  Understanding how and how far information, behaviors, or pathogens spread in
social networks is an important problem, having implications for both
predicting the size of epidemics, as well as for planning effective
interventions. There are, however, two main challenges for inferring spreading
paths in real-world networks. One is the practical difficulty of observing a
dynamic process on a network, and the other is the typical constraint of only
partially observing a network. Using a static, structurally realistic social
network as a platform for simulations, we juxtapose three distinct paths: (1)
the stochastic path taken by a simulated spreading process from source to
target; (2) the topologically shortest path in the fully observed network, and
hence the single most likely stochastic path, between the two nodes; and (3)
the topologically shortest path in a partially observed network. In a sampled
network, how closely does the partially observed shortest path (3) emulate the
unobserved spreading path (1)? Although partial observation inflates the length
of the shortest path, the stochastic nature of the spreading process also
frequently derails the dynamic path from the shortest path. We find that the
partially observed shortest path does not necessarily give an inflated estimate
of the length of the process path; in fact, partial observation may,
counterintuitively, make the path seem shorter than it actually is.
