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We propose a conceptually novel method of reconstructing the topology ofdynamical networks. By examining the correlation between the variable of onenode and the derivative of another node, we derive a simple matrix equationyielding the network adjacency matrix. Our assumptions are the possession oftime series describing the network dynamics, and the precise knowledge of theinteraction functions. Our method involves a tunable parameter, allowing forthe reconstruction precision to be optimized within the constraints of givendynamical data. The method is illustrated on a simple example, and thedependence of the reconstruction precision on the dynamical properties of timeseries is discussed. Our theory is in principle applicable to any weighted ordirected network whose internal interaction functions are known.

Derivative-variable correlation reveals the structure of dynamical networks