  In a joint work with D. Bennequin, we suggested that the (negative) minima of
the 3-way multivariate mutual information correspond to Borromean links, paving
the way for providing probabilistic analogs of linking numbers. This short note
generalizes the correspondence of the minima of k multivariate interaction
information with k Brunnian links in the binary variable case. Following
Jakulin and Bratsko, we also note that the negativity of the associated K-L
divergence of the joint probability law with its Kirkwood approximation implies
their contextuality in the sens of Abramsky. Those negative k-interactions
links, that cannot be captured in lower dimensions then k, provide a
straightforward definition of collective emergence in complex k-body
interacting systems or dataset.
