diff --git a/regress/expected/catalog.out b/regress/expected/catalog.out
index 8a83f45a6..4fca3e6ab 100644
--- a/regress/expected/catalog.out
+++ b/regress/expected/catalog.out
@@ -97,9 +97,11 @@ SELECT count(*) FROM pg_namespace WHERE nspname = 'g';
 
 -- invalid cases
 SELECT create_graph(NULL);
-ERROR:  graph name must not be NULL
+ERROR:  graph name can not be NULL
 SELECT drop_graph(NULL);
-ERROR:  graph name must not be NULL
+ERROR:  graph name can not be NULL
+SELECT create_graph('');
+ERROR:  graph name can not be empty
 --
 -- alter_graph() RENAME function tests
 --
diff --git a/regress/sql/catalog.sql b/regress/sql/catalog.sql
index 6bc19814c..59a720f06 100644
--- a/regress/sql/catalog.sql
+++ b/regress/sql/catalog.sql
@@ -52,7 +52,7 @@ SELECT count(*) FROM pg_namespace WHERE nspname = 'g';
 -- invalid cases
 SELECT create_graph(NULL);
 SELECT drop_graph(NULL);
-
+SELECT create_graph('');
 --
 -- alter_graph() RENAME function tests
 --
diff --git a/src/backend/commands/graph_commands.c b/src/backend/commands/graph_commands.c
index c298324c8..bb21f8a9c 100644
--- a/src/backend/commands/graph_commands.c
+++ b/src/backend/commands/graph_commands.c
@@ -67,11 +67,18 @@ Datum create_graph(PG_FUNCTION_ARGS)
     if (PG_ARGISNULL(0))
     {
         ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
-                        errmsg("graph name must not be NULL")));
+                        errmsg("graph name can not be NULL")));
     }
     graph_name = PG_GETARG_NAME(0);
 
     graph_name_str = NameStr(*graph_name);
+
+    if (strlen(graph_name_str) == 0)
+    {
+        ereport(ERROR,
+                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+                        errmsg("graph name can not be empty")));
+    }
     if (graph_exists(graph_name_str))
     {
         ereport(ERROR,
@@ -158,7 +165,7 @@ Datum drop_graph(PG_FUNCTION_ARGS)
     if (PG_ARGISNULL(0))
     {
         ereport(ERROR, (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
-                        errmsg("graph name must not be NULL")));
+                        errmsg("graph name can not be NULL")));
     }
     graph_name = PG_GETARG_NAME(0);
     cascade = PG_GETARG_BOOL(1);