| Networks with N vertices are considered, each vertex is associated to a wide-sense stationary ergodic stochastic process, and links represent cross correlation functions between the nodes. We establish the conditions for the reconstruction of the entire cross correlation structure given a subnetwork. Except for subnetworks with certain loop structures, we show that either N cross correlation functions, or N-1 cross correlation functions together with a single autocorrelation function determine all missing correlation functions. The framework allows for reconstruction of the full network dynamics given N-1 cross correlation functions and a single signal. |
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