If current user

If current user

<?php
global $current_user;
get_currentuserinfo();
 
if ($current_user->ID == '') { 
    //show nothing to user
}
else { 
    //write code to show menu here
}
?>

Live Demo: ===========

<?php
    global $current_user;
        get_currentuserinfo();
    if ($current_user->ID == '') { 
     
    ?>
        <?php
         
        $options = get_option( 'theme_settings' ); ?>
         
        <?php if($options['custom_profile']) { ?>
        <img src="<?php echo $options['custom_profile']; ?>" />
         
        <?php } else { ?>
        <?php echo get_avatar( get_the_author_email(), '50' ); ?>
         
        <?php } ?>
         
        <br/>
         
        <?php if($options['author']) { ?>
        <strong><?php echo $options['author']; ?></strong>
        <?php } else { ?>
        <strong>Welcome</strong>
        <?php } ?>
         
    <?php 
         
    }
    else { 
    ?>
        <?php
            global $current_user;
            get_currentuserinfo();
                 
                echo get_avatar( $current_user->ID, 50 );
         ?><br/>
         <strong>Hi  <?php global $current_user;
                get_currentuserinfo();
                echo ' ' . $current_user->user_login . "\n"; ?> </strong>
         
        <?php 
    }
?>