neuralqx.graph.single_vertex module

class SingleVertexGraph(valence, orientation=None, *, plot=False, non_planar=False, random_embedding=False, random_embedding_mean=0.0, random_embedding_std=5.0, random_embedding_seed=123)

Bases: Graph

Star graph with one central vertex and prescribed edge orientations.

This graph has a distinguished central vertex labelled 0 and valence external vertices labelled 1,2,\dots,valence. For each external vertex \(i\), there is exactly one edge connecting \(0\) and \(i\). The orientation of each edge is controlled by an integer direction \(d_i\in\{+1,-1\}\):

  • \(d_i=+1\) gives an edge \(0\to i\),

  • \(d_i=-1\) gives an edge \(i\to 0\).

If orientation is not provided, all edges are oriented outwards (all \(d_i=+1\)).

If non_planar=True, vertices are relabelled to fixed-length 3-tuples and may be given a random spatial embedding.

Parameters:

  • valence (int) – Number of edges incident at the central vertex.

  • orientation (Optional[list]) – Optional list of length valence with entries in {+1, -1}.

  • plot (bool) – If True, produce a visualisation via the base graph machinery.

  • non_planar (bool) – If True, relabel vertices to 3-tuples to trigger the non-planar pipeline.

  • random_embedding (bool) – If True, assign a random 3D embedding to vertices (non-planar only).

  • random_embedding_mean (float) – Mean of the Gaussian used for the random embedding.

  • random_embedding_std (float) – Standard deviation of the Gaussian used for the random embedding.

  • random_embedding_seed (int) – Seed controlling the random embedding.

Raises:

OrientationValenceMismatchError – If orientation is provided with the wrong length.

property orientation
property vertex_valence: int