Source

File: wp-includes/rest-api/endpoints/class-wp-rest-comments-controller.php

protected function prepare_links( $comment ) {
		$links = array(
			'self'       => array(
				'href' => rest_url( sprintf( '%s/%s/%d', $this->namespace, $this->rest_base, $comment->comment_ID ) ),
			),
			'collection' => array(
				'href' => rest_url( sprintf( '%s/%s', $this->namespace, $this->rest_base ) ),
			),
		);

		if ( 0 !== (int) $comment->user_id ) {
			$links['author'] = array(
				'href'       => rest_url( 'wp/v2/users/' . $comment->user_id ),
				'embeddable' => true,
			);
		}

		if ( 0 !== (int) $comment->comment_post_ID ) {
			$post = get_post( $comment->comment_post_ID );

			if ( ! empty( $post->ID ) ) {
				$obj  = get_post_type_object( $post->post_type );
				$base = ! empty( $obj->rest_base ) ? $obj->rest_base : $obj->name;

				$links['up'] = array(
					'href'       => rest_url( 'wp/v2/' . $base . '/' . $comment->comment_post_ID ),
					'embeddable' => true,
					'post_type'  => $post->post_type,
				);
			}
		}

		if ( 0 !== (int) $comment->comment_parent ) {
			$links['in-reply-to'] = array(
				'href'       => rest_url( sprintf( '%s/%s/%d', $this->namespace, $this->rest_base, $comment->comment_parent ) ),
				'embeddable' => true,
			);
		}

		// Only grab one comment to verify the comment has children.
		$comment_children = $comment->get_children(
			array(
				'number' => 1,
				'count'  => true,
			)
		);

		if ( ! empty( $comment_children ) ) {
			$args = array(
				'parent' => $comment->comment_ID,
			);

			$rest_url = add_query_arg( $args, rest_url( $this->namespace . '/' . $this->rest_base ) );

			$links['children'] = array(
				'href' => $rest_url,
			);
		}

		return $links;
	}