test(metamorphic): directed distance-metric relations [br-r37-c1-e04a1]

Skill: /testing-metamorphic (different from this 30-min window's
/mock-code-finder, /profiling-software-performance,
/modes-of-reasoning-project-analysis, /porting-to-rust,
/testing-conformance-harnesses, /testing-fuzzing).

The directed-distance-metric wrapper fixes (br-r37-c1-89n9d
center/periphery and br-r37-c1-wojl3 diameter/radius) lacked
metamorphic-property coverage. The differential fuzz lock
(br-r37-c1-kitjs) catches divergence from nx, but if both libraries
drift the same way (e.g. nx is pinned to a buggy version), the
fuzz silently passes. Metamorphic guards catch nx-independent drift
because they're rooted in mathematical identities.

Adds 4 metamorphic-property tests, each parametrized over 5
random strongly-connected DiGraph seeds:

  1. test_directed_diameter_invariant_under_reverse
     diameter(G) == diameter(reverse(G)) — reversing every edge
     maps each shortest u→v path to a shortest v→u path in the
     reverse, so the max over all pairs is preserved.

  2. test_directed_radius_diameter_ordering
     radius(G) ≤ diameter(G) — fundamental inequality.

  3. test_directed_center_is_subset_of_eccentricity_minimizers
     center(G) == {n : ecc[n] == radius(G)} — definitional, verified
     against an independent recomputation from fnx.eccentricity.

  4. test_directed_periphery_is_max_eccentricity_set
     periphery(G) == {n : ecc[n] == diameter(G)} — same, dual side.

All 4 hold by mathematical identity (independent of any nx behavior),
so they catch the case where both libs drift together.

86 metamorphic tests pass total (was 66) — 1 vacuous skip on the
older complement-of-disconnected-is-connected theorem.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: Dicklesworthstone

tests/python/test_review_mode_metamorphic.py

@@ -300,6 +300,73 @@ def test_triangles_consistent_with_transitivity_zero(seed):
     assert all(t == 0 for t in triangles.values())
 
 
+# ---- directed distance-metrics metamorphic (br-r37-c1-kitjs) -------
+
+def _scc_digraph(seed):
+    """Random directed graph with a Hamiltonian cycle injected (so the
+    result is always strongly connected, distance metrics defined)."""
+    rng = random.Random(seed)
+    n = rng.randint(5, 12)
+    p = rng.uniform(0.2, 0.5)
+    G = fnx.DiGraph()
+    for i in range(n):
+        G.add_node(i)
+    edges = []
+    for i in range(n):
+        for j in range(n):
+            if i != j and rng.random() < p:
+                edges.append((i, j))
+    for i in range(n):
+        edges.append((i, (i + 1) % n))
+    G.add_edges_from(edges)
+    return G
+
+
+@pytest.mark.parametrize("seed", [0, 1, 7, 11, 42])
+def test_directed_diameter_invariant_under_reverse(seed):
+    """For a strongly-connected DiGraph, ``diameter(reverse(G)) ==
+    diameter(G)``: reversing every edge maps the shortest path from
+    u to v in G to the shortest path from v to u in reverse(G), so
+    the maximum over all (u, v) pairs is preserved."""
+    G = _scc_digraph(seed)
+    Gr = G.reverse()
+    assert fnx.diameter(G) == fnx.diameter(Gr)
+
+
+@pytest.mark.parametrize("seed", [0, 1, 7, 11, 42])
+def test_directed_radius_diameter_ordering(seed):
+    """Radius ≤ diameter is a fundamental graph-distance inequality.
+    For finite strongly-connected DiGraphs both are well-defined and
+    finite."""
+    G = _scc_digraph(seed)
+    assert fnx.radius(G) <= fnx.diameter(G)
+
+
+@pytest.mark.parametrize("seed", [0, 1, 7, 11, 42])
+def test_directed_center_is_subset_of_eccentricity_minimizers(seed):
+    """The center is exactly the set of nodes attaining the minimum
+    eccentricity. Verify against an independent computation of the
+    minimum-eccentricity set from fnx.eccentricity."""
+    G = _scc_digraph(seed)
+    ecc = fnx.eccentricity(G)
+    r = fnx.radius(G)
+    expected_center = sorted(n for n, e in ecc.items() if e == r)
+    actual_center = sorted(fnx.center(G))
+    assert actual_center == expected_center
+
+
+@pytest.mark.parametrize("seed", [0, 1, 7, 11, 42])
+def test_directed_periphery_is_max_eccentricity_set(seed):
+    """The periphery is exactly the set of nodes attaining the
+    maximum eccentricity (i.e., diameter)."""
+    G = _scc_digraph(seed)
+    ecc = fnx.eccentricity(G)
+    d = fnx.diameter(G)
+    expected_periphery = sorted(n for n, e in ecc.items() if e == d)
+    actual_periphery = sorted(fnx.periphery(G))
+    assert actual_periphery == expected_periphery
+
+
 # ---- harmonic_centrality (br-r37-c1-rsom6 dict-order fix) ----------
 
 def test_harmonic_centrality_value_invariant_under_relabeling():