add_action not calling back to function

I understand that you are adding the post from wp-admin / Posts / Add New panel? If so then note that the publish_post action is run and the WP is doing redirect so you cannot see any printed data.

Also, your add_action call is missing 4th argument which is number of arguments passed to cdn_capture_data(), by default there is only 1 argument passed so in your case the $post is always null.

The correct code (to actually print the result) should be

class Classnetwork {
    public function __construct() {
        add_action( 'publish_post', array ($this, 'cdn_capture_data'), 10, 2 );
    }

    public function cdn_capture_data( $post_id, $post ) {
        print_r ($post);  
        exit;          
    }
}