This paper explores the propagation effect of flight delays among airports in the aviation system and proposes a new measure, the propagation index, to effectively analyze the interrelationship among airports in relation to flight delays. This index quantifies the effect of delay propagation by measuring the causality among delay time series. To assess the effectiveness of the proposed index on airport delays, three neural network-based regression models are built. The comparative experiments demonstrate that the propagation index proposed is highly correlated with observed airport delays.