feat(cat5): representative cycles alongside Betti-1

sme/categories/gap_detection.py

@@ -80,6 +80,7 @@ class GapDetectionReport:
     h1_max_persistence: float
     h1_skipped: bool = False
     h1_skip_reason: str = ""
+    representative_cycles: list[list[str]] = field(default_factory=list)
 
     # Candidate gaps across components (top-K by score, post-filter)
     candidate_gaps: list[CandidateGap] = field(default_factory=list)
@@ -290,6 +291,17 @@ def score_gap_detection(
                 "Betti-1 persistence readings"
             )
 
+    representative_cycles: list[list[str]] = []
+    if largest:
+        sub_undirected = nx.Graph()
+        sub_undirected.add_nodes_from(largest)
+        for u, v, _ in G.edges(keys=True):
+            if u in largest and v in largest and u != v:
+                sub_undirected.add_edge(u, v)
+        raw_cycles = nx.cycle_basis(sub_undirected)
+        raw_cycles.sort(key=lambda c: (len(c), c))
+        representative_cycles = raw_cycles[:10]
+
     candidates, considered = _candidate_gaps(
         analyzer,
         components,
@@ -340,6 +352,7 @@ def score_gap_detection(
         h1_max_persistence=h1_max_persistence,
         h1_skipped=h1_skipped,
         h1_skip_reason=h1_skip_reason,
+        representative_cycles=representative_cycles,
         candidate_gaps=candidates,
         candidate_gaps_considered=considered,
         gap_recall=gap_recall,
@@ -418,6 +431,18 @@ def format_report(report: GapDetectionReport) -> str:
     if report.h1_skipped:
         lines.append(f"    (homology skipped: {report.h1_skip_reason})")
 
+    if report.representative_cycles:
+        lines.append(
+            f"  Representative cycles ({len(report.representative_cycles)}):"
+        )
+        for cycle in report.representative_cycles[:5]:
+            nodes_str = " → ".join(cycle) + " → " + cycle[0]
+            lines.append(f"      [{len(cycle)}-cycle] {nodes_str}")
+        if len(report.representative_cycles) > 5:
+            lines.append(
+                f"      ... +{len(report.representative_cycles) - 5} more"
+            )
+
     lines.append("")
     lines.append(
         f"  Candidate gaps:        {len(report.candidate_gaps):,} shown"

tests/test_gap_detection.py

@@ -14,7 +14,7 @@
 
 import pytest
 
-from sme.categories.gap_detection import score_gap_detection
+from sme.categories.gap_detection import format_report, score_gap_detection
 
 ripser = pytest.importorskip  # alias for readability below
 
@@ -154,3 +154,25 @@ def test_empty_graph_is_all_zeros():
     assert report.isolated_nodes == 0
     assert report.bridges == []
     assert report.candidate_gaps == []
+
+
+# --- Representative cycles (#16) -------------------------------------
+
+
+def test_representative_cycles(gap_graph):
+    """Issue #16 — representative cycles from largest component."""
+    entities, edges, _ = gap_graph
+    report = score_gap_detection(entities, edges, run_homology=False)
+    assert len(report.representative_cycles) >= 1
+    cycle_nodes = [set(c) for c in report.representative_cycles]
+    five_cycle_nodes = {"A", "B", "C", "D", "E"}
+    assert any(five_cycle_nodes <= nodes for nodes in cycle_nodes)
+
+
+def test_format_report_shows_cycles(gap_graph):
+    """Issue #16 — format_report includes cycle descriptions."""
+    entities, edges, _ = gap_graph
+    report = score_gap_detection(entities, edges, run_homology=False)
+    rendered = format_report(report)
+    assert "Representative cycles" in rendered
+    assert "-cycle]" in rendered