TECHNISCHE UNIVERSITEIT EINDHOVEN Department of Mathematics and Computing Science MASTER’S THESIS Visualisation of State Transition Graphs by F.J.J. van Ham Supervisors: H.M.M. van de Wetering

Although graph drawing and graph visualisation have often been the subject of research, most of this research focuses on creating tidier drawings of relatively small graphs. However, in today's complex society, research into the visualisation of large graphs is becoming increasingly important. One can think of maps of the entire internet or call graphs for very large software programs, for example. This thesis presents a visualisation method for a class of large graphs called state transition graphs. State transition graphs can be used as a mathematical description for processes or programs, and their analysis gives much insight into the process or program they describe. The major problem in the visualisation of large graphs is the size of the graph. Displaying an entire large graph all at once may overload the user with information, making it more difficult to comprehend. We attempt to overcome this problem by grouping nodes based on a local structural property. This reduces the complexity of the original graph and by initially displaying groups of nodes instead of individual nodes, the overall structure of the graph is revealed to the user. Further, instead of minimising the number of line crossings in a graph, as is often done in the visualisation of small graphs, we focus our attention on a different, global aesthetic aspect of a graph, namely symmetry. A clear picture of the symmetry in a graph allows the user to mentally split it into a number of smaller parts. Another advantage is that only one of the symmetrical parts has to be analysed, considerably reducing the amount of work necessary. After a description of the concepts behind this visualisation method, we present results obtained from working with a prototype. Finally, we discuss the advantages and disadvantages of this type of visualisation.