Measuring the Balance Between Synergy and Redundancy in Network Systems by Using Information Theory

Statistical synergy and redundancy are important concepts in network systems. The literature includes multiple implementations of these concepts, such as interaction information, O-information and its dynamic extension, the O-Information rate. However, these measures typically do not focus on how pairs of nodes interact with each other in the context of the whole network. This work proposes a novel metric called the B-index, which utilizes mutual information and its conditional form to analyze how pairs of nodes interact with each other in the con text of the entire network. By extending the concept of pairwise functional connectivity to higher-order interactions, the B-index provides a clear characterization of the balance between redundant and synergis tic interactions of between a given pair of nodes and the rest of the network. Simultaneously, it allows investigating the structure of the ana lyzed network, relying out spurious links due to common driver, cascade and collider effects. The proposed index is first validated using a sim ulated network, demonstrating its effectiveness in uncovering direct in teractions and characterizing them in terms of synergy and redundancy. Afterwards, the index is applied to real-data subjects from two sources: fMRI from a pediatric patient with hepatic cavernoma and an in-vitro cortical neuronal culture observed at various stages of maturation, pro viding insight into their network structures.