Whether it is density based, partitioning based etc, you can use internal or external evaluation approaches to check the performance of your clustering algorithm. You can read more here:
https://en.wikipedia.org/wiki/Cluster_analysis
Also, you can read this article for cluster path lengths approach.
...For this purpose is possible to use several methods: Neural Networks, Multivariate Methods, Factorial Methods, Statistical diagnostic test, etc. But firstly is necessary obtains very clear information as input of all method mentioned in order to get logic results.