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A vehicular ad hoc network (VANET) may exhibit a bipolar behavior, i.e., the network can either be fully connected or sparsely connected depending on the time of day or on the market penetration rate of the wireless communication devices. In this paper, we use empirical vehicle traffic data measured on 1-80 freeway in California to develop a comprehensive analytical framework to study the disconnected network phenomenon and its network characteristics. These characteristics shed light on the key routing performance metrics of interest in disconnected VANETs, such as the average time taken to propagate a packet to disconnected nodes (i.e., the re-healing time). Our results show that, depending on the sparsity of vehicles or the market penetration rate of cars using Dedicated Short Range Communication (DSRC) technology, the network re-healing time can vary from a few seconds to several minutes. This suggests that, for vehicular safety applications, a new ad hoc routing protocol will be needed as the conventional ad hoc routing protocols such as Dynamic Source Routing (DSR) and Ad Hoc On-Demand Distance Vector Routing (AODV) will not work with such long re-healing times. In addition, the developed analytical framework and its predictions provide valuable insights into the VANET routing performance in the disconnected network regime.