### Abstract

Complex dynamical networks consisting of a large number of interacting units are ubiquitous in nature and society. There are situations where the interactions in a network of interest are unknown and one wishes to reconstruct the full topology of the network through measured time series. We present a general method based on compressive sensing. In particular, by using power series expansions to arbitrary order, we demonstrate that the network-reconstruction problem can be casted into the form X = G . a, where the vector X and matrix G are determined by the time series and a is a sparse vector to be estimated that contains all nonzero power series coefficients in the mathematical functions of all existing couplings among the nodes. Since a is sparse, it can be solved by the standard L-1-norm technique in compressive sensing. The main advantages of our approach include sparse data requirement and broad applicability to a variety of complex networked dynamical systems, and these are illustrated by concrete examples of model and real-world complex networks. Copyright (C) EPLA, 2011

Original language | English |
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Article number | 48006 |

Number of pages | 6 |

Journal | Europhysics Letters |

Volume | 94 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2011 |

### Cite this

*Europhysics Letters*,

*94*(4), [48006]. https://doi.org/10.1209/0295-5075/94/48006