How can I show contextual links on my node's full content view mode?
if you want to show contextual link on a node view 
try out this code on your custom module file.

function mymodulename_node_view_alter(&amp;$build) {
  $node = $build['#node'];
  if (!empty($node-&gt;nid)) {
    $build['#contextual_links']['node'] = array('node', array($node-&gt;nid));
  }
}