Community Detection

Matheus Schmitz
LinkedIn

Github Portfolio

Load Libraries

# Imports
import sys
import os
import time
import random
from pyspark import SparkContext, SparkConf
from collections import defaultdict
from operator import add
from itertools import combinations

# Track the time taken
start_time = time.time()

Spark

import findspark
findspark.init()
sc = SparkContext.getOrCreate(SparkConf().setMaster("local[*]").set("spark.executor.memory", "4g").set("spark.driver.memory", "4g"))
sc.setLogLevel("ERROR")

Load Data

# Define user inputs
filter_threshold = 7
input_file_path = "data/ub_sample_data.csv"
betweenness_output_file_path = "betweenness.csv"
community_output_file_path = "communities.csv"

# Read the CSV skipping its header, and reshape it as (user_a, user_b)
inputRDD = sc.textFile(input_file_path)
inputHeader = inputRDD.first()
inputRDD = inputRDD.filter(lambda row: row != inputHeader).map(lambda row: row.split(',')).groupByKey().map(lambda x: (x[0], set(x[1]))).collect()

Create Graph

# Convert users to nodes and create edges between those whose shared business cross the threshold
nodes = set()
edges = set()
for user_a in inputRDD:
    for user_b in inputRDD:
        # Ensure we don't compare an user against itself
        if user_a[0] != user_b[0]:
            # Then check if the intersection of rated businesses is above the threshold
            if len(user_a[1].intersection(user_b[1])) >= filter_threshold:
                # If so, add both users to the set of nodes
                nodes.update([user_a[0], user_b[0]])
                # And also add an edge between the users
                edges.add(tuple((user_a[0], user_b[0])))
                edges.add(tuple((user_b[0], user_a[0])))

# For each node, get a set of all other nodes it connects to (it has edges with)
adjacency_dict = {}
for (left_node, right_node) in edges:
    if adjacency_dict.get(left_node) == None:
        adjacency_dict[left_node] = set()
    adjacency_dict[left_node].add(right_node)

Edge Betweenness Scores

def GN(root_node):
    # Track the depth level on the tree
    depth = 0

    # Use dictionaries to construct a tree connecting nodes
    tree, parent_to_child, child_to_parent, distances, node_scores, explored_nodes = {}, {}, defaultdict(set), {}, {}, set()

    # Draw the beginning of the tree
    while depth == 0:

        # Update the tree with the nodes at this level
        tree[depth] = root_node

        # Update the list of used nodes to include the ones from this iteration
        explored_nodes.add(root_node)

        # Find the nodes at the next depth
        next_depth_nodes = adjacency_dict[root_node] #adjacency_dict.value[root_node]

        # Update the dict mapping the current node to its children (the yet unexplored nodes)
        parent_to_child[root_node] = next_depth_nodes

        # Update the dict mapping the current children to its parent node
        [child_to_parent[child].add(parent) for parent, all_childs in parent_to_child.items() for child in all_childs]

        # The distance from the root to all its direct children is 1
        distances[root_node] = 1

        # Move to the next depth
        depth += 1


    # Iteratively explore the tree's depth until all nodes have been explored
    while len(next_depth_nodes) > 0:

        # Update the tree with the nodes at this level
        tree[depth] = next_depth_nodes

        # Update the list of used nodes to include the ones from the new iteration
        explored_nodes.update(next_depth_nodes)

        # For all current nodes, get their children
        iteration_nodes = set()
        for node in next_depth_nodes:

            # Find all nodes that share edges with the current node
            connected_nodes = adjacency_dict[node]

            # From those, keep the ones that have not yet been explored
            child_nodes = connected_nodes - explored_nodes

            # Update the dict mapping the current node to its children (the yet unexplored nodes)
            parent_to_child[node] = child_nodes

            # Update the dict mapping the current children to its parent node
            [child_to_parent[child].add(parent) for parent, all_childs in parent_to_child.items() for child in all_childs]

            # Get all parents of the current node
            parent_nodes = child_to_parent[node]

            # The denominator is the sum of the shortest distance of each parent to the root
            if len(parent_nodes) > 0:
                distances[node] = sum([distances[parent] for parent in parent_nodes])
            else:
                distances[node] = 1

