The reliability, scalability, and stability of routing schemes are open challenges in highly evolving vehicular ad hoc networks (VANETs). Cluster-based routing is an efficient solution to cope with the dynamic and inconsistent structure of VANETs. In this paper, we propose a cluster-based routing scheme (hereinafter referred to as connectivity-based clustering), where link connectivity is used as a metric for cluster formation and cluster head (CH) selection. Link connectivity is a function of vehicle density and transmission range in the proposed connectivity-based clustering scheme. Moreover, we used a heuristic approach of spectral clustering for the optimal number of cluster formation. Lastly, an appropriate vehicle is selected as a CH based on the maximum Eigen-centrality score. The simulation results show that the suggested connectivity-based clustering scheme performs well in the optimal number of cluster selections, strongly connected (STC) route selection, and route request messages (RRMs) in the discovery of a particular path to the destination. Thus, we conclude that link connectivity and the heuristic approach of spectral clustering are valuable additions to existing routing schemes for high evolving networks.