  Inferring the connectivity structure of networked systems from data is an
extremely important task in many areas of science. Most of real-world networks
exhibit sparsely connected topologies, with links between nodes that in some
cases may be even associated to a binary state (0 or 1, denoting respectively
the absence or the existence of a connection). Such un-weighted topologies are
elusive to classical reconstruction methods such as Lasso or Compressed Sensing
techniques. We here introduce a novel approach called signal Lasso, where the
estimation of the signal parameter is subjected to 0 or 1 values. The
theoretical properties and algorithm of proposed method are studied in detail.
Applications of the method are illustrated to an evolutionary game and
synchronization dynamics in several synthetic and empirical networks, where we
show that the novel strategy is reliable and robust, and outperform the
classical approaches in terms of accuracy and mean square errors.
