How to log out user using facebook SDK?

I am using a facebook log in for my web site using facebook php sdk.

What I noticed is the logout link doesn't do anything. After I logout, the user can still navigate the site. Here is my code in facebook.php:

<?php
    require 'src/facebook.php';
    $facebook = new Facebook(array(
           'appId'  => '*************',
           'secret' => '******************************',
    ));
    $user = $facebook->getUser();
    $loginUrl = $facebook->getLoginUrl();
    echo "<a href='$loginUrl'>login</a>";

    $logoutUrl = $facebook->getLogoutUrl();
    echo $loginUrl; 
    if($user){
        session_start() ; 
        $_SESSION['user_info'] = $user; 
        $_SESSION['user_pro']= $facebook->api('/me');
        print_r($_SESSION);
    }
    else{
        echo 'not logged in '; 
    }

    echo "<a href='example.com/logout.php'>log out </a>"
?>

This code works fine on log in. The log out link should destroy the session. Here is the header of the page:

<?php 
    print_r($_SESSION) ; 
    header('example.com') ; 
?>

The problem with my logout.php page is it doesn't detect the session at all. I don't know if this is a facebook api problem or my php problem.

How do you log the user out using the facebook SDK?