Named motifs

The catalog arm queries named motifs over the census substrate. It threads Induced as a real parameter — both values are honoured:

use graphlet::catalog::{count_diamonds, find_diamonds, count_pattern, Induced, Pattern};

let induced     = count_diamonds(&g, Induced::Yes); // exact K4-minus-an-edge subgraphs
let non_induced = count_diamonds(&g, Induced::No);  // diamond monomorphisms (K4s count too)

let occurrences = find_diamonds(&g, Induced::Yes);  // each: spine (shared edge) + tips

// Arbitrary connected catalog pattern:
let pat = Pattern::new(4, &[(0, 1), (1, 2), (2, 3), (3, 0), (0, 2)]);
let n = count_pattern(&g, &pat, Induced::No);

Induced vs. non-induced

• Induced counts are read straight off the census.

• Non-induced (monomorphism) counts are derived from the induced census by a fixed per-(P,C) table s(P,C) — the number of edge-preserving bijections of the pattern P into graphlet class C. The identity

  mono_labelled(P in G) = Σ_C indCount(C) · s(P,C)

  was verified against an independent brute-force monomorphism oracle (1105/1105 over 45 hosts, k = 3,4,5). There is no separate monomorphism enumerator — the non-induced readout is a bounded post-pass. For example, every K4 contains exactly 6 non-induced diamonds (its C(4,2) tip-pairs).

Both sides report distinct occurrences, obtained from the labelled identity by dividing by |Aut(P)| = s(P,P).