            # Go adding all newly discovered nodes to the list of nodes to be ran in the next iterations
            iteration_nodes.update(connected_nodes)

        # Get the nodes to be evaluated on the next depth level
        next_depth_nodes = iteration_nodes - explored_nodes

        # Move to the next depth
        depth += 1


    # Give all nodes (except the root) their starting score of 1.0
    for node in nodes:
        if node == root_node:
            node_scores[node] = 0.0
        else:
            node_scores[node] = 1.0

    # Calculate edge betweenness from the bottom up		
    while depth > 1:

        # For each node in the current depth (starting from the deepest point)
        for node in tree[depth-1]:

            # Iterate over the node's parents
            for parent in child_to_parent[node]:

                # Calculate their betweennes
                child_parent_betweennees = node_scores[node] * (distances[parent] / distances[node]) 

                # Update the parent's score (which will matter when comparing it to its parents, aka the grandparents)
                node_scores[parent] += child_parent_betweennees

                # Output the betweenness of the two current nodes (child and parent)
                yield (tuple(sorted((node, parent))), child_parent_betweennees)

        # Iteratively go upper in depth until the root is reached		
        depth -= 1

# Apply the Girvan Newman algorithm and find communities
communities = sc.parallelize(nodes).map(lambda n: GN(n))

# From the communities, calculate betweennees of nodes (dividing by two to accout for the two-way road)
B_score = communities.flatMap(lambda child_parent_betweennees: [*child_parent_betweennees]).reduceByKey(add).map(lambda row: (row[0], row[1]/2)).sortBy(lambda row: (-row[1], row[0])).collect()

