# Problem in understanding a notation in graph theory (intersection of edges)

On the French wikipedia, one can read:

Soit un graphe simple non orienté $G = ( S, A )$ (où $S$ est l'ensemble des sommets et $A$ l'ensemble des arêtes, qui sont certaines paires de sommets), un couplage $M$ est un ensemble d'arêtes deux à deux non adjacentes. C'est-à-dire que M est une partie de l'ensemble A des arêtes telle que $\forall (a, a') \in M, a \neq a' \Rightarrow a \cap a' = \emptyset$.

which translates to:

Let $G = (S, A)$ be a simple non-oriented graph (where $S$ is the set of vertices and $A$ is the set of edges, which are pairs of vertices), a matching $M$ is a set of pairwise non-adjacent edges. In other words it means that $M$ is a subset of the set $A$ ($M \in \mathcal{P}(A)$) so that, $\forall (a, a') \in M, a \neq a' \Rightarrow a \cap a' = \emptyset$.

I can't understand what does mean $a \cap a' = \emptyset$. Because, to my view, $a$ and $a'$ are two different edges (not two different sets of edges or if it's the case I can't see why it would) how it is possible to apply them the cap operator? And what does it mean?