graphdb: add benchmark for isPublicNode query

diff --git a/graph/db/graph_test.go b/graph/db/graph_test.go
index 590c077..3e5c931 100644
--- a/graph/db/graph_test.go
+++ b/graph/db/graph_test.go
@@ -1640,6 +1640,8 @@ func TestGraphCacheTraversal(t *testing.T) {
 	require.Equal(t, numChannels*2*(numNodes-1), numNodeChans)
 }
 
+// fillTestGraph fills the graph with a given number of nodes and create a given
+// number of channels between each node.
 func fillTestGraph(t testing.TB, graph *ChannelGraph, numNodes,
 	numChannels int) (map[uint64]struct{}, []*models.Node) {
 
@@ -4042,6 +4044,28 @@ func TestNodeIsPublic(t *testing.T) {
 	)
 }
 
+// BenchmarkIsPublicNode measures the performance of IsPublicNode when checking
+// a large number of nodes.
+func BenchmarkIsPublicNode(b *testing.B) {
+	graph := MakeTestGraph(b)
+
+	// Create a graph with a reasonable number of nodes and channels.
+	numNodes := 100
+	numChans := 4
+	_, nodes := fillTestGraph(b, graph, numNodes, numChans)
+
+	// Use deterministic random number generator for reproducible results.
+	rng := prand.New(prand.NewSource(42))
+
+	for b.Loop() {
+		// Query random nodes to avoid query caching and better
+		// represent real-world query patterns.
+		nodePub := nodes[rng.Intn(len(nodes))].PubKeyBytes
+		_, err := graph.IsPublicNode(nodePub)
+		require.NoError(b, err)
+	}
+}
+
 // TestDisabledChannelIDs ensures that the disabled channels within the
 // disabledEdgePolicyBucket are managed properly and the list returned from
 // DisabledChannelIDs is correct.