I have a clustering algorithm (not k-means) with input parameter $k$ (number of clusters). After performing clustering I'd like to get some quantitative measure of quality of this clustering. The clustering algorithm has one important property. For $k=2$ if I feed $N$ data points without any significant distinction among them to this algorithm as a result I will get one cluster containing $N-1$ data points and one cluster with $1$ data point. Obviously this is not what I want. So I want to calculate this quality measure to estimate reasonability of this clustering. Ideally I will be able to compare this measures for different $k$. So I will run clustering in the range of $k$ and choose the one with the best quality. How do I calculate such quality measure?
Here's an example when $(N-1, 1)$ is a bad clustering. Let's say there are 3 points on a plane forming equilateral triangle. Splitting these points into 2 clusters is obviously worse than splitting them into 1 or 3 clusters.