neuralqx.graph.hypercube module

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

Bases: Graph

\(N\)-dimensional hypercube graph \(Q_N\).

Vertices correspond to bit-strings of length \(N\), i.e. \(\{0,1\}^N\), and two vertices are adjacent iff they differ in exactly one bit (Hamming distance one). Consequently:

\[|V| = 2^N,\qquad |E| = N\,2^{N-1}.\]

The graph is constructed from networkx.generators.hypercube_graph(), then relabelled to consecutive integer vertex labels before being passed to Graph. If non_planar=True, vertices are relabelled to 3-tuples and may be given a random spatial embedding.

Parameters:

  • N (int) – Hypercube dimension.

  • 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.

property N