Source

File: wp-admin/includes/template.php

function wp_link_category_checklist( $link_id = 0 ) {
	$default = 1;

	$checked_categories = array();

	if ( $link_id ) {
		$checked_categories = wp_get_link_cats( $link_id );
		// No selected categories, strange.
		if ( ! count( $checked_categories ) ) {
			$checked_categories[] = $default;
		}
	} else {
		$checked_categories[] = $default;
	}

	$categories = get_terms(
		array(
			'taxonomy'   => 'link_category',
			'orderby'    => 'name',
			'hide_empty' => 0,
		)
	);

	if ( empty( $categories ) ) {
		return;
	}

	foreach ( $categories as $category ) {
		$cat_id = $category->term_id;

		/** This filter is documented in wp-includes/category-template.php */
		$name    = esc_html( apply_filters( 'the_category', $category->name, '', '' ) );
		$checked = in_array( $cat_id, $checked_categories, true ) ? ' checked="checked"' : '';
		echo '<li id="link-category-', $cat_id, '"><label for="in-link-category-', $cat_id, '" class="selectit"><input value="', $cat_id, '" type="checkbox" name="link_category[]" id="in-link-category-', $cat_id, '"', $checked, '/> ', $name, '</label></li>';
	}
}