Module growing_random 

Growing random graph (ALGO-GN-003).

Counterpart of igraph_growing_random_game() in references/igraph/src/games/growing_random.c:55-105.

The model starts with a single vertex and grows the graph one step at a time. On each step a fresh vertex is added together with m new edges. Two endpoint-selection rules are supported:

• Citation mode (citation = true): every new edge originates at the freshly-added vertex and connects to a uniformly random earlier vertex. Each new edge therefore points from i (the freshly-added id) to some to ∈ [0, i - 1].
• Free mode (citation = false): both endpoints are uniformly sampled — from from [0, i] (the new vertex itself is allowed) and to from [1, i]. The asymmetric bounds are inherited from upstream, where the closed interval [0, i] includes the new vertex and [1, i] excludes vertex 0 from the sink side to avoid pinning every edge at the seed.

Compared with the BAG variant of Barabási–Albert (crate::barabasi_game_bag) the per-step kernel here is uniform rather than degree-proportional — the bag bookkeeping disappears and every step is a constant-time RNG draw. The resulting degree distribution decays exponentially (not as a power law).

Time complexity: O(|V| + |E|) = O(n · m). Memory is the edge list only: O(n · m).

Scope

The full upstream call signature is (graph, n, m, directed, citation) — exposed here as four arguments plus a seed. There are no special parameters or start_from hooks to translate.

Functions

growing_random_game

Generate a growing random graph on n vertices, adding m new edges per step.