diameter of Barabasi graph:
Diameter: 2
diameter of ring and the path in terms of edges and vertices 
diameter: 9, from 0 to 9
( 0 1 2 3 4 5 6 7 8 9 )
( 0 1 2 3 4 5 6 7 8 )
disconnected ring graph
The largest path in one connected component
5
uconn = False 
Inf
graph with zero nodes
NaN
from = -1, to = -1
graph with one node
0
from = 0, to = 0