Detect graphs in a set of arbitrary edges

Question

I've got a set of potentially unrelated edges and need to transform it into graphs. For example, the set contains $A\leftrightarrow B$ and $Z\leftrightarrow X$. $A$ and $B$ are not connected with $Z$ and $X$, so I expect to detect two isolated graphs. Is there a specific name for an operation/algorithm that makes such detection? I'm looking at a big programming library with lots of algorithms, but am lost in the terminology.