<?php 
// Same for hook_node_save!
function my_module_node_update($node) {
  if ($node->type == 'content_type_name') {
    // Invoke your callback function AFTER the node is updated.
    drupal_register_shutdown_function('_my_module_the_function_to_call', $node);
  }
}


function _my_module_the_function_to_call($node) {
  // do stuff...
}