Module symmetric_tree 

Symmetric tree constructor (ALGO-CN-005).

Counterpart of igraph_symmetric_tree() in references/igraph/src/constructors/regular.c:706-808.

A symmetric tree is a rooted tree where every vertex at depth d has exactly branches[d] children. Unlike kary_tree, where every internal vertex has the same number of children, a symmetric tree lets the branching factor vary per level — for example branches = [3, 2, 2] produces a tree where the root has 3 kids, each of those has 2, and each of those has 2 again (so the leaves sit at depth 3).

Vertex layout follows the same BFS scheme as kary_tree: vertex 0 is the root, then all depth-1 vertices in arrival order, then all depth-2 vertices in their arrival order, and so on. Arc direction is controlled by the shared TreeMode enum:

• TreeMode::Out — directed, every edge flows from parent to child (parent → child).
• TreeMode::In — directed, every edge flows from child to parent (child → parent).
• TreeMode::Undirected — undirected; raw endpoints are (parent, child) but stored as canonical (min, max) by Graph::add_edges.

The C implementation walks one BFS level at a time, expanding every parent of that level in turn, pushing exactly branches[k] outgoing arcs per parent. The Rust port mirrors that level-by-level loop.

Vertex count is 1 + Σ_{i=0..d} Π_{j=0..=i} branches[j]. Empty branches collapses to the singleton root (n = 1, 0 edges).

Edge counts:

• branches.is_empty() — singleton root, no edges.
• non-empty branches — n - 1 edges (always a tree).

Time complexity: O(|V|).

Functions

symmetric_tree

Build a symmetric tree where each vertex at depth d has branches[d] children.