I’m afraid this isn’t possible (in general). There is only one page for an event (regardless of whether it recurs or not – there are performance/SEO concerns which influenced this decision). So the idea of a ‘next’ event after this event doesn’t make sense: ‘next’ after which date of this event?
Of course, if you’re dealing solely with single events, then yes it does make sense – but that’s why it doesn’t exist ‘out of the box’.
If you are dealing with single events, first find the next event (the event which starts after this event (and is not this event)):
$next_event = eo_get_events( array(
'post_not__in' => array( get_the_ID() ),
'event_start_after' => eo_get_the_start( 'Y-m-d H:i:s' )
) );
if( $next_event ){
$permalink = get_permalink( $next_event[0] );
printf( '<a href="%s">Next event</a>', $permalink );
}
(You’ll want that ‘in the loop’).
Similar code for the ‘previous’ events:
$next_event = eo_get_events( array(
'post_not__in' => array( get_the_ID() ),
'event_start_before' => eo_get_the_start( 'Y-m-d H:i:s' ),
'showpastevents' => true,
) );
(Code is completely untested and may have syntax errors)
(The whole thing can be complicated more if you throw in the fact that events can overlap: In the above I’ve taken next to mean the event which starts next, which probably makes the most sense).