You can position new polygon points directly on existing polygon points and merge them, if required. Permit snapping option via Edit > User Preferences > GUI > Network editor menu and define a snap radius. Then adjacent polygon points of other polygons are displayed as small circles and the mouse pointer turns into a lasso as soon as an existing polygon point can be snapped. This way, you can use existing points explicitly. If you don't want to snap the point just hold down the Shift key or switch off the option 'Permit snapping'.