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I thought about the following structure: $G=(U,\,\mathbb{N}\cup\{0\}\mid R)$, where $U$ is the set of vertices, and $R(a,n)$ means that vertice $a$ has $n$ adjacent edges. This looks suspicious: I learned that a structure has a single underlying set.Suppose we are presented with a graph $G$ that has multiple edges.This means that there may be more than one edge between two vertices of $G$ (so, by our strict definition of "graph", a graph with multiple edges is not a graph). Describe $G$ as a first-order $\nu$-structure for a suitable vocabulary $\nu.$

How do you understand this exercise?