# View results
B_score

[(('cyuDrrG5eEK-TZI867MUPA', 'l-1cva9rA8_ugLrtSdKAqA'), 4234.0),
 (('1st2ltGKJ00ZcRsev-Ieew', 'DKolrsBSwMTpTJL22dqJRQ'), 3986.487301587302),
 (('1st2ltGKJ00ZcRsev-Ieew', 'HLY9oDcVBH9D25lU4X_V5Q'), 3857.0),
 (('1st2ltGKJ00ZcRsev-Ieew', 'Hv_q_ZnSIoZwdcoH0CyV2Q'), 3724.0),
 (('1st2ltGKJ00ZcRsev-Ieew', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 3669.5126984126982),
 (('HLY9oDcVBH9D25lU4X_V5Q', 'l-1cva9rA8_ugLrtSdKAqA'), 3335.0),
 (('Hv_q_ZnSIoZwdcoH0CyV2Q', 'l-1cva9rA8_ugLrtSdKAqA'), 3289.0),
 (('0FVcoJko1kfZCrJRfssfIA', 'DKolrsBSwMTpTJL22dqJRQ'), 2216.61747130141),
 (('a48HhwcmjFLApZhiax41IA', 'o-t-i7nbT5N_cmkCXs5oDQ'), 1969.0),
 (('A-U-K9z9oraMH7eBZW1dOA', 'l-1cva9rA8_ugLrtSdKAqA'), 1898.0),
 (('cyuDrrG5eEK-TZI867MUPA', 'o-t-i7nbT5N_cmkCXs5oDQ'), 1862.0000000000005),
 (('39FT2Ui8KUXwmUt6hnwy-g', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 1400.881419228444),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'KLB3wIYUwKDPMbijIE92vg'), 1308.1145213602306),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'e5kg9bLvlJz-MEUrGjIeVQ'), 1070.3719891219894),
 (('cyuDrrG5eEK-TZI867MUPA', 'pDNeS1nbkKS7mJmhRQJPig'), 780.0),
 (('A-U-K9z9oraMH7eBZW1dOA', 'pDNeS1nbkKS7mJmhRQJPig'), 764.75),
 (('DKolrsBSwMTpTJL22dqJRQ', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 743.2490653250375),
 (('MtdSCXtmrSxj_uZOJ5ZycQ', 'ay4M5J28kBUf0odOQct0BA'), 644.5901335727829),
 (('0FVcoJko1kfZCrJRfssfIA', '39FT2Ui8KUXwmUt6hnwy-g'), 638.0675969927122),
 (('QvLg2kxqHHahxxOlHlEIZw', 'cyuDrrG5eEK-TZI867MUPA'), 624.5),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'fLnkI1uHtXEsjtF6KoBHbQ'), 612.6982794982796),
 (('A-U-K9z9oraMH7eBZW1dOA', 'QvLg2kxqHHahxxOlHlEIZw'), 612.25),
 (('DKolrsBSwMTpTJL22dqJRQ', 'bSUS0YcvS7UelmHvCzNWBA'), 608.622466306405),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'tekHDsd0fskYG3tqu4sHQw'), 582.0982794982797),
 (('39FT2Ui8KUXwmUt6hnwy-g', 'Uo5dPwoDpYBzOnmUnjxJ6A'), 561.0),
 (('DKolrsBSwMTpTJL22dqJRQ', '_VTEyUzzH92X3w-IpGaXVA'), 554.4504476817548),
 (('0FVcoJko1kfZCrJRfssfIA', 'KLB3wIYUwKDPMbijIE92vg'), 529.747269281208),
 (('KLB3wIYUwKDPMbijIE92vg', 'hilL60vuuh06sMxs6Ckkog'), 500.21428571428567),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'MtdSCXtmrSxj_uZOJ5ZycQ'), 467.1333333333333),
 (('0FVcoJko1kfZCrJRfssfIA', 'ay4M5J28kBUf0odOQct0BA'), 407.3201585415396),
 (('0FVcoJko1kfZCrJRfssfIA', 'LcCRMIDz1JgshpPGYfLDcA'), 390.6882006882007),
 (('39FT2Ui8KUXwmUt6hnwy-g', 'DKolrsBSwMTpTJL22dqJRQ'), 387.88373015873026),
 (('5DgFmyjW6hkBtXtTMKl4tA', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 379.1039924876678),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'OoyQYSeYNyRVOmdO3tsxYA'), 377.4968363807751),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'hLVq7VSJBHZwqurwWoCmpg'), 376.0),
 (('0QREkWHGO8-Z_70qx1BIWw', 'LcCRMIDz1JgshpPGYfLDcA'), 372.0),
 (('7G8w2SnaC-qDVQ7_GqTxMg', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 363.16666666666663),
 (('IuaAfrkirlfzY3f4PkgSmw', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 344.4666666666667),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'm1IVpXClMox1VGw5hO2LhQ'), 340.00000000000006),
 (('0FVcoJko1kfZCrJRfssfIA', 'OoyQYSeYNyRVOmdO3tsxYA'), 330.57183638077504),
 (('DKolrsBSwMTpTJL22dqJRQ', 'bE7Yd0jI_P6g27MWEKKalA'), 326.59187098092275),
 (('0FVcoJko1kfZCrJRfssfIA', 'Ams0iLRd0AhZZectGKA8fw'), 280.0),
 (('0FVcoJko1kfZCrJRfssfIA', 'EiwxlbR8fb68lMgEXhcWKA'), 278.0),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'Zk95TMXDx0zMUhYq5u8pxw'), 265.0881860718614),
 (('4pc_EyanaC3ARh0MZZyouA', 'DKolrsBSwMTpTJL22dqJRQ'), 247.53829313960895),
 (('LcCRMIDz1JgshpPGYfLDcA', '_VTEyUzzH92X3w-IpGaXVA'), 245.80791430791433),
 (('MtdSCXtmrSxj_uZOJ5ZycQ', 'kwIhn1_cnQeUaLN0CuWWHw'), 243.0),
 (('KLB3wIYUwKDPMbijIE92vg', 'kwIhn1_cnQeUaLN0CuWWHw'), 238.07142857142858),
 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'dzJDCQ5vubQBJTfYTEmcbg'), 215.63333333333335),
 (('MtdSCXtmrSxj_uZOJ5ZycQ', 'e5kg9bLvlJz-MEUrGjIeVQ'), 203.17801087801087),
 (('0FMte0z-repSVWSJ_BaQTg', '0FVcoJko1kfZCrJRfssfIA'), 189.0),
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 (('0KhRPd66BZGHCtsb9mGh_g', 'dzJDCQ5vubQBJTfYTEmcbg'), 189.0),
 (('0QREkWHGO8-Z_70qx1BIWw', 'kKTcYPz47sCDH1_ylnE4ZQ'), 189.0),
 (('23o7tyUGlC6FCDVcyqLeFA', 'ay4M5J28kBUf0odOQct0BA'), 189.0),
 (('2k8OVAPxlXHsA5X6EIoQpQ', 'JM0GL6Dx4EuZ1mprLk5Gyg'), 189.0),
 (('2xVrxhQJUBmOyG4ML77XKw', 'MtdSCXtmrSxj_uZOJ5ZycQ'), 189.0),
 (('37HswRimgBEf7_US-c3CDA', 'e5kg9bLvlJz-MEUrGjIeVQ'), 189.0),
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 (('7RCz4Ln_FaTvNrdwe251Dg', '9xM8upr_n9jchUDKxqSGHw'), 189.0),
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 (('JM0GL6Dx4EuZ1mprLk5Gyg', 'ajxohdcsKhRGFlEvHZDyTw'), 179.16666666666669),
 (('39FT2Ui8KUXwmUt6hnwy-g', 'dzJDCQ5vubQBJTfYTEmcbg'), 177.28072254542843),
 (('DKolrsBSwMTpTJL22dqJRQ', 'dTeSvET2SR5LDF_J07wJAQ'), 170.35557219199234),
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 (('ZXyGw3Z1DyhK1sfNtpcyYA', 'tcWnoX_IfuDmlDl6o6y3_g'), 1.0),
 (('_m1ot2zZetDgjerAD2Sidg', 'vENR70IrUsDNTDebbuxyQA'), 1.0),
 (('ae7zi8F0B6l_JCITh1mXDg', 'h-ajC_UHD0QAyAzySN6g2A'), 1.0),
 (('ae7zi8F0B6l_JCITh1mXDg', 'k58KNO8Rya-q8njKq8-uBQ'), 1.0),
 (('ae7zi8F0B6l_JCITh1mXDg', 'tcWnoX_IfuDmlDl6o6y3_g'), 1.0),
 (('angEr2YcXmCl20s8WQu32w', 'frQs7y5qa-X1pvAM0sJe1w'), 1.0),
 (('gUu0uaiU7UEUVIgCdnqPVQ', 'jJDUCuPwVqwjbth3s92whA'), 1.0),
 (('h-ajC_UHD0QAyAzySN6g2A', 'k58KNO8Rya-q8njKq8-uBQ'), 1.0),
 (('h-ajC_UHD0QAyAzySN6g2A', 'tcWnoX_IfuDmlDl6o6y3_g'), 1.0),
 (('k58KNO8Rya-q8njKq8-uBQ', 'tcWnoX_IfuDmlDl6o6y3_g'), 1.0)]

