my question particularly applies to network reconstruction
Answer
Correlation measures the linear relationship (Pearson’s correlation) or monotonic relationship (Spearman’s correlation) between two variables, X and Y.
Mutual information is more general and measures the reduction of uncertainty in Y after observing X. It is the KL distance between the joint density and the product of the individual densities. So MI can measure non-monotonic relationships and other more complicated relationships.
Attribution
Source : Link , Question Author : Community , Answer Author : Rob Hyndman