Parallel Betweenness

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.

This doesn’t work in python2.7.13. It does work in 3.6, 3.5, 3.4, and 3.3.

It may be related to this: https://stackoverflow.com/questions/1816958/cant-pickle-type-instancemethod-when-using-multiprocessing-pool-map

Out:

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 2991
Average degree:   5.9820
        Parallel version
                Time: 1.1383
                Betweenness centrality for node 0: 0.06604
        Non-Parallel version
                Time: 3.8886 seconds
                Betweenness centrality for node 0: 0.06604

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 4993
Average degree:   9.9860
        Parallel version
                Time: 1.4202
                Betweenness centrality for node 0: 0.00340
        Non-Parallel version
                Time: 4.7634 seconds
                Betweenness centrality for node 0: 0.00340

Computing betweenness centrality for:
Name:
Type: Graph
Number of nodes: 1000
Number of edges: 2000
Average degree:   4.0000
        Parallel version
                Time: 1.0098
                Betweenness centrality for node 0: 0.02397
        Non-Parallel version
                Time: 3.2523 seconds
                Betweenness centrality for node 0: 0.02397

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 _betmap(G_normalized_weight_sources_tuple):
    """Pool for multiprocess only accepts functions with one argument.
    This function uses a tuple as its only argument. We use a named tuple for
    python 3 compatibility, and then unpack it when we send it to
    `betweenness_centrality_source`
    """
    return nx.betweenness_centrality_source(*G_normalized_weight_sources_tuple)


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.map(_betmap,
                  zip([G] * num_chunks,
                      [True] * num_chunks,
                      [None] * num_chunks,
                      node_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


if __name__ == "__main__":
    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("\t\tTime: %.4F" % (time.time() - start))
        print("\t\tBetweenness centrality for node 0: %.5f" % (bt[0]))
        print("\tNon-Parallel version")
        start = time.time()
        bt = nx.betweenness_centrality(G)
        print("\t\tTime: %.4F seconds" % (time.time() - start))
        print("\t\tBetweenness centrality for node 0: %.5f" % (bt[0]))
    print("")

    nx.draw(G_ba)
    plt.show()