Clustering Within Timetabling Conflict Graphs

A key concept in timetabling problems is that of the conflict graph with edges representing pairs of events that are not allowed to occur at the same time. Usually, the only information presented about such graphs is their density. However, intuitively, it seems likely that such graphs are structured, and most likely have some clustering. In analysing the structure of social networks or of the world-wide web it is common to use various measures. Amongst these is the “clustering coefficient”. We propose using this coefficient in order to analyse timetabling conflict graphs, and give results showing that on some common benchmarks the graphs are indeed clustered by this measure.