Shared Information for the Cliqueylon Graph

Shared information is a measure of mutual dependence among m≥2 jointly distributed discrete random variables. A new undirected probabilistic graphical model, a cliqueylon graph, is introduced, with potential applications in leader-follower swarms and neuron clusters with correlations of varying strength. Shared information is characterized explicitly for the cliqueylon, relying on structural properties of an underlying optimization. Implications for the data compression problem of omniscience are highlighted.