Given a networkx graph containing weighted edges and a threshold parameter alpha, this code will return another networkx graph with the "backbone" of the graph containing a subset of weighted edges that fall above the threshold following the method in Serrano et al. 2008.

backbone_extractor.py

# Serrano, Boguna, Vespigani backbone extractor
# from http://www.pnas.org/content/106/16/6483.abstract
# Thanks to Michael Conover and Qian Zhang at Indiana with help on earlier versions
# Thanks to Clay Davis for pointing out an error

import networkx as nx
import numpy as np

def extract_backbone(g, weight='weight', alpha=.05):
    backbone_graph = nx.Graph()
    for node in g:
        k_n = len(g[node])
        if k_n > 1:
            sum_w = sum( g[node][neighbor][weight] for neighbor in g[node] )
            for neighbor in g[node]:
                edge_weight = g[node][neighbor][weight]
                pij = float(edge_weight)/sum_w
                if (1-pij)**(k_n-1) < alpha: # equation 2
                    backbone_graph.add_edge( node,neighbor, weight = edge_weight)
    return backbone_graph