wp_nav_menu_update_menu_items

function wp_nav_menu_update_menu_items( $nav_menu_selected_id, $nav_menu_selected_title ) {
	$unsorted_menu_items = wp_get_nav_menu_items(
		$nav_menu_selected_id,
		array(
			'orderby'     => 'ID',
			'output'      => ARRAY_A,
			'output_key'  => 'ID',
			'post_status' => 'draft,publish',
		)
	);

	$messages   = array();
	$menu_items = array();

	// Index menu items by DB ID.
	foreach ( $unsorted_menu_items as $_item ) {
		$menu_items[ $_item->db_id ] = $_item;
	}

	$post_fields = array(
		'menu-item-db-id',
		'menu-item-object-id',
		'menu-item-object',
		'menu-item-parent-id',
		'menu-item-position',
		'menu-item-type',
		'menu-item-title',
		'menu-item-url',
		'menu-item-description',
		'menu-item-attr-title',
		'menu-item-target',
		'menu-item-classes',
		'menu-item-xfn',
	);

	wp_defer_term_counting( true );

	// Loop through all the menu items' POST variables.
	if ( ! empty( $_POST['menu-item-db-id'] ) ) {
		foreach ( (array) $_POST['menu-item-db-id'] as $_key => $k ) {

			// Menu item title can't be blank.
			if ( ! isset( $_POST['menu-item-title'][ $_key ] ) || '' === $_POST['menu-item-title'][ $_key ] ) {
				continue;
			}

			$args = array();
			foreach ( $post_fields as $field ) {
				$args[ $field ] = isset( $_POST[ $field ][ $_key ] ) ? $_POST[ $field ][ $_key ] : '';
			}

			$menu_item_db_id = wp_update_nav_menu_item( $nav_menu_selected_id, ( $_POST['menu-item-db-id'][ $_key ] != $_key ? 0 : $_key ), $args );

			if ( is_wp_error( $menu_item_db_id ) ) {
				$messages[] = '<div id="message" class="error"><p>' . $menu_item_db_id->get_error_message() . '</p></div>';
			} else {
				unset( $menu_items[ $menu_item_db_id ] );
			}
		}
	}

	// Remove menu items from the menu that weren't in $_POST.
	if ( ! empty( $menu_items ) ) {
		foreach ( array_keys( $menu_items ) as $menu_item_id ) {
			if ( is_nav_menu_item( $menu_item_id ) ) {
				wp_delete_post( $menu_item_id );
			}
		}
	}

	// Store 'auto-add' pages.
	$auto_add        = ! empty( $_POST['auto-add-pages'] );
	$nav_menu_option = (array) get_option( 'nav_menu_options' );

	if ( ! isset( $nav_menu_option['auto_add'] ) ) {
		$nav_menu_option['auto_add'] = array();
	}

	if ( $auto_add ) {
		if ( ! in_array( $nav_menu_selected_id, $nav_menu_option['auto_add'], true ) ) {
			$nav_menu_option['auto_add'][] = $nav_menu_selected_id;
		}
	} else {
		$key = array_search( $nav_menu_selected_id, $nav_menu_option['auto_add'], true );
		if ( false !== $key ) {
			unset( $nav_menu_option['auto_add'][ $key ] );
		}
	}

	// Remove non-existent/deleted menus.
	$nav_menu_option['auto_add'] = array_intersect( $nav_menu_option['auto_add'], wp_get_nav_menus( array( 'fields' => 'ids' ) ) );
	update_option( 'nav_menu_options', $nav_menu_option );

	wp_defer_term_counting( false );

	/** This action is documented in wp-includes/nav-menu.php */
	do_action( 'wp_update_nav_menu', $nav_menu_selected_id );

	$messages[] = '<div id="message" class="updated notice is-dismissible"><p>' .
		sprintf(
			/* translators: %s: Nav menu title. */
			__( '%s has been updated.' ),
			'<strong>' . $nav_menu_selected_title . '</strong>'
		) . '</p></div>';

	unset( $menu_items, $unsorted_menu_items );

	return $messages;
}