Derivative-variable correlation reveals the structure of dynamical networks

Abstract

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the network adjacency matrix. Our assumptions are the possession of time series describing the network dynamics, and the precise knowledge of the interaction functions. Our method involves a tunable parameter, allowing for the reconstruction precision to be optimized within the constraints of given dynamical data. The method is illustrated on a simple example, and the dependence of the reconstruction precision on the dynamical properties of time series is discussed. Our theory is in principle applicable to any weighted or directed network whose internal interaction functions are known.

Submitted to EPJ B

References in corpus (7)

• Synchronization in complex networks
• From time series to complex networks: the visibility graph
• The backbone of the climate network
• Revealing Network Connectivity From Dynamics
• Noise bridges dynamical correlation and topology in coupled oscillator networks
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Exploring complex networks by means of adaptive walkers

Cited by in corpus (4)

• A comparative analysis of knowledge acquisition performance in complex networks
• Reconstruction of a scalar voltage-based neural field network from observed time series
• Effective phase connectivity from observations
• Network topology reconstructed from derivative-variable correlations