Subgraph Drawing

[subhabangalore at gmail.com]

Dear Group,

I have two questions, if I take a subseries of the matrix as in eigenvalue here,
provided I have one graph of the full form in G, how may I show it, as if I do the nx.draw(G) it takes only the original graph. 

>>> import numpy
>>> import networkx as nx
>>> import matplotlib.pyplot as plt
>>> G=nx.Graph()
>>> G.add_edges_from([(1,2),(1,3),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)])
>>> L =nx.laplacian(G)
>>> print L
[[ 7. -1. -1. -1. -1. -1. -1. -1.]
 [-1.  1.  0.  0.  0.  0.  0.  0.]
 [-1.  0.  1.  0.  0.  0.  0.  0.]
 [-1.  0.  0.  1.  0.  0.  0.  0.]
 [-1.  0.  0.  0.  1.  0.  0.  0.]
 [-1.  0.  0.  0.  0.  1.  0.  0.]
 [-1.  0.  0.  0.  0.  0.  1.  0.]
 [-1.  0.  0.  0.  0.  0.  0.  1.]]
>>> print numpy.linalg.eigvals(L)
[  8.00000000e+00   2.22044605e-16   1.00000000e+00   1.00000000e+00
   1.00000000e+00   1.00000000e+00   1.00000000e+00   1.00000000e+00]

for more than 1000 nodes it is coming too slow on Windows 7 machine with 3GB RAM.

If any one of the learned members can help.

Apology for any indentation error etc.

Thanking all in Advance,

Regards,
Subhabrata Banerjee.