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.

Note: The example output below shows that the non-parallel implementation is faster. This is a limitation of our CI/CD pipeline running on a single core.

Depending on your setup, you will likely observe a speedup.

Computing betweenness centrality for:
Graph with 1000 nodes and 2991 edges
        Parallel version
                Time: 2.0715 seconds
                Betweenness centrality for node 0: 0.13556
        Non-Parallel version
                Time: 3.3854 seconds
                Betweenness centrality for node 0: 0.13556

Computing betweenness centrality for:
Graph with 1000 nodes and 5005 edges
        Parallel version
                Time: 2.6297 seconds
                Betweenness centrality for node 0: 0.00372
        Non-Parallel version
                Time: 4.4859 seconds
                Betweenness centrality for node 0: 0.00372

Computing betweenness centrality for:
Graph with 1000 nodes and 2000 edges
        Parallel version
                Time: 1.8590 seconds
                Betweenness centrality for node 0: 0.00462
        Non-Parallel version
                Time: 3.0242 seconds
                Betweenness centrality for node 0: 0.00462

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(), 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(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()