Module wheel 

Wheel graph constructor (ALGO-CN-003).

Counterpart of igraph_wheel() in references/igraph/src/constructors/regular.c:145-287.

A wheel graph on n vertices is the union of a star and a cycle: one vertex (the centre) is connected to every other vertex via star-spokes, and those n - 1 rim vertices are linked by a cycle. Wheel layout is controlled by WheelMode, whose four cases line up with crate::StarMode:

• WheelMode::Out — directed, every spoke flows from the centre to a leaf, every rim edge is prev → next (visited in the [0, center) ∪ (center, n) raw vertex order).
• WheelMode::In — directed, every spoke flows from each leaf to the centre, rim direction prev → next matches Out.
• WheelMode::Mutual — directed, every spoke and every rim edge is emitted in both directions. Star-spokes are added first (forward arc before back-arc, per leaf); the rim is then appended as e_0, e_1, …, e_{n-2}, rev(e_{n-2}), rev(e_{n-3}), …, rev(e_0) — i.e. forward rim sweep followed by the reverse of each forward arc in reverse-discovery order, matching the upstream C loop verbatim.
• WheelMode::Undirected — undirected; each spoke and each rim edge is added once, Graph::add_edges canonicalises endpoints to (min, max).

Edge counts:

• n = 0 or n = 1 — wheel ≡ star; no edges.
• n ≥ 2, mode ∈ {Out, In, Undirected} — 2(n − 1) edges (n − 1 spokes plus n − 1 rim edges).
• n ≥ 2, mode = Mutual — 4(n − 1) edges.

Degenerate two- and three-vertex wheels are intentionally non-simple (upstream igraph_wheel documents this): the two-vertex wheel contains a self-loop on the only rim vertex (the rim collapses to a 1-cycle), and the three-vertex wheel produces parallel edges between the two rim vertices (rim collapses to a 2-cycle).

Time complexity: O(|V|).

Enums

WheelMode

Direction policy for wheel_graph.

Functions

wheel_graph

Build a wheel graph on n vertices with the given center and arc policy mode.