Path analysis in Ising models: an application to cyber-security risk assessment

We propose a method for path analysis in undirected graph models for binary variables to quantify the strength of association in multiple paths joining a pair of vertices in the underlying graph. With special focus on Ising models, we provide a decomposition of a marginal pairwise parameter into the sum of measures uniquely associated to the edge set of the paths linking the related couple of vertices. The work has been stimulated by a collaboration with a consultant company working in cyber-security risk assessment in industrial Operational Technology systems.