Name of a property in Graph Theory

Question

A multigraph is a graph which allows for more than one edge between a pair of nodes in a graph. What would be the name of a graph which allows for more than one type of node. For example, buyers and sellers. I've heard multimodal, but I don't know if that is correct.

Answer 1

I believe what you are describing is referred to in network science as a heterogeneous graph. A heterogeneous graph is a graph $G = (V, E)$ such that the vertex set $V$ is a disjoint union $V = V_1 \cup V_2 \cup \dots V_n$ where each $V_i$ denotes some set of vertices that share a common label. If $G$ is a directed graph then $E$ is the disjoint union of $n^2$ edge sets, where where each edge set is denoted by $E_{(i, j)}$ and consists of edges from vertices in $V_i$ to vertices in $V_j$. When $G$ is undirected we have $E_{(i, j)} = E_{(j, i)}$ and there are only $\binom{n}{2}$ edge sets.