Certainly, here is the formula for the Normalized Mutual Information (NMI) as described in your request.1
References
1Tiamat BM, Abdulsahib LA. A Constrained Louvain Algorithm with Novel Modularity for Enhanced Community Detection in Complex Networks. Migration Letters. 2023;20(S2):871-882. doi:10.59670/ml.v20iS2.3740