playground:playground [polymake wiki]

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These properties are for visualization.

MIXED_GRAPH

Type: /topaz/objects/SimplicialComplex/properties/Visualization/MIXED_GRAPH
The nodes of the mixed graph are the nodes of the primal GRAPH and the DUAL_GRAPH. Additional to the primal and dual edges, there is an edge between a primal and a dual node iff the primal node represents a vertex of the corresponding facet of the dual node.
Properties of MIXED_GRAPH:

EDGE_WEIGHTS
Type: /common/property_types/Graph Types/EdgeMap
Associated edge weights.

VERTEX_LABELS

Type: /common/property_types/Basic Types/Array
Labels of the vertices.

These methods capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

BIPARTITE()

Returns: /common/property_types/Basic Types/Bool
True if GRAPH is a bipartite.

CONNECTED_COMPONENTS()

Returns: /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>
The connected components of the GRAPH, encoded as node sets.

CONNECTIVITY()

Returns: /common/property_types/Basic Types/Int
Node connectivity of the GRAPH, that is, the minimal number of nodes to be removed from the graph such that the result is disconnected.

DUAL_BIPARTITE()

Returns: /common/property_types/Basic Types/Bool
True if DUAL_GRAPH is a bipartite.

DUAL_CONNECTED_COMPONENTS()

Returns: /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>
The connected components of the DUAL_GRAPH, encoded as node sets.

DUAL_CONNECTIVITY()

Returns: /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>
Node connectivity of the DUAL_GRAPH. Dual to CONNECTIVITY.

DUAL_GRAPH_SIGNATURE()

Returns: /common/property_types/Basic Types/Int
Difference of the black and white nodes if the DUAL_GRAPH is BIPARTITE. Otherwise -1.

DUAL_MAX_CLIQUES()

Returns: /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>
The maximal cliques of the DUAL_GRAPH, encoded as node sets.

GRAPH_SIGNATURE()

Returns: /common/property_types/Basic Types/Int
Difference of the black and white nodes if the GRAPH is BIPARTITE. Otherwise -1.

MAX_CLIQUES()

Returns: /common/property_types/Set Types/PowerSet</common/property_types/Basic Types/Int>
The maximal cliques of the GRAPH, encoded as node sets.

VERTEX_DEGREES()

Returns: /common/property_types/Basic Types/Array</common/property_types/Basic Types/Int>
Degrees of the vertices in the GRAPH.

boundary_matrix(Int d)

Parameters: /common/property_types/Basic Types/Int d : Dimension of the boundary matrix.

Returns: /common/property_types/Algebraic Types/SparseMatrix</common/property_types/Basic Types/Integer>
Output the boundary matrix of dimension d. Indexing is according to

the face indices in the HASSE_DIAGRAM of the complex. The matrix is a map via multiplying it to a vector from the left. Beware, this computes the whole face lattice of your complex, which is expensive.

labeled_vertices(String label ...)

Parameters: /common/property_types/Basic Types/String label … : vertex labels

Returns: /common/property_types/Set Types/Set</common/property_types/Basic Types/Int>
Find the vertices by given labels.

The following methods compute topological invariants.

CONNECTED()

Returns: /common/property_types/Basic Types/Bool
True if the GRAPH is a connected graph.

DUAL_CONNECTED()

Returns: /common/property_types/Basic Types/Bool
True if the DUAL_GRAPH is a connected graph.

N_CONNECTED_COMPONENTS()

Returns: /common/property_types/Basic Types/Int
Number of connected components of the GRAPH.

fundamental2gap(String filename)

Parameters: /common/property_types/Basic Types/String filename :
Returns: /common/property_types/Basic Types/String
Writes the FUNDAMENTAL_GROUP using FUNDAMENTAL_GROUP_GEN_LABELS to

the given file in GAP input format.

These methods are for visualization.

VISUAL()

Returns: /topaz/objects/Visual::SimplicialComplex
Visualizes the complex.

If G_DIM < 4, the GRAPH and the facets are visualized using the COORDINATES.

Otherwise, the spring embedder and the GRAPH are used to produce coordinates for the visualization.

If JavaView is used to visualize the complex, all faces of one facet build a geometry in the jvx-file, so you may use Method → Effect → Explode Group of Geometries in the JavaView menu.

VISUAL_DUAL_GRAPH()

Returns: /topaz/objects/Visual::SimplicialComplex
Uses the spring embedder to visualize the DUAL_GRAPH.

VISUAL_FACE_LATTICE()

Returns: /topaz/objects/Visual::SimplicialComplexLattice
Visualize the HASSE_DIAGRAM of a simplicial complex as a multi-layer graph.

VISUAL_GRAPH()

Returns: /topaz/objects/Visual::SimplicialComplex
Uses the spring embedder to visualize the GRAPH.

VISUAL_MIXED_GRAPH()

Returns: /common/objects/Visualization/Visual::Container
Uses the spring embedder to visualize the MIXED_GRAPH.

Visualization