Cryptographic hash functions are fundamental elements in cryptography, used as building blocks for cryptographic systems. In recent years, there have been attempts to define hash functions using different mathematical structures, including finite groups and graphs. In particular, Cayley graphsCayley graph have received considerable attention due to the existence of known families of graphs with good properties. In this paper, we give an overview of graph hash functions, focusing on Cayley hash functions, and discuss possible extensions to non-regular graphs using as a basis a non-regular generalization of Cayley graphs called group-subgroup pair graphs.