Cannot access $node on Computed field
First of all, you are supposed to write to $entity_field[0]['value']. Second problem is that fields operate on entities, not nodes, so you need to use $entity instead. You can always use Devel module and dpr($entity) to see what's in it. 

node id should be in the entity field if it is a node. In which case you can load it with node_load().