In modern-day digital systems, cryptographic hash functions can be highly important in providing data integrity, authentication and security. They present in this paper a new model of constructing hash functions out of expander graphs, which is well-connected and has a pseudo-random property. The suggested strategy makes use of algebraic constructions of Cayley and Ramanujan graphs to obtain better diffusion and confusion. It is suggested to generate a deterministic node labelling and state transitioning mechanism, which generates fixed length hash values of high entropy. Through experimental analysis, the collision resistance of 98.2, preimage resistance of 97.5 and reduced computational cost of 12.6 are observed to be better than the traditional hash schemes. The architecture is very scalable and not vulnerable to cryptanalytic attacks. The paper highlights the potential of the expander-based constructions to the next generation of lightweight and secure cryptographic applications.