Our ability to uncover complex network structure and dynamics from data is
fundamental to understanding and controlling collective dynamics in complex
systems. Despite recent progress in this area, reconstructing networks with
stochastic dynamical processes from limited time series remains to be an
outstanding problem. Here we develop a framework based on compressed sensing to
reconstruct complex networks on which stochastic spreading dynamics take place.
We apply the methodology to a large number of model and real networks, finding
that a full reconstruction of inhomogeneous interactions can be achieved from
small amounts of polarized (binary) data, a virtue of compressed sensing.
Further, we demonstrate that a hidden source that triggers the spreading
process but is externally inaccessible can be ascertained and located with high
confidence in the absence of direct routes of propagation from it. Our approach
thus establishes a paradigm for tracing and controlling epidemic invasion and
information diffusion in complex networked systems.Comment: 20 pages and 5 figures. For Supplementary information, please see
http://www.nature.com/ncomms/2014/140711/ncomms5323/full/ncomms5323.html#
