I want to create a graph in the following fashion:
However, I don't see how it is possible to connect edges with yEd. Am I missing something or is this currently not possible?
yEd is an editor for graphs (see Wikipedia for a formal definition) and in a graph there can be no edge-to-edge connections. The "restriction" to graphs is essential for many of yEd's features (most notably its layout algorithms).
The common workaround is to split the edges you want to connect using size 1 nodes and then connect these split nodes.