The paper proposes and investigates a new index of flow autocorrelation, based upon a generalization of Moran’s I, and made of two ingredients. The first one consists of a family of spatial weights matrix, the exchange matrix, possessing a freely adjustable parameter interpretable as the age of the network, and controlling for the distance decay range. The second one is a matrix of chi-square dissimilarities between outgoing or incoming flows. Flows have to be adjusted, that is their diagonal part must first be calibrated from their off-diagonal part, thanks to a new iterative procedure procedure aimed at making flows as independent as possible. Commuter flows in Western Switzerland as well as migration flows in Western US illustrate the statistical testing of flow autocorrelation, as well as the computation, mapping and interpretation of local indicators of flow autocorrelation. We prove the present dyadic formalism to be equivalent to the “origin-based” tetradic formalism found in alternative studies of flow autocorrelation.