  Reconstructing complex networks from measurable data is a fundamental problem
for understanding and controlling collective dynamics of complex networked
systems. However, a significant challenge arises when we attempt to decode
structural information hidden in limited amounts of data accompanied by noise
and in the presence of inaccessible nodes. Here, we develop a general framework
for robust reconstruction of complex networks from sparse and noisy data.
Specifically, we decompose the task of reconstructing the whole network into
recovering local structures centered at each node. Thus, the natural sparsity
of complex networks ensures a conversion from the local structure
reconstruction into a sparse signal reconstruction problem that can be
addressed by using the lasso, a convex optimization method. We apply our method
to evolutionary games, transportation and communication processes taking place
in a variety of model and real complex networks, finding that universal high
reconstruction accuracy can be achieved from sparse data in spite of noise in
time series and missing data of partial nodes. Our approach opens new routes to
the network reconstruction problem and has potential applications in a wide
range of fields.
