The structure of G can be analyzed using various graph-theoretic functions such as:

G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3)])
G.add_node("spam")       # adds node "spam"
list(nx.connected_components(G))

sorted(d for n, d in G.degree())

nx.clustering(G)

Some functions with large output iterate over (node, value) 2-tuples. These are easily stored in a dict (opens new window) structure if you desire.

sp = dict(nx.all_pairs_shortest_path(G))
sp[3]

See Algorithms (opens new window) for details on graph algorithms supported.