The is_taxonomy_hierarchical() WordPress PHP function determines whether a taxonomy object is hierarchical.
Usage
is_taxonomy_hierarchical( $taxonomy );
Example:
$taxonomy = 'category'; $is_hierarchical = is_taxonomy_hierarchical( $taxonomy ); echo $is_hierarchical; // Output: true
Parameters
$taxonomy(string) (Required) – Name of the taxonomy object.
More information
See WordPress Developer Resources: is_taxonomy_hierarchical()
Examples
Check if a Custom Taxonomy is Hierarchical
$taxonomy = 'custom_taxonomy';
$is_hierarchical = is_taxonomy_hierarchical( $taxonomy );
if ( $is_hierarchical ) {
    echo 'This taxonomy is hierarchical.';
} else {
    echo 'This taxonomy is not hierarchical.';
}
Display Hierarchical Taxonomies
$taxonomies = get_taxonomies();
foreach ( $taxonomies as $taxonomy ) {
    if ( is_taxonomy_hierarchical( $taxonomy ) ) {
        echo $taxonomy . ' is hierarchical.<br>';
    }
}
Add Custom Styling for Hierarchical Taxonomies
$taxonomy = 'custom_taxonomy';
$style = '';
if ( is_taxonomy_hierarchical( $taxonomy ) ) {
    $style = 'hierarchical-style';
}
echo '<div class="' . $style . '">Taxonomy Content</div>';
Show Parent Terms Only for Hierarchical Taxonomies
$taxonomy = 'custom_taxonomy';
if ( is_taxonomy_hierarchical( $taxonomy ) ) {
    $terms = get_terms( array(
        'taxonomy'   => $taxonomy,
        'parent'     => 0,
    ) );
    foreach ( $terms as $term ) {
        echo $term->name . '<br>';
    }
}
Check if Post Type Supports Hierarchical Taxonomies
$post_type = 'post';
$taxonomies = get_object_taxonomies( $post_type );
$hierarchical_taxonomies = array();
foreach ( $taxonomies as $taxonomy ) {
    if ( is_taxonomy_hierarchical( $taxonomy ) ) {
        $hierarchical_taxonomies[] = $taxonomy;
    }
}
if ( !empty( $hierarchical_taxonomies ) ) {
    echo 'The ' . $post_type . ' post type supports the following hierarchical taxonomies:';
    echo implode( ', ', $hierarchical_taxonomies );
} else {
    echo 'The ' . $post_type . ' post type does not support any hierarchical taxonomies.';
}