Communication is the main driving force behind the emerging intelligent transportation systems, which are expected to make traveling safer, more ecological, and faster. The most challenging among all the different communication technologies that will be used are the direct vehicle-to-vehicle communications, because vehicles move with high speeds and in different directions. Apart from that, it is expected that vehicles should be able to organize themselves in an ad hoc network without any assistance from outside entities, such as road side units. To make the ad hoc network less dynamic and communications more reliable, vehicles with similar movement patterns can be grouped together in clusters. Clustering is a well-known method for organizing ad hoc networks and is used in mobile and wireless sensor networks, but with different constraints and goals, so new clustering solutions for vehicular ad hoc networks (VANET) have to be developed. In recent years, this has been a hot topic among researchers and many different clustering algorithms for VANET have been proposed. In this paper, we propose a new clustering metric for VANET, named vehicle interconnection metric, which is based on sending periodic beacons among vehicles and reflects the communication abilities between them. We also propose a new clustering algorithm whose primary goal is increased connectivity and lower number of disconnects. The working principle of this algorithm is also inverted compared to others and uses unneeded cluster head elimination instead of cluster head election. Mathematical analysis of memory usage and communication overhead are provided, predicting low-resource usage. Simulation results, obtained with the ns-3 network simulator and the SUMO vehicle movement simulator, have confirmed the analysis and expected performance in terms of cluster head duration, number of connectivity losses and role switches.