A single node can be selected with a single left mouse click with the Edit Graph tool.
The rubberband is the rectangle that will select the nodes inside it. It's triggered by a mouse drag from an empty spot of the canvass. With the Edit Graph tool this works both with the left and the right mouse buttons, with the Edge Chain tool only the right mouse button will start this.
If Ctr or Shift are pressed when the rubberband is used, the nodes inside it will be either removed from the selection or added to the selection depending on their state.
When such modifier keys are down nodes that are currently not selected will be added to the selection. If all nodes are already selected they will be removed from the selection.
A connected component can be selected if some of its nodes are already selected and then use Nodes → Select Connected
As with most applications, Edit → Select All will select the entire graph.