This metricThe Adjusted Rand Index can calculate the agreement between two cluster labelings, even if the labels don't match. Scikit Learn has a good implementation of this. The original paper describing this index is Hubert and Arabie, 1985 [1].
This might be a good point to start your investigation:
[1] Hubert, Lawrence, and Phipps Arabie. 1985. “Comparing Partitions.” Journal of Classification 2 (1). Springer-Verlag: 193–218.