In the current era, the rapid growth of digital connected devices makes it essential to ensure that wireless sensor networks provide reliable, energy-efficient, and scalable communication. This research work shows the combination of graph theory and discrete structures to enhance the data transmission in wireless sensor networks. In this work spectral clustering and centrality measures are used to model network topologies as graph. To identify the optimal routing paths, we created the network using Laplacian matrices. Discrete methods such as Fuzzy C clustering and eigenvector analysis are employed to form energy-aware clusters and select robust cluster heads.  During the analysis of energy efficiency, our proposed algorithm K-GLARE was found to be 3.22% more efficient than LEACH and 2.38% better than EECDA. The analysis of throughput has shown prominent results, as K-GLARE achieved a 133% improvement over EECDA and was six times better than LEACH, which is a significant improvement to ensure better data delivery and communication reliability. During the network longevity analysis, K-GLARE maintained the highest proportion of live nodes at 38.61%, compared to 31.98% for EECDA and 29.41% for LEACH. Making K-GLARE a promising solution for next-generation wireless communication systems.