  Stochastic spreading models defined on complex network topologies are used to
mimic the diffusion of diseases, information, and opinions in real-world
systems. Existing theoretical approaches to the characterization of the models
in terms of microscopic configurations rely on some approximation of
independence among dynamical variables, thus introducing a systematic bias in
the prediction of the ground-truth dynamics. Here, we develop a combinatorial
framework based on the approximation that spreading may occur only along the
shortest paths connecting pairs of nodes. The approximation overestimates
dynamical correlations among node states and leads to biased predictions.
Systematic bias is, however, pointing in the opposite direction of existing
approximations. We show that the combination of the two biased approaches
generates predictions of the ground-truth dynamics that are more accurate than
the ones given by the two approximations if used in isolation. We further take
advantage of the combinatorial approximation to characterize theoretical
properties of some inference problems, and show that the reconstruction of
microscopic configurations is very sensitive to both the place where and the
time when partial knowledge of the system is acquired.
