Dunn index

The Dunn Index (DI) is a metric for judging a clustering algorithm. A higher DI implies better clustering. It assumes that better clustering means that clusters are compact and well-separated from other clusters.
There are many ways to define the size of a cluster and distance between clusters.
The DI is equal to the minimum inter-cluster distance divided by the maximum cluster size. Note that larger inter-cluster distances (better separation) and smaller cluster sizes (more compact clusters) lead to a higher DI value.
In mathematical terms:
Let the size of cluster C be denoted by: formula_1
Let the distance between clusters i and j be denoted by: formula_2
formula_3