I'm wondering what are the most common/recognized methods to assess the quality of a clustering.
That is because I have developed a tool that can cluster/partition a network (in this case, a public transport network represented by a GTFS feed) in several different manners (graph partitioning, hierarchical clustering, etc ...) and my 'real' metric is almost impossible to get.
In brief, the 'real' metric would be the speed-up obtained using a cluster-based searched against the non cluster-based search. This depends on too many factors (input distribution, implementation of the search algorithms, architecture, etc ....).
I have developed a small function that can evaluate the quality of a clustering using the ratio of vertices of the border of a cluster, against the total amount of vertices. That is because it makes sense, intuitively, with my problem. But there is no mathematic foundation behind it.
My question is: What are the most common methods to assess the quality of a clustering/partitioning ?