The functionality you're looking for is built in to GoJS. For instance have a look at the
Org Chart Editor Sample.
You can double click on nodes in order to add a new person, drag a node onto another in order to change relationships, and draw links (with a click drag operation) from a node's background to other nodes that have no "boss".
(If you want a node to have no Boss in this simple sample, you can select and delete links)