diff --git a/src/strands/multiagent/graph.py b/src/strands/multiagent/graph.py
index cbba0fecf..68628029a 100644
--- a/src/strands/multiagent/graph.py
+++ b/src/strands/multiagent/graph.py
@@ -1,13 +1,14 @@
-"""Directed Acyclic Graph (DAG) Multi-Agent Pattern Implementation.
+"""Directed Graph Multi-Agent Pattern Implementation.
 
-This module provides a deterministic DAG-based agent orchestration system where
+This module provides a deterministic graph-based agent orchestration system where
 agents or MultiAgentBase instances (like Swarm or Graph) are nodes in a graph,
 executed according to edge dependencies, with output from one node passed as input
 to connected nodes.
 
 Key Features:
 - Agents and MultiAgentBase instances (Swarm, Graph, etc.) as graph nodes
-- Deterministic execution order based on DAG structure
+- Deterministic execution order based on graph structure
+- Cycles are permitted only if at least one edge is conditional.
 - Output propagation along edges
 - Topological sort for execution ordering
 - Clear dependency management
@@ -253,18 +254,21 @@ def has_cycle_from(node_id: str) -> bool:
             colors[node_id] = GRAY
             # Check all outgoing edges for cycles
             for edge in self.edges:
-                if edge.from_node.node_id == node_id and has_cycle_from(edge.to_node.node_id):
+                if not edge.condition and edge.from_node.node_id == node_id and has_cycle_from(edge.to_node.node_id):
                     return True
             colors[node_id] = BLACK
             return False
 
         # Check for cycles from each unvisited node
         if any(colors[node_id] == WHITE and has_cycle_from(node_id) for node_id in self.nodes):
-            raise ValueError("Graph contains cycles - must be a directed acyclic graph")
+            raise ValueError(
+                "Graph contains unconditional cycles — it must either be a Directed Acyclic Graph (DAG) "
+                "or contain at least one conditional edge within each cycle."
+            )
 
 
 class Graph(MultiAgentBase):
-    """Directed Acyclic Graph multi-agent orchestration."""
+    """Directed graph multi-agent orchestration."""
 
     def __init__(self, nodes: dict[str, GraphNode], edges: set[GraphEdge], entry_points: set[GraphNode]) -> None:
         """Initialize Graph."""
@@ -332,45 +336,35 @@ def _validate_graph(self, nodes: dict[str, GraphNode]) -> None:
 
     async def _execute_graph(self) -> None:
         """Unified execution flow with conditional routing."""
-        ready_nodes = list(self.entry_points)
+        ready_nodes = set(self.entry_points)
 
         while ready_nodes:
-            current_batch = ready_nodes.copy()
-            ready_nodes.clear()
-
             # Execute current batch of ready nodes concurrently
-            tasks = [
-                asyncio.create_task(self._execute_node(node))
-                for node in current_batch
-                if node not in self.state.completed_nodes
-            ]
+            tasks = [asyncio.create_task(self._execute_node(node)) for node in ready_nodes]
 
             for task in tasks:
                 await task
 
             # Find newly ready nodes after batch execution
-            ready_nodes.extend(self._find_newly_ready_nodes())
+            ready_nodes = self._find_newly_ready_nodes(ready_nodes)
 
-    def _find_newly_ready_nodes(self) -> list["GraphNode"]:
+    def _find_newly_ready_nodes(self, executed_nodes: set["GraphNode"]) -> set["GraphNode"]:
         """Find nodes that became ready after the last execution."""
         newly_ready = []
         for _node_id, node in self.nodes.items():
             if (
-                node not in self.state.completed_nodes
+                node.dependencies & executed_nodes
                 and node not in self.state.failed_nodes
                 and self._is_node_ready_with_conditions(node)
             ):
                 newly_ready.append(node)
-        return newly_ready
+        return set(newly_ready)
 
     def _is_node_ready_with_conditions(self, node: GraphNode) -> bool:
         """Check if a node is ready considering conditional edges."""
         # Get incoming edges to this node
         incoming_edges = [edge for edge in self.edges if edge.to_node == node]
 
-        if not incoming_edges:
-            return node in self.entry_points
-
         # Check if at least one incoming edge condition is satisfied
         for edge in incoming_edges:
             if edge.from_node in self.state.completed_nodes:
diff --git a/tests/strands/multiagent/test_graph.py b/tests/strands/multiagent/test_graph.py
index cb74f515c..2cb58ec14 100644
--- a/tests/strands/multiagent/test_graph.py
+++ b/tests/strands/multiagent/test_graph.py
@@ -1,3 +1,4 @@
+import re
 from unittest.mock import AsyncMock, MagicMock, Mock, patch
 
 import pytest
@@ -378,9 +379,26 @@ def test_graph_builder_validation():
     builder.add_edge("c", "a")  # Creates cycle
     builder.set_entry_point("a")
 
-    with pytest.raises(ValueError, match="Graph contains cycles"):
+    with pytest.raises(
+        ValueError,
+        match=re.escape(
+            "Graph contains unconditional cycles — it must either be a Directed Acyclic Graph (DAG) "
+            "or contain at least one conditional edge within each cycle."
+        ),
+    ):
         builder.build()
 
+    # Test cycle detection with back edge condition
+    builder = GraphBuilder()
+    builder.add_node(agent1, "a")
+    builder.add_node(agent2, "b")
+    builder.add_node(create_mock_agent("agent3"), "c")
+    builder.add_edge("a", "b")
+    builder.add_edge("b", "c")
+    builder.add_edge("c", "a", condition=lambda _: True)  # Creates cycle
+    builder.set_entry_point("a")
+    builder.build()
+
     # Test auto-detection of entry points
     builder = GraphBuilder()
     builder.add_node(agent1, "entry")