Here is a very interesting graphical way to represent timetable information for a regularly running service, whose clockface schedule repeats every hour (but not necessarily at equal time intervals between trains). The authors of the idea called it a “netgraph”. To illustrate this idea, take a look at the netgraph of Zurich S-Bahn or the netgraph for the entire Swiss rail network (the latter has an English version of the legend).
In essence, each solid line represents a train per hour running every hour. Different colors represent different types of trains (on the netgraph of Switzerland) or different S-Bahn routes (on the netgraph of Zurich S-Bahn). If a train runs every two hours, it is represented by a dashed line. If a train runs during rush hours only or makes just a few trips per day, it is represented by a dash-dot line. The numbers near each station represent the train’s arrival time from a particular direction (the one closer to the station rectangle) and the train’s departure time to the same direction (the one further from the station rectangle) in minutes after each hour. You can find the other (less important) notations in the legend.
As a result, it becomes possible to display all the timetable information for the entire network on a single page. I find this idea fascinating and promising. It makes it so easy to grasp general tendencies of the timetable and so simple to use it for both passengers and operators. For example, it is extremely easy to see all possible transfers at a given station, and how long each transfer takes (the time between the arrival of one train and the departure of another). That is, one can perceive the timetable not at the “one train at a time” level or even the “one route or line at a time” level, but as “the entire network at a time”.
Of course, such “netgraphs” require regular clockface timetables repeating every hour, like they do in Switzerland. There are many other benefits of having a regular timetable with coordinated/timed transfers (such as the ability to remember the timetable for the lines you use frequently), but this simplified way to represent it is an additional benefit that should not be overlooked.
If you’d like to see more netgraphs, there are several others (Luxemburg, Basel, etc.) here.