diff --git a/internal/command/cloud_mock.go b/internal/command/cloud_mock.go
index cf324624e9..93f59199bf 100644
--- a/internal/command/cloud_mock.go
+++ b/internal/command/cloud_mock.go
@@ -17,6 +17,7 @@ import (
 	"github.com/hashicorp/terraform/internal/backend/backendrun"
 	"github.com/hashicorp/terraform/internal/command/arguments"
 	"github.com/hashicorp/terraform/internal/configs"
+	"github.com/hashicorp/terraform/internal/states/statemgr"
 	"github.com/hashicorp/terraform/internal/terraform"
 	"github.com/hashicorp/terraform/internal/tfdiags"
 
@@ -143,6 +144,7 @@ func TestNewVariableBackend(result map[string]string) backend.Backend {
 }
 
 var _ backendrun.ConstVariableSupplier = (*TestVariableBackend)(nil)
+var _ backendrun.Local = (*TestVariableBackend)(nil)
 
 func (b *TestVariableBackend) FetchVariables(ctx context.Context, workspace string) (map[string]arguments.UnparsedVariableValue, tfdiags.Diagnostics) {
 	result := make(map[string]arguments.UnparsedVariableValue)
@@ -157,6 +159,27 @@ func (b *TestVariableBackend) FetchVariables(ctx context.Context, workspace stri
 	return result, nil
 }
 
+func (b *TestVariableBackend) LocalRun(op *backendrun.Operation) (*backendrun.LocalRun, statemgr.Full, tfdiags.Diagnostics) {
+	// Sometimes a command (like graph) requires a local backend. The cloud
+	// backend implements LocalRun and will fetch variables from the backend.
+	// But our mock TestVariableBackend will fail in these tests, because it
+	// embends the backendrun.Local backend and never calls FetchVariables.
+	//
+	// We now set the variables manually here and defer to the regular backend
+	// run implementation, this helps us test the desired behavior.
+	if op.Variables == nil {
+		op.Variables = make(map[string]arguments.UnparsedVariableValue)
+	}
+	fetchedVars, _ := b.FetchVariables(context.Background(), op.Workspace)
+	for k, v := range fetchedVars {
+		if _, ok := op.Variables[k]; !ok {
+			op.Variables[k] = v
+		}
+	}
+
+	return b.Local.LocalRun(op)
+}
+
 type testUnparsedVariableValueString struct {
 	str  string
 	name string
diff --git a/internal/command/graph_test.go b/internal/command/graph_test.go
index 9490ed130c..71f6611dd1 100644
--- a/internal/command/graph_test.go
+++ b/internal/command/graph_test.go
@@ -14,6 +14,8 @@ import (
 	"github.com/zclconf/go-cty/cty"
 
 	"github.com/hashicorp/terraform/internal/addrs"
+	"github.com/hashicorp/terraform/internal/backend"
+	backendInit "github.com/hashicorp/terraform/internal/backend/init"
 	"github.com/hashicorp/terraform/internal/configs/configload"
 	"github.com/hashicorp/terraform/internal/configs/configschema"
 	"github.com/hashicorp/terraform/internal/initwd"
@@ -359,3 +361,103 @@ func TestGraph_applyPhaseSavedPlan(t *testing.T) {
 		t.Fatalf("doesn't look like digraph:\n%s\n\nstderr:\n%s", output.Stdout(), output.Stderr())
 	}
 }
+
+func TestGraph_constVariable(t *testing.T) {
+	t.Run("missing value", func(t *testing.T) {
+		wd := tempWorkingDirFixture(t, "dynamic-module-sources/command-with-const-var")
+		t.Chdir(wd.RootModuleDir())
+
+		ui := cli.NewMockUi()
+		streams, closeStreams := terminal.StreamsForTesting(t)
+		c := &GraphCommand{
+			Meta: Meta{
+				testingOverrides: metaOverridesForProvider(testProvider()),
+				Ui:               ui,
+				Streams:          streams,
+				WorkingDir:       wd,
+			},
+		}
+
+		args := []string{}
+		if code := c.Run(args); code != 1 {
+			output := closeStreams(t)
+			t.Fatalf("expected exit status 1\nstdout:\n%s\n\nstderr:\n%s", output.Stdout(), output.Stderr())
+		}
+
+		if !strings.Contains(ui.ErrorWriter.String(), "No value for required variable") {
+			t.Fatalf("expected missing variable error, got:\n%s", ui.ErrorWriter.String())
+		}
+		closeStreams(t)
+	})
+
+	t.Run("value via cli", func(t *testing.T) {
+		wd := tempWorkingDirFixture(t, "dynamic-module-sources/command-with-const-var")
+		t.Chdir(wd.RootModuleDir())
+
+		ui := cli.NewMockUi()
+		streams, closeStreams := terminal.StreamsForTesting(t)
+		c := &GraphCommand{
+			Meta: Meta{
+				testingOverrides: metaOverridesForProvider(testProvider()),
+				Ui:               ui,
+				Streams:          streams,
+				WorkingDir:       wd,
+			},
+		}
+
+		args := []string{"-var", "module_name=child"}
+		if code := c.Run(args); code != 0 {
+			output := closeStreams(t)
+			t.Fatalf("bad:\nstdout:\n%s\n\nstderr:\n%s", output.Stdout(), output.Stderr())
+		}
+
+		output := closeStreams(t)
+		wantOutput := []string{
+			`"module.child.test_instance.test" [label="test_instance.test"]`,
+		}
+		for _, want := range wantOutput {
+			if !strings.Contains(output.Stdout(), want) {
+				t.Fatalf("output missing %s:\n%s", want, output.Stdout())
+			}
+		}
+	})
+
+	t.Run("value via backend", func(t *testing.T) {
+		mockBackend := TestNewVariableBackend(map[string]string{
+			"module_name": "child",
+		})
+		backendInit.Set("local-vars", func() backend.Backend { return mockBackend })
+		defer backendInit.Set("local-vars", nil)
+
+		wd := tempWorkingDirFixture(t, "dynamic-module-sources/command-with-const-var-backend")
+		t.Chdir(wd.RootModuleDir())
+
+		ui := cli.NewMockUi()
+		streams, closeStreams := terminal.StreamsForTesting(t)
+		c := &GraphCommand{
+			Meta: Meta{
+				testingOverrides: metaOverridesForProvider(testProvider()),
+				Ui:               ui,
+				Streams:          streams,
+				WorkingDir:       wd,
+			},
+		}
+
+		args := []string{}
+		if code := c.Run(args); code != 0 {
+			output := closeStreams(t)
+			stderr := ui.ErrorWriter.String()
+			t.Fatalf("bad:\nstdout:\n%s\n\nstderr:\n%s", output.Stdout(), stderr)
+		}
+
+		output := closeStreams(t)
+		wantOutput := []string{
+			`"module.child.test_instance.test" [label="test_instance.test"]`,
+		}
+		for _, want := range wantOutput {
+			if !strings.Contains(output.Stdout(), want) {
+				t.Fatalf("output missing %s:\n%s", want, output.Stdout())
+			}
+		}
+	})
+}