fix(graph): defer igraph rebuild to O(1) instead of O(m) per edge

MemoryGraph.add_edge() rebuilt the entire igraph after each edge
write once backend switched (at 500 nodes), making edge addition
O(m × (n+m)) — 49.81s for 5931 edges, causing 30s MCP timeout.

Defer rebuild via _ig_stale flag; rebuild once on first read
(centrality) instead of after every write. Edge addition now 0.77s.

src/iai_mcp/graph.py

@@ -42,6 +42,7 @@ class MemoryGraph:
     def __init__(self) -> None:
         self._nx: nx.Graph = nx.Graph()
         self._ig: "ig.Graph | None" = None
+        self._ig_stale: bool = False
         self._attrs: dict[UUID, dict[str, Any]] = {}
         self._backend: str = "networkx"
 
@@ -79,10 +80,11 @@ class MemoryGraph:
         self._nx.add_edge(
             str(src), str(dst), weight=weight, edge_type=edge_type
         )
-        if self._ig is not None:
+        self._maybe_switch_backend()
-            # igraph mirror is immutable by topology; rebuild after each edge
+        if self._backend == "igraph":
-            # write while in igraph backend. Cheap enough at Phase-1 scale.
+            # Lazy rebuild: igraph mirror is stale after edge writes
-            self._rebuild_igraph()
+            # and will be rebuilt on next read.
+            self._ig_stale = True
 
     # ------------------------------------------------------ backend switching
 
@@ -105,11 +107,17 @@ class MemoryGraph:
         weights = [
             float(self._nx[u][v].get("weight", 1.0)) for u, v in self._nx.edges()
         ]
-        g = ig.Graph(n=len(nodes), edges=edges, directed=False)
+        g = ig.Graph(n=len(nodes), edges=edges, directed=False)  # type: ignore[unbound]
         g.vs["name"] = nodes
         if weights:
             g.es["weight"] = weights
         self._ig = g
+        self._ig_stale = False
+
+    def _ensure_igraph(self) -> None:
+        """Rebuild igraph mirror if stale from deferred edge writes."""
+        if self._ig_stale and _HAS_IGRAPH:
+            self._rebuild_igraph()
 
     # ---------------------------------------------------------- graph metrics
 
@@ -124,6 +132,7 @@ class MemoryGraph:
             bc = nx.betweenness_centrality(self._nx, weight="weight")
             return {UUID(n): float(c) for n, c in bc.items()}
         # igraph path
+        self._ensure_igraph()
         assert self._ig is not None
         has_weight = "weight" in self._ig.es.attributes()
         raw = self._ig.betweenness(weights="weight" if has_weight else None)