In recent years, there has been renewed interest in casting graph algorithms in the language of linear algebra. By replacing the computations with appropriate operations over different semi-rings, different graph algorithms can be cast as a sequence of linear algebra operations. In this work, we study the use of the linear algebraic approach to graph algorithms within the context of graph database systems. Specifically, we identify the issues with using existing linear algebraic graph libraries, such as SuiteSparse, which conform to the GraphBLAS specifications. We also highlight gaps between the GraphBLAS specification and computations that are required by the graph query algorithms utilized in graph databases. We show that overcoming these challenges in using a linear algebraic approach within a graph database system can lead to significant performance improvements to an open-source graph database system.