Roberts' website contains a wealth of interesting history and comment on the London Tube diagram. In particular, he points out a variety of continental precursors, and he discounts the supposed connection between the network diagram and electrical circuit diagrams. Go explore!
One of his most interesting pages is devoted to denying what he calls London Underground myths about the Harry Beck diagram. There he points to the following Berlin S-Bahn diagram of 1931:
Any stranger can check the distance off--by means of the most curious map I am acquainted with. It is issued by the city government and can be bought in any shop for a trifle. In it every street is sectioned off like a string of long beads of different colors. Each long bead represents a minute's travel, and when you have covered fifteen of the beads you have got your money's worth. This map of Berlin is a gay-colored maze, and looks like pictures of the circulation of the blood.I have not been able to discover any images or paper copies of the map Twain saw, but it certainly does sound as if it too was based on a system of nodes and lines.