diff --git a/docs/source/cli/graph-construction/single-machine-gconstruct.rst b/docs/source/cli/graph-construction/single-machine-gconstruct.rst
index d0d75c2d32..f0d7849c61 100644
--- a/docs/source/cli/graph-construction/single-machine-gconstruct.rst
+++ b/docs/source/cli/graph-construction/single-machine-gconstruct.rst
@@ -33,7 +33,7 @@ Full argument list of the ``gconstruct.construct_graph`` command
 * **-\-num-processes-for-nodes**: the number of processes to process node data simultaneously. Increase this number can speed up node data processing.
 * **-\-num-processes-for-edges**: the number of processes to process edge data simultaneously. Increase this number can speed up edge data processing.
 * **-\-output-dir**: (**Required**) the path of the output data files.
-* **-\-graph-name**: (**Required**) the name assigned for the graph. The graph name must adhere to the Python identifier naming rules with the exception that hyphens (``-``) are permitted.
+* **-\-graph-name**: (**Required**) the name assigned for the graph. The graph name must adhere to the Python identifier naming rules with the exception that hyphens (``-``) are permitted and the name can start with numbers.
 * **-\-remap-node-id**: boolean value to decide whether to rename node IDs or not. Adding this argument will set it to be true, otherwise false.
 * **-\-add-reverse-edges**: boolean value to decide whether to add reverse edges for the given graph. Adding this argument sets it to true; otherwise, it defaults to false. It is **strongly** suggested to include this argument for graph construction, as some nodes in the original data may not have in-degrees, and thus cannot update their presentations by aggregating messages from their neighbors. Adding this arugment helps prevent this issue.
 * **-\-output-format**: the format of constructed graph, options are ``DGL``,  ``DistDGL``.  Default is ``DistDGL``. It also accepts multiple graph formats at the same time separated by an space, for example ``--output-format "DGL DistDGL"``. The output format is explained in the :ref:`Output <gcon-output-format>` section above.
diff --git a/docs/source/cli/model-training-inference/distributed/sagemaker.rst b/docs/source/cli/model-training-inference/distributed/sagemaker.rst
index 5b111726cb..ab1c892271 100644
--- a/docs/source/cli/model-training-inference/distributed/sagemaker.rst
+++ b/docs/source/cli/model-training-inference/distributed/sagemaker.rst
@@ -388,7 +388,7 @@ The rest of the arguments are passed on to ``sagemaker_train.py`` or ``sagemaker
 
 * **--task-type**: Task type.
 * **--graph-data-s3**: S3 location of the input graph.
-* **--graph-name**: Name of the input graph.
+* **--graph-name**: Name of the input graph. The graph name must adhere to the Python identifier naming rules with the exception that hyphens (``-``) are permitted and the name can start with numbers.
 * **--yaml-s3**: S3 location of yaml file for training and inference.
 * **--custom-script**: Custom training script provided by customers to run customer training logic. This should be a path to the Python script within the Docker image.
 * **--output-emb-s3**: S3 location to store GraphStorm generated node embeddings. This is an inference only argument.
diff --git a/graphstorm-processing/graphstorm_processing/distributed_executor.py b/graphstorm-processing/graphstorm_processing/distributed_executor.py
index ffe2bd8a1a..295ccad60b 100644
--- a/graphstorm-processing/graphstorm_processing/distributed_executor.py
+++ b/graphstorm-processing/graphstorm_processing/distributed_executor.py
@@ -543,7 +543,8 @@ def parse_args() -> argparse.Namespace:
         help="Name for the graph being processed."
         "The graph name must adhere to the Python "
         "identifier naming rules with the exception "
-        "that hyphens (-) are permitted.",
+        "that hyphens (-) are permitted and the name "
+        "can start with numbers",
         required=False,
         default=None,
     )
@@ -573,7 +574,8 @@ def check_graph_name(graph_name):
         We enforce that the graph name adheres to the Python
         identifier naming rules as in
         https://docs.python.org/3/reference/lexical_analysis.html#identifiers,
-        with the exception that hyphens (-) are permitted.
+        with the exception that hyphens (-) are permitted
+        and the name can start with numbers.
         This helps avoid the cases when an invalid graph name,
         such as `/graph`, causes unexpected errors.
 
@@ -587,7 +589,8 @@ def check_graph_name(graph_name):
     assert graph_name.replace("-", "_").isidentifier(), (
         "GraphStorm expects the graph name adheres to the Python"
         "identifier naming rules with the exception that hyphens "
-        f"(-) are permitted. But we get {graph_name}"
+        f"(-) are permitted and the name can start with numbers. "
+        "But we get {graph_name}"
     )
 
 
diff --git a/python/graphstorm/gconstruct/construct_graph.py b/python/graphstorm/gconstruct/construct_graph.py
index 56d9b4b64e..ceaee5adfd 100644
--- a/python/graphstorm/gconstruct/construct_graph.py
+++ b/python/graphstorm/gconstruct/construct_graph.py
@@ -913,7 +913,8 @@ def process_graph(args):
                            help="Name for the graph being processed."
                                 "The graph name must adhere to the Python "
                                 "identifier naming rules with the exception "
-                                "that hyphens (-) are permitted.",)
+                                "that hyphens (-) are permitted "
+                                "and the name can start with numbers",)
     argparser.add_argument("--remap-node-id", action='store_true',
                            help="Whether or not to remap node IDs.")
     argparser.add_argument("--add-reverse-edges", action='store_true',
diff --git a/python/graphstorm/utils.py b/python/graphstorm/utils.py
index a58c9daafd..72bb6465e6 100644
--- a/python/graphstorm/utils.py
+++ b/python/graphstorm/utils.py
@@ -21,6 +21,7 @@
 import resource
 import logging
 import psutil
+import re
 
 import pandas as pd
 import dgl
@@ -37,7 +38,8 @@ def check_graph_name(graph_name):
         We enforce that the graph name adheres to the Python
         identifier naming rules as in
         https://docs.python.org/3/reference/lexical_analysis.html#identifiers,
-        with the exception that hyphens (-) are permitted.
+        with the exception that hyphens (-) are permitted
+        and the name can start with numbers.
         This helps avoid the cases when an invalid graph name,
         such as `/graph`, causes unexpected errors.
 
@@ -46,10 +48,12 @@ def check_graph_name(graph_name):
     graph_name: str
         Graph Name.
     """
-    assert graph_name.replace('-', '_').isidentifier(), \
+    gname = re.sub(r'^\d+', '', graph_name)
+    assert gname.replace('-', '_').isidentifier(), \
         "GraphStorm expects the graph name adheres to the Python" \
         "identifier naming rules with the exception that hyphens " \
-        f"(-) are permitted. But we get {graph_name}"
+        f"(-) are permitted and the name can start with numbers. " \
+        "But we get {graph_name}"
 
 def get_graph_name(part_config):
     """ Get graph name from graph partition config file
diff --git a/tests/unit-tests/test_gsf.py b/tests/unit-tests/test_gsf.py
index 6be5958788..1f3e1d58d0 100644
--- a/tests/unit-tests/test_gsf.py
+++ b/tests/unit-tests/test_gsf.py
@@ -457,6 +457,10 @@ def test_check_graph_name():
     check_graph_name(graph_name)
     graph_name = "graph-name"
     check_graph_name(graph_name)
+    graph_name = "123-graph-name"
+    check_graph_name(graph_name)
+    graph_name = "_Graph-name"
+    check_graph_name(graph_name)
 
     # test with invalid graph name
     graph_name = "/graph_name"