Which algorithms should I use for recommendation system using a graph database?
A biadjacency matrix of a bipartite graph admits matrix factorisation. 

For $m$ items and $n$ users, the biadjacency matrix is an $m \times n$ matrix which can be factorised into two lower-rank factor matrices of sizes $m \times k$ and $k \times n$ respectively. This provides a lower-dimensional representation of how users' preferences vary over products.

This model also has the property that the inner product of the $i$th row and $j$th column of the two factor matrices provide an approximation of user $j$'s rating of item $i$. In other words, the product of the two matrices is an approximation of the original ratings matrix.