Create vertex and edges using this code?

Coding Python Support
3

Yes, it’s possible. There’s a utility function for this simple case. The script assumes vertices to be sorted and simply casts the numeric part of the vertex names in the edge list to compute the indices:

import bpy

verts_raw = (
    ["a0",1.0,-1.0,-1.0],
    ["a1",1.0,-1.0,1.0],
    ["a2",-1.0,-1.0,-1.0],
    ["a3",-1.0,-1.0,1.0],
    ["a4",1.0,1.0,-1.0],
    ["a5",1.0,1.0,1.0],
    ["a6",-1.0,1.0,-1.0],
    ["a7",-1.0,1.0,1.0],
)

edges_raw = (
    ["a4","a0"],
    ["a4","a6"],
    ["a4","a5"],
    ["a0","a2"],
    ["a0","a1"],
    ["a2","a6"],
    ["a2","a3"],
    ["a6","a7"],
    ["a5","a1"],
    ["a5","a7"],
    ["a1","a3"],
    ["a3","a7"],
)

verts = []
for v in verts_raw:
    verts.append(v[1:])
    
edges = []
for a, b in edges_raw:
    edges.append((int(a[1:]), int(b[1:])))

me = bpy.data.meshes.new("")
me.from_pydata(verts, edges, [])
me.validate()
me.update()

ob = bpy.data.objects.new("", me)
scene = bpy.context.scene
scene.objects.link(ob)
scene.update()