We developed a novel network to probe pathological states with the aid of heartbeat time series, by regarding each vector in the embedding phase space as one node of the network and using a permutation-based measure to determine links between nodes. The entropy of the degree distribution of the network shows a general and significant reduction under pathological conditions, even when there are only ultra short-term heartbeats available. The reduction of is possibly a dynamic marker of cardiac disorders. Our results reveal that a comparatively strong "memory" should usually exist in the healthy cardiovascular system whereas it dramatically declines when a cardiac disease is arising. The proposed method shows great promise in screening cardiac diseases and monitoring dynamic changes of the autonomic nervous system. Besides, as a universal method for analyzing the time series, the proposed approach seems to be promising also for other research disciplines.