neuralqx.graph.k5_graph module

class K5Graph(*, plot=False, non_planar=False, random_embedding=False, random_embedding_mean=0.0, random_embedding_std=5.0, random_embedding_seed=123)

Bases: Graph

Complete graph on five vertices \(K_5\).

This graph has vertex set \(\{0,1,2,3,4\}\) and an edge between every distinct pair, hence

\[|V| = 5,\qquad |E| = \binom{5}{2} = 10.\]

In neuraLQX this class provides a small, fixed test graph. When non_planar=True, a pre-defined 3-tuple vertex labelling is used so that the non-planar pipeline (including the non-planar sign computation) can be exercised without relying on a planar embedding.

Parameters:

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

  • non_planar (bool) – If True, use the pre-defined 3-tuple vertex labels for the non-planar path.

  • 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.