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Summary: Vehicular ad‐hoc network (VANET) is the unstructured evolving conception of a wireless network; clustering in these networks is perplexing due to continuously varying topology and recurrent disconnection in networks. The cluster head (CH) stability plays a noticeable role in robustness and scalability in the network. The author designs a model that includes cluster generation and maintenance. The cluster formation is conceived on the notion that the changes that are brought about due to the vehicle's speed are inevitable. A directed hypergraph approach is used to comprehend this problem, and then, based on the spectral clustering through tensor trace maximization, an optimal number of the cluster is formed. The centers of these clusters are used to place the auxiliary facilities that aid cluster maintenance. In the maintenance phase, the author has envisioned a CH selection method based on a summed amalgamation of three metrics: link lifetime, cooperative connectivity level, and relative cooperative speed superimposed on the vehicular hypergraph network to design the metric for choosing a stable CH. The proposed scheme is tested on the old Delhi area that includes a market area with urban inclusion. Also, the area is highly crowded as being the marketplace. The region also has a tourist attraction as being part of the heritage of Delhi. The traffic density and the variety are high in peak hours—a complete analysis of the different vehicular mobility and routing analysis. The analysis done through microscopic and macroscopic parameters has projected significant improvement in the CH stability and a promising solution for dynamic networks. [ABSTRACT FROM AUTHOR]