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Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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Parallel BetweennessΒΆ

Example of parallel implementation of betweenness centrality using the multiprocessing module from Python Standard Library.

The function betweenness centrality accepts a bunch of nodes and computes the contribution of those nodes to the betweenness centrality of the whole network. Here we divide the network in chunks of nodes and we compute their contribution to the betweenness centrality of the whole network.

plot parallel betweenness

Out:

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 2991
Average degree:   5.9820
        Parallel version
                Time: 1.4551 seconds
                Betweenness centrality for node 0: 0.01863
        Non-Parallel version
                Time: 6.4654 seconds
                Betweenness centrality for node 0: 0.01863

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 5088
Average degree:  10.1760
        Parallel version
                Time: 1.7938 seconds
                Betweenness centrality for node 0: 0.00281
        Non-Parallel version
                Time: 8.0934 seconds
                Betweenness centrality for node 0: 0.00281

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 2000
Average degree:   4.0000
        Parallel version
                Time: 1.2444 seconds
                Betweenness centrality for node 0: 0.00412
        Non-Parallel version
                Time: 5.5613 seconds
                Betweenness centrality for node 0: 0.00412

from multiprocessing import Pool
import time
import itertools

import matplotlib.pyplot as plt
import networkx as nx


def chunks(l, n):
    """Divide a list of nodes `l` in `n` chunks"""
    l_c = iter(l)
    while 1:
        x = tuple(itertools.islice(l_c, n))
        if not x:
            return
        yield x


def betweenness_centrality_parallel(G, processes=None):
    """Parallel betweenness centrality  function"""
    p = Pool(processes=processes)
    node_divisor = len(p._pool) * 4
    node_chunks = list(chunks(G.nodes(), int(G.order() / node_divisor)))
    num_chunks = len(node_chunks)
    bt_sc = p.starmap(
        nx.betweenness_centrality_subset,
        zip(
            [G] * num_chunks,
            node_chunks,
            [list(G)] * num_chunks,
            [True] * num_chunks,
            [None] * num_chunks,
        ),
    )

    # Reduce the partial solutions
    bt_c = bt_sc[0]
    for bt in bt_sc[1:]:
        for n in bt:
            bt_c[n] += bt[n]
    return bt_c


G_ba = nx.barabasi_albert_graph(1000, 3)
G_er = nx.gnp_random_graph(1000, 0.01)
G_ws = nx.connected_watts_strogatz_graph(1000, 4, 0.1)
for G in [G_ba, G_er, G_ws]:
    print("")
    print("Computing betweenness centrality for:")
    print(nx.info(G))
    print("\tParallel version")
    start = time.time()
    bt = betweenness_centrality_parallel(G)
    print(f"\t\tTime: {(time.time() - start):.4F} seconds")
    print(f"\t\tBetweenness centrality for node 0: {bt[0]:.5f}")
    print("\tNon-Parallel version")
    start = time.time()
    bt = nx.betweenness_centrality(G)
    print(f"\t\tTime: {(time.time() - start):.4F} seconds")
    print(f"\t\tBetweenness centrality for node 0: {bt[0]:.5f}")
print("")

nx.draw(G_ba, node_size=100)
plt.show()

Total running time of the script: ( 0 minutes 40.629 seconds)

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