Limits the adjacent post to just parents (no children)

adjacent-parent-post.php

<?php

/**
 * Get the next adjacent parent post.
 *
 * This function extends the SQL WHERE query of the WordPress get_adjacent_post()
 * function. It registers a callback to the `get_next_post_where` event filter,
 * which then adds a new WHERE parameter.
 *
 * @uses get_next_post()
 * @uses `get_next_post_where` filter
 * @uses fulcrum_add_parent_post_to_adjacent_sql()
 *
 * @since 1.0.6
 *
 * @param bool         $in_same_term   Optional. Whether post should be in a same taxonomy term. Default false.
 * @param array|string $excluded_terms Optional. Array or comma-separated list of excluded term IDs. Default empty.
 * @param string       $taxonomy       Optional. Taxonomy, if $in_same_term is true. Default 'category'.
 *
 * @return null|string|WP_Post Post object if successful. Null if global $post is not set. Empty string if no
 *                             corresponding post exists.
 */
function fulcrum_get_next_parent_post( $in_same_term = false, $excluded_terms = '', $taxonomy = 'category') {
	add_filter( 'get_next_post_where', 'fulcrum_add_parent_post_to_adjacent_sql' );

	return get_next_post( $in_same_term, $excluded_terms, $taxonomy );
}

/**
 * Get the previous adjacent parent post.
 *
 * This function extends the SQL WHERE query of the WordPress get_adjacent_post()
 * function. It registers a callback to the `get_previous_post_where` event filter,
 * which then adds a new WHERE parameter.
 *
 * @uses get_previous_post()
 * @uses `get_previous_post_where` filter
 * @uses fulcrum_add_parent_post_to_adjacent_sql()
 *
 * @since 1.0.6
 *
 * @param bool         $in_same_term   Optional. Whether post should be in a same taxonomy term. Default false.
 * @param array|string $excluded_terms Optional. Array or comma-separated list of excluded term IDs. Default empty.
 * @param string       $taxonomy       Optional. Taxonomy, if $in_same_term is true. Default 'category'.
 *
 * @return null|string|WP_Post Post object if successful. Null if global $post is not set. Empty string if no
 *                             corresponding post exists.
 */
function fulcrum_get_previous_parent_post( $in_same_term = false, $excluded_terms = '', $taxonomy = 'category') {
	add_filter( 'get_previous_post_where', 'fulcrum_add_parent_post_to_adjacent_sql' );

	return get_previous_post( $in_same_term, $excluded_terms, $taxonomy );
}

/**
 * Adds a post parent WHERE SQL check to the adjacent SQL.  
 * 
 * In WordPress, the column `post_parent` is 0 when the content is
 * the root parent.
 * 
 * Callback for the WordPress filter events `get_previous_post_where` and
 * `get_next_post_where`.
 *
 * @since 1.0.6
 *
 * @param string $where_sql
 *
 * @return string
 */
function fulcrum_add_parent_post_to_adjacent_sql( $where_sql ) {
	$where_sql .= ' AND p.post_parent = 0';

	return $where_sql;
}

Thanks, this is really helpful!