diff --git a/cmd/nomos/store.go b/cmd/nomos/store.go
index 682eb83..7d4ec99 100644
--- a/cmd/nomos/store.go
+++ b/cmd/nomos/store.go
@@ -179,6 +179,15 @@ func (s *store) createTaskEntity(ctx context.Context, sessionID, title string) s
 		`UPDATE agent_sessions SET entity_id = $1 WHERE id = $2`, entityID, sessionID); err != nil {
 		slog.Warn("nomos: could not link task entity", "session", sessionID, "error", err)
 	}
+	// Graph edge: task —involves→ agent:nomos (gives every task at least one
+	// edge from creation, even if no run calls are ever made).
+	s.pool.Exec(ctx, `INSERT INTO relationships (source_id, target_id, type, attributes, valid_from)
+		SELECT $1, id, 'involves', '{"by":"nomos"}'::jsonb, now()
+		FROM entities WHERE slug = 'agent:nomos'
+		AND NOT EXISTS (
+			SELECT 1 FROM relationships r
+			WHERE r.source_id = $1 AND r.target_id = entities.id AND r.type = 'involves' AND r.valid_to IS NULL)`,
+		entityID)
 	return entityID.String()
 }