This menu lets you choose between different modes. Your actual mode is visible in the statusbar on the bottom of the main window and in the menu itself (the little 
in front of the mode). If you are in the 'Edit Node' mode, you can move the nodes (= vertices) and therefore adjusting the graph for your needs. In the 'Add/Delete Node' mode you can add nodes by clicking on an empty space in the active graph window. If you click on an existing node, the node will be deleted. In the 'Add/Delete Edge' mode, adding edges is as easy as deleting them. Just click on a vertex and then on the vertex you want to connect with the formerly clicked vertex. If these vertices are already connected, then the edge is deleted.