What hook for triggering an action after saving a new node? I'm running Drupal 7 and I want to re-save the user account of the node author after deleting a node of content type picture. I want to do this because I have some code called in hook_user_presave() that counts the number of pictures a user has added and saves it in an integer field in the user.

I looked at hook_node_submit() and hook_node_update(), but when then are invoked, the node is not yet saved, so if I save the user at that point, the int value is one less than it should be (because the added node has not actually been saved yet).

Is there a hook for reacting after a node has been added?

Related question: Hook for reacting after deleting node
You can use Hook Post Action module which will provide you hooks like:

hook_entity_postsave

hook_entity_postinsert

hook_entity_postupdate

hook_entity_postdelete

hook_node_postsave

hook_node_postinsert

hook_node_postupdate

hook_node_postdelete
These hooks are fired after node is saved to the database. So the process you want to do after node save can be done using these hooks which comes with Hook Post action module.