Datasets:
Tasks:
Feature Extraction
Formats:
csv
Size:
< 1K
Tags:
graph-theory
graph-isomorphism
color-refinement
weisfeiler-lehman
structural-invariants
graph-kernels
License:
| """Multicapa (v2): refinamiento conjunto y tres dualidades — autocontenido. | |
| - `refinar_conjunto(n, capas, variante)`: 1-WL conjunto de (V, E_1..E_L) | |
| en variantes "ordenada" (capas etiquetadas) y "canonica" (S_L-invariante). | |
| - `complemento_total`, `complemento_capa`, `complemento_canales`. | |
| - `t4`: perfil + partición fuerte. | |
| Ley (EXP-162/163): T4 vive con el complemento TOTAL (uniforme); con el | |
| complemento POR CAPA muere en la variante canónica (coherencia | |
| multicanal); las permutaciones de canales preservan (la partición es | |
| ciega al orden). | |
| """ | |
| import hashlib | |
| from collections import Counter | |
| from itertools import combinations | |
| def _h(s): | |
| return hashlib.sha256(s.encode()).hexdigest()[:12] | |
| def _adj(n, E): | |
| d = {v: set() for v in range(n)} | |
| for a, b in E: | |
| d[a].add(b) | |
| d[b].add(a) | |
| return d | |
| def refinar_conjunto(n, capas, variante="canonica"): | |
| if variante not in ("ordenada", "canonica"): | |
| raise ValueError("variante ∈ {'ordenada','canonica'}") | |
| adj = [_adj(n, E) for E in capas] | |
| L = len(capas) | |
| if variante == "ordenada": | |
| colors = {v: _h("|".join(str(len(adj[l][v])) | |
| for l in range(L))) for v in range(n)} | |
| else: | |
| colors = {v: _h(",".join(sorted(str(len(adj[l][v])) | |
| for l in range(L)))) | |
| for v in range(n)} | |
| prev = None | |
| for _ in range(n + 2): | |
| nuevos = {} | |
| for v in range(n): | |
| if variante == "ordenada": | |
| datos = "|".join( | |
| ",".join(sorted(colors[u] for u in adj[l][v])) | |
| for l in range(L)) | |
| else: | |
| por = [tuple(sorted(colors[u] for u in adj[l][v])) | |
| for l in range(L)] | |
| datos = ";".join(",".join(x) for x in sorted(por)) | |
| nuevos[v] = _h(f"{colors[v]}|{datos}") | |
| colors = nuevos | |
| part = tuple(sorted(Counter(colors.values()).values())) | |
| if part == prev: | |
| break | |
| prev = part | |
| clases = {} | |
| for v, c in colors.items(): | |
| clases.setdefault(c, set()).add(v) | |
| particion = frozenset(frozenset(s) for s in clases.values()) | |
| firma = tuple(sorted(colors.values())) | |
| return firma, colors, particion | |
| def complemento_total(n, capas): | |
| todas = {tuple(sorted(p)) for p in combinations(range(n), 2)} | |
| return [sorted(todas - {tuple(sorted(e)) for e in E}) for E in capas] | |
| def complemento_capa(n, capas, ell): | |
| c = complemento_total(n, capas) | |
| return [c[i] if i == ell else capas[i] for i in range(len(capas))] | |
| def complemento_canales(capas, pi): | |
| if sorted(pi) != list(range(len(capas))): | |
| raise ValueError("pi debe ser permutación") | |
| return [capas[i] for i in pi] | |
| def t4(n, capas, capas_iota, variante="canonica"): | |
| _, c1, p1 = refinar_conjunto(n, capas, variante) | |
| _, c2, p2 = refinar_conjunto(n, capas_iota, variante) | |
| perfil = lambda c: tuple(sorted(Counter(c.values()).values())) # noqa: E731 | |
| return {"perfil_igual": perfil(c1) == perfil(c2), | |
| "particion_igual": p1 == p2} | |