Multi-relational graphs have different types of edges. The edge notation can be rewritten as $(u, \tau, v) \in \mathcal{E}$, where $\tau$ is the relation type. An adjacency matrix $A_{\tau}$ has to be defined for each edge type. The entire graph is summarized by an adjacency tensor $\mathcal{A} \in \mathbb{R}^{|\mathcal{V}| \times |\mathcal{R}| \times |\mathcal{V}|}$, where $\mathcal{R}$ is the set of relations. Two important subsets of multi-relational graphs are:

• Heterogeneous graphs
• Multiplex graphs