Different behavior labeled_graph::add_vertex()/labeled_graph::insert_vertex() with label as string and as integer.

[AlekseyMuraviev]

If I try to use a string as a label, the result is expected. If an integer, then the result is different than expected.

#include <iostream>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/labeled_graph.hpp>

int main()
{
		using namespace std;
		cout << "add_vertex():\n";
		{
			using LabeledGraph = boost::labeled_graph<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>, string>;
			LabeledGraph g;
			const auto vd1 = g.add_vertex("123");
			const auto vd2 = g.add_vertex("123");
			cout << " string:\n";
			cout << "  " << boolalpha << (vd1 == vd2) << endl;
		}
		{
			using LabeledGraph = boost::labeled_graph<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>, size_t>;
			LabeledGraph g;
			const auto vd1 = g.add_vertex(123);
			const auto vd2 = g.add_vertex(123);
			cout << " size_t:\n";
			cout << "  " << boolalpha << (vd1 == vd2) << endl;
		}
		cout << "insert_vertex():\n";
		{
			using LabeledGraph = boost::labeled_graph<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>, string>;
			LabeledGraph g;
			cout << " string:\n";
			cout << "  " << boolalpha << g.insert_vertex("123").second << endl;
			cout << "  " << boolalpha << g.insert_vertex("123").second << endl;
		}
		{
			using LabeledGraph = boost::labeled_graph<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>, size_t>;
			LabeledGraph g;
			cout << " size_t:\n";
			cout << "  " << boolalpha << g.insert_vertex(123).second << endl;
			cout << "  " << boolalpha << g.insert_vertex(123).second << endl;
		}
}

If I compile this code using the following command line, I get this result. g++ prog.cc -Wall -Wextra -I/opt/wandbox/boost-1.71.0/gcc-head/include -std=gnu++2a

add_vertex():
 string:
  true
 size_t:
  false
insert_vertex():
 string:
  true
  false
 size_t:
  true
  true