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Enrico @enricocaprioglio.bsky.social · 18/09/2025

First, we used the O-information and (social) structural balanced theory to show that the O-information can be expanded in terms of closed walks in the correlation matrix Σ. The terms that contribute synergistically are exactly the kind of walks that you would find in antibalanced graphs!

LEFT: if the graph G is antibalanced, every closed walk in G contributes negatively in the expansion of the O-information.

RIGHT: examples of synergistic (correlation) motifs that ensure synergy-dominance

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Enrico @enricocaprioglio.bsky.social · 18/09/2025

Then we asked: how do we get here? What kind of interactions are needed to obtain these correlational structures? Note: the structures above are all made of "forbidden triads" (see e.g., "the strength of weak ties")

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Enrico @enricocaprioglio.bsky.social · 18/09/2025

Basically, in diffusive systems with +ve couplings, we expect triadic closure in the correlations. In other words, it's weird when two nodes are (anti)uncorrelated, but both are correlated with a third node. The intuition being there must be a negative underlying interaction between the two nodes.

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