Next/Previous Url only

There are no functions for that in WordPress core (yet), however, you can:

• Use get_previous_post() to get the previous post.
• Use get_next_post() to get the next post.
• Or you can also make a direct call to get_adjacent_post() which is used by the above functions.

And then just use get_permalink() to get the previous/next post’s URL.

For example:

$post = get_post(); // get the current post

$next_post     = get_next_post();     // or use get_adjacent_post( false, '', false, 'category' );
$next_post_url = $next_post ? get_permalink( $next_post ) : '';

$prev_post     = get_previous_post(); // or use get_adjacent_post( false, '', true, 'category' );
$prev_post_url = $prev_post ? get_permalink( $prev_post ) : '';