Nodes are what defines the main shape of the knot, any transformation of the knot is actually a result of nodes being moved.
Snap to the grid
Selected nodes can be snapped to the grid using Grid → Snap to Grid.
In Edit Graph mode a double click on a node will snap it to the grid.
To mirror the selection, use Nodes → Horizontal Flip and Nodes → Vertical Flip.
When moving a part of the graph it can be rotated scrolling the mouse wheel while holding Shift.
When the transformation mode is set to Rotate (Nodes → Rotate) the transformation handles will rotate the selection. The default is to rotate freely around the center, holding Ctrl will snap the rotation to steps of 15 degrees. Pressing Shift when you start dragging the handle will make the selection rotate around the opposing corner.
When moving a part of the graph it can be scaled using the mouse wheel.
When the transformation mode is set to Scale (Nodes → Scale) the transformation handles will scale the selection.
The default is to scale freely from the opposing angle, holding Ctrl will snap increase the selection size with steps equal to the grid size. Pressing Shift when you start dragging the handle will make the selection scale on the selection center.