From a quick search it seems neither Cycles nor Eevee support vertex shaders so there will probably only be workarounds.
I’ve played around a little and found a way to create something close-ish. Though it’s kind of a poor imitation and pretty limited:
This setup is instancing small spheres to each vertext of the bigger mesh (I deleted the faces of that mesh). Those small spheres get an emission shader to make them light up and Eevee’s bloom is emulating the glow.
I’ve included all relevant settings in the screenshot, but I can explain things further, if you’re interested.
If you really wanted, you could probably get something closer to your screenshot by shading the instanced spheres with a volume shader, though that would will increase rendering time a lot.
What exactly is it, that you’re trying to make? Knowing the goal could maybe help coming up with more suitable workarounds.
Anyway I’m curious if someone knows a good way to recreate that kind of look.