Edge-transitive graph

This article defines a property that can be evaluated to true/false for any undirected graph, and is invariant under graph isomorphism. Note that the term "undirected graph" as used here does not allow for loops or parallel edges, so there can be at most one edge between two distinct vertices, the edge is completely described by the vertices it joins, and there can be no edge from a vertex to itself.
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Definition

An undirected graph is termed edge-transitive if it is either an empty graph or the induced action of its automorphism group on its edge set is transitive on all edges.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
symmetric graph