Strange. Nowhere in the definition is there talk of dots or lines. From the definition, a graph could be

\begin{equation*} (\{a,b,c,d\}, \{\{a,b\}, \{a,c\}, \{b,c\}, \{b,d\}, \{c,d\}\})\text{.} \end{equation*}

Here we have a graph with four vertices (the letters \(a, b, c, d\)) and five edges (the pairs \(\{a,b\}, \{a,c\}, \{b,c\}, \{b,d\}, \{c,d\})\)).