I haven't been able to find any forum where this question has been asked. To clarify: every definition of vertex I've seen makes reference to edges, and vice versa. Is it possible to define one or both of these terms independently of the other?
2026-04-09 00:24:19.1775694259
Can "edge" and "vertex" be defined in a way that isn't circular?
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Sure. A vertex is an element of a set $V$. And an edge is an element of a set $E$. Period.
If we additionally have an incidence relation $I\subseteq V\times E$ with the properties
(i.e., each edge is incident with exactly two vertices) then the tuple $(V,E,I)$ is a simple undirected graph.