bp_post_published_notification.php

function custom_filter_notifications_publish_post_get_registered_components( $component_names = array() ) {
 
    // Force $component_names to be an array
    if ( ! is_array( $component_names ) ) {
        $component_names = array();
    }
 
    // Add 'custom' component to registered components array
    array_push( $component_names, 'custom' );
 
    // Return component's with 'custom' appended
    return $component_names;
}
add_filter( 'bp_notifications_get_registered_components', 'custom_filter_notifications_publish_post_get_registered_components' );

function bp_custom_format_buddypress_notifications( $action, $item_id, $secondary_item_id, $total_items, $format = 'string' ) {
 
    // New custom notifications
    if ( 'custom_action' === $action ) {
    
        $post_info = get_post( $item_id );

        $custom_title = get_the_author_meta( 'display_name', $post_info->post_author ) . ' posted a new post ' . get_the_title( $item_id );
        $custom_link  = get_post_permalink( $item_id );
        $custom_text = get_the_author_meta( 'display_name', $post_info->post_author ) . ' posted a new post ' . get_the_title( $item_id );
 
        // WordPress Toolbar
        if ( 'string' === $format ) {
            $return = apply_filters( 'custom_filter', '<a href="' . esc_url( $custom_link ) . '" title="' . esc_attr( $custom_title ) . '">' . esc_html( $custom_text ) . '</a>', $custom_text, $custom_link );
 
        // Deprecated BuddyBar
        } else {
            $return = apply_filters( 'custom_filter', array(
                'text' => $custom_text,
                'link' => $custom_link
            ), $custom_link, (int) $total_items, $custom_text, $custom_title );
        }
        
        return $return;
        
    }
    
}
add_filter( 'bp_notifications_get_notifications_for_user', 'bp_custom_format_buddypress_notifications', 10, 5 );


function bp_post_published_notification( $post_id, $post ) {
    $author_id = $post->post_author; /* Post author ID. */
    if ( bp_is_active( 'notifications' ) ) {
	    bp_notifications_add_notification( array(
	        'user_id'           => $author_id,
	        'item_id'           => $post_id,
	        'component_name'    => 'custom',
	        'component_action'  => 'custom_action',
	        'date_notified'     => bp_core_current_time(),
	        'is_new'            => 1,
	    ) );
 	}
}
add_action( 'publish_post', 'bp_post_published_notification', 99, 2 );