In current digital systems, such as blockchain, secure communications, and distributed computing environments, cryptographic hash functions are basic primitives to guarantee data integrity, authentication and security. The current design of hash functions (SHA-2 and SHA-3) are however limited in their ability to trade off computational efficiency and good theoretical diffusion and security guarantees, especially with new high-performance and post-quantum demands. This gap is filled in this paper by exploring expander graph families as a mathematical basis to designing high-performance cryptographic hash functions. The main aim of the research is to create a new expander-based hash-function framework exploiting the expansion strength and speed of mixing to achieve a higher level of security as well as efficiency. The suggested methodology combines the message-dependent random walks on d-regular expander graphs, and non-linear compression functions to build the hash output. Spectral properties and expansion measures are also used to achieve good diffusion and anti-cryptographic attacks resistance. Experimental analysis and comparison prove that the proposed model has better performance with a lower execution time (10.3 ms), higher throughput (92 MB/s), and a more prominent avalanche effect (50.6%) compared to the use of SHA-256, SHA-3 and ZemorTillich hash functions.