Orbits (GDV / GDD)

Two nodes of one graphlet are in the same orbit when an automorphism of that graphlet maps one to the other. There are 73 orbits across connected graphlets of order 2..=5 (undirected). The graphlet-degree vector (GDV) of a node counts, per orbit, the instances in which that node occupies the orbit.

use graphlet::{graphlet_degree_vectors, Registry};

let reg = Registry::build();               // 73 orbits; reusable across graphs
let gdv = graphlet_degree_vectors(&g, &reg);

let row = gdv.row(0);                       // 73-entry vector for node index 0
let dist = gdv.degree_distribution(orbit);  // GDD: degree → number of nodes

For every subgraph instance, each participating node is attributed to its orbit via the arg-permutation witnessing the instance→canonical isomorphism; the orbit is looked up in a union-find automorphism registry. Because orbit ids are automorphism-invariant, the attribution is independent of enumeration order.

The attribution is verified against an independent brute-force per-node oracle (zero mismatches on paths, cycles, stars, cliques, and fuzzed random graphs) and satisfies Σ_v GDV[v][orbit] = census(class) · orbit_size.

Orbit numbering

The internal orbit ids are stable and deterministic but are not ORCA's published orbit ordering — aligning to ORCA is a mechanical relabelling.