  Recently, a new way of avoiding crossings in straight-line drawings of
non-planar graphs has been investigated. The idea of partial edge drawings
(PED) is to drop the middle part of edges and rely on the remaining edge parts
called stubs. We focus on a symmetric model (SPED) that requires the two stubs
of an edge to be of equal length. In this way, the stub at the other endpoint
of an edge assures the viewer of the edge's existence. We also consider an
additional homogeneity constraint that forces the stub lengths to be a given
fraction $\delta$ of the edge lengths ($\delta$-SHPED). Given length and
direction of a stub, this model helps to infer the position of the opposite
stub.
  We show that, for a fixed stub--edge length ratio $\delta$, not all graphs
have a $\delta$-SHPED. Specifically, we show that $K_{241}$ does not have a
1/4-SHPED, while bandwidth-$k$ graphs always have a $\Theta(1/\sqrt{k})$-SHPED.
We also give bounds for complete bipartite graphs. Further, we consider the
problem \textsc{MaxSPED} where the task is to compute the SPED of maximum total
stub length that a given straight-line drawing contains. We present an
efficient solution for 2-planar drawings and a 2-approximation algorithm for
the dual problem.
