • GraphData
  • GraphComplement
  • CompleteGraphQ
• Related Guides
  • Graph Construction & Representation
  • Graphs & Networks

CompleteGraph[{n₁,n₂,…,n_k}]

gives the complete k-partite graph with n₁+n₂+⋯+n_k vertices .

The first few complete graphs :

Bipartite graphs :

Directed complete graphs use two directional edges for each undirected edge:

Directed complete -partite graphs use directed edges from one group to another:

Specify an annotation for vertices:

Edges:

By default, an undirected graph is generated:

Use DirectedEdges->True to generate a directed graph:

Generate directed -partite graphs:

Label the edge 1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 23:

Highlight the vertices and edges:

Use a common base theme:

Use a monochrome theme:

Use a large graph theme:

Use a classic diagram theme:

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:

Or StatusArea:

Use more elaborate formatting functions:

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:

Set the weight for all vertices:

Use any numeric expression as a weight:

The GraphCenter of a complete graph includes all its vertices:

The GraphPeriphery includes all vertices:

The VertexEccentricity for all vertices is 1:

Highlight the vertex eccentricity path:

The GraphRadius is 1:

Highlight the radius path:

The GraphDiameter is 1:

Highlight the diameter path:

Vertex connectivity from to is the number of vertex-independent paths from to :

There are 3 vertex-independent paths between any pair of vertices:

The vertex connectivity for CompleteGraph[n] is :

Highlight the vertex degree for CompleteGraph:

Highlight the closeness centrality:

Highlight the eigenvector centrality:

Number of vertices of CompleteGraph[n]:

Number of edges of CompleteGraph[n]:

A complete graph is an -regular graph:

The subgraph of a complete graph is a complete graph:

The neighborhood of a vertex in a complete graph is the graph itself:

Complete graphs are their own cliques:

The GraphComplement of a complete graph with no edges:

For a complete graph, all entries outside the diagonal are 1s in the AdjacencyMatrix:

For a complete -partite graph, all entries outside the block diagonal are 1s:

The complete graph is the cycle graph :

The complete graph is the wheel graph :

The complete graph is the line graph of the star graph :

Random collage of complete graphs:

Coloring cycle decompositions in complete graphs on a prime number of vertices:

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