Multi relational graphs have different types of edges. The edge notation can be rewritten as $(u, \tau,v) \in \mathcal{E}$ $\tau$ - relation type

Adjacency matrix $A_{\tau}$, has to be defined for each edge type.

Entire graph is summarized by an adjacency tensor $\mathcal{A} \in {\rm I\!R} ^{|\mathcal{V}| \times |\mathcal{R}| \times |\mathcal{V}| }$ $\mathcal{R}$ , set of relations

Two important subsets of multi relational graphs are

• Heterogeneous graphs
• Multiplex graphs