diff --git a/lightrag/api/routers/graph_routes.py b/lightrag/api/routers/graph_routes.py
index d9380094..124240a7 100644
--- a/lightrag/api/routers/graph_routes.py
+++ b/lightrag/api/routers/graph_routes.py
@@ -31,9 +31,10 @@ def create_graph_routes(rag, api_key: Optional[str] = None):
         Retrieve a connected subgraph of nodes where the label includes the specified label.
         Maximum number of nodes is constrained by the environment variable `MAX_GRAPH_NODES` (default: 1000).
         When reducing the number of nodes, the prioritization criteria are as follows:
-            1. Label matching nodes take precedence
-            2. Followed by nodes directly connected to the matching nodes
-            3. Finally, the degree of the nodes
+            1. min_degree does not affect nodes directly connected to the matching nodes
+            2. Label matching nodes take precedence
+            3. Followed by nodes directly connected to the matching nodes
+            4. Finally, the degree of the nodes
         Maximum number of nodes is limited to env MAX_GRAPH_NODES(default: 1000)
 
         Args:
diff --git a/lightrag/kg/networkx_impl.py b/lightrag/kg/networkx_impl.py
index 2c76a67d..84518523 100644
--- a/lightrag/kg/networkx_impl.py
+++ b/lightrag/kg/networkx_impl.py
@@ -242,9 +242,11 @@ class NetworkXStorage(BaseGraphStorage):
         Retrieve a connected subgraph of nodes where the label includes the specified `node_label`.
         Maximum number of nodes is constrained by the environment variable `MAX_GRAPH_NODES` (default: 1000).
         When reducing the number of nodes, the prioritization criteria are as follows:
-            1. Label matching nodes take precedence
-            2. Followed by nodes directly connected to the matching nodes
-            3. Finally, the degree of the nodes
+            1. min_degree does not affect nodes directly connected to the matching nodes
+            2. Label matching nodes take precedence
+            3. Followed by nodes directly connected to the matching nodes
+            4. Finally, the degree of the nodes
+
 
         Args:
             node_label: Label of the starting node
@@ -289,12 +291,25 @@ class NetworkXStorage(BaseGraphStorage):
                 node_subgraph = nx.ego_graph(graph, start_node, radius=max_depth)
                 combined_subgraph = nx.compose(combined_subgraph, node_subgraph)
 
-            # Filter nodes based on min_degree
+            # Get start nodes and direct connected nodes
+            start_nodes = set()
+            direct_connected_nodes = set()
+
+            if node_label != "*" and nodes_to_explore:
+                start_nodes = set(nodes_to_explore)
+                # Get nodes directly connected to all start nodes
+                for start_node in start_nodes:
+                    direct_connected_nodes.update(combined_subgraph.neighbors(start_node))
+
+                # Remove start nodes from directly connected nodes (avoid duplicates)
+                direct_connected_nodes -= start_nodes
+
+            # Filter nodes based on min_degree, but keep start nodes and direct connected nodes
             if min_degree > 0:
                 nodes_to_keep = [
                     node
                     for node, degree in combined_subgraph.degree()
-                    if degree >= min_degree
+                    if node in start_nodes or node in direct_connected_nodes or degree >= min_degree
                 ]
                 combined_subgraph = combined_subgraph.subgraph(nodes_to_keep)
 
@@ -303,21 +318,8 @@ class NetworkXStorage(BaseGraphStorage):
         # Check if number of nodes exceeds max_graph_nodes
         if len(subgraph.nodes()) > MAX_GRAPH_NODES:
             origin_nodes = len(subgraph.nodes())
-
             node_degrees = dict(subgraph.degree())
 
-            start_nodes = set()
-            direct_connected_nodes = set()
-
-            if node_label != "*" and nodes_to_explore:
-                start_nodes = set(nodes_to_explore)
-                # Get nodes directly connected to all start nodes
-                for start_node in start_nodes:
-                    direct_connected_nodes.update(subgraph.neighbors(start_node))
-
-                # Remove start nodes from directly connected nodes (avoid duplicates)
-                direct_connected_nodes -= start_nodes
-
             def priority_key(node_item):
                 node, degree = node_item
                 # Priority order: start(2) > directly connected(1) > other nodes(0)