System Information
Operating system: Windows-10-10.0.17134 64 Bits
Graphics card: GeForce GTX 970/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 430.86

Blender Version
Broken: version: 2.80 (sub 75), branch: master, commit date: 2019-07-24 12:32, hash: rBbfe580642f46
Worked: (optional)

Short description of error
An wire edge mesh combined with a vertex bevel modifier and skin modifier creates bad geometry. Here's a picture showing the problem:

Exact steps for others to reproduce the error

1. Make a simple, angular wire edge mesh.
2. Add a bevel modifier with only vertices ticked.
3. Add a skin modifier.
4. (Optional) Add a subdivision surface modifier to make the problem more apparent.

Here's a blendfile with the models shown above:
http://pasteall.org/blend/index.php?id=52104

Potential solutions:

1. Change how the skin modifier does tessellation on smaller edges.
2. Make the wireframe modifier work on wire edge meshes (it wouldn't create this extra geometry to begin with).