Plotting 3D points connected by arbitrary lines (i.e. a 3D graph)

In my head this sounds like a 3D version of this:

Or complete decoupled from the networkx:

import plotly.graph_objects as go
import itertools

# Define vertices
vertices = [
    (1, 0, 0), (-1, 0, 0),
    (0, 1, 0), (0, -1, 0),
    (0, 0, 1), (0, 0, -1)
]

# Function to determine if two vertices form an edge
def is_edge(v1, v2):
    diff = sum(abs(a - b) for a, b in zip(v1, v2))
    return diff == 2  # octahedron edge condition

# Build edge traces
edge_traces = []
for v1, v2 in itertools.combinations(vertices, 2):
    if is_edge(v1, v2):
        edge_traces.append(
            go.Scatter3d(
                x=[v1[0], v2[0]],
                y=[v1[1], v2[1]],
                z=[v1[2], v2[2]],
                mode="lines",
                line=dict(color="black", width=4),
                hoverinfo="none"
            )
        )

# Vertex trace
x, y, z = zip(*vertices)
vertex_trace = go.Scatter3d(
    x=x,
    y=y,
    z=z,
    mode="markers",
    marker=dict(
        size=8,
        color="red",
        symbol="circle"
    ),
    name="Vertices"
)

# Create figure
fig = go.Figure(data=edge_traces + [vertex_trace])

fig.update_layout(
    scene=dict(
        xaxis=dict(visible=False),
        yaxis=dict(visible=False),
        zaxis=dict(visible=False),
        aspectmode="data"
    ),
    margin=dict(l=0, r=0, t=0, b=0)
)

fig.show()