Graph database

This is a module for providing common types of graphs.

pyrigi.graphDB.CnSymmetricFourRegular(n=8)

Return a C_n-symmetric graph.

Todo

use in tests

Definitions

• Example with a free group action

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.CnSymmetricFourRegularWithFixedVertex(n=8)

Return a C_n-symmetric graph with a fixed vertex. The cyclical group C_n needs to have even order of at least 8.

The returned graph satisfies the expected symmetry-adapted Laman count for rotation but is infinitesimally flexible.

Todo

use in tests

Definitions

• Example with joint at origin

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.Complete(n)

Return the complete graph on n vertices.

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.CompleteBipartite(m, n)

Return the complete bipartite graph on m+n vertices.

Parameters:

• m (int)

• n (int)

Return type:

Graph

pyrigi.graphDB.CompleteMinusOne(n)

Return the complete graph on n vertices minus one edge.

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.CubeWithDiagonal()

Return the graph given by the skeleton of the cube with a main diagonal.

Return type:

Graph

pyrigi.graphDB.Cycle(n)

Return the cycle graph on n vertices.

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.Diamond()

Return the complete graph on 4 vertices minus an edge.

Return type:

Graph

pyrigi.graphDB.DoubleBanana(d=3, t=2)

Return the d-dimensional double banana graph.

Parameters:

• d (integer, must be at least 3)

• t (integer, must be 2 <= t <= d-1)

Return type:

Graph

Definitions

Generalized Double Banana

Examples

>>> DoubleBanana()
Graph with vertices [0, 1, 2, 3, 4, 5, 6, 7] and edges [[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [3, 4], [5, 6], [5, 7], [6, 7]]
>>> DoubleBanana(d = 4)
Graph with vertices [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] and edges [[0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]]

pyrigi.graphDB.Frustum(n)

Return the n-Frustum graph

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.K33plusEdge()

Return the complete bipartite graph on 3+3 vertices with an extra edge.

Return type:

Graph

pyrigi.graphDB.K66MinusPerfectMatching()

Return a complete bipartite graph minus a perfect matching.

A matching is formed by six non-incident edges.

Todo

use in tests

pyrigi.graphDB.Octahedral()

Return the graph given by the skeleton of an octahedron.

Return type:

Graph

pyrigi.graphDB.Path(n)

Return the path graph with n vertices.

Parameters:

n (int)

Return type:

Graph

pyrigi.graphDB.ThreeConnectedR3Circuit()

Return a 3-connected R_3-circuit.

The returned graph is hypothesized to be the smallest 3-connected R_3-circuit.

Todo

use in tests

pyrigi.graphDB.ThreePrism()

Return the 3-prism graph.

Return type:

Graph

pyrigi.graphDB.ThreePrismPlusEdge()

Return the 3-prism graph with one extra edge.

Return type:

Graph