# Save the pairs and thei betweenness to a txt
with open(betweenness_output_file_path, 'w') as f_out:
    for node_pair, betweenness in B_score:
        f_out.write(str(node_pair) + ',' + str(round(betweenness, 5)) + '\n')

Detect Communities

# Calculate the degree matrix
DM = {left_node: len(right_node) for left_node, right_node in adjacency_dict.items()}

# Calculate the adjacency matrix
AM = {(left_node, right_node): 1 if (left_node, right_node) in edges else 0 for left_node in nodes for right_node in nodes}

# Calculate m (number of edges in the original graph)
m = len(edges) / 2

# Track the number of edges remaning
remaning_edges = m 

Use Modularity to Define the Best Community Split

def compute_communities(adjacency_dict, nodes):
    # Objects to store data over iterations
    communities = []
    remaning_nodes = nodes.copy()

    # Generate nodes until there are no more "remaining_nodes"
    while len(remaning_nodes) > 0:

        # Pick one node at random as seed and generate communities
        curr_community = compute_community(random.sample(remaning_nodes, 1)[0], adjacency_dict)

        # Then update the objects storing the status of the nodes and communities
        communities.append(curr_community)
        remaning_nodes.difference_update(curr_community)

    return communities

def compute_community(root_node, adjacency_dict):
    community = set()
    #community = {root_node}

    # Find all nodes that share edges with the current node
    connected_nodes = adjacency_dict[root_node]

    # Recursively explore all connected nodes
    while len(connected_nodes) > 0:

        # Update the list of used nodes to include the ones from the new iteration
        community.update(connected_nodes)

        # For all current nodes, get their children
        iteration_nodes = set()
        for node in connected_nodes:

            # Get the next set of nodes to explore
            connected_nodes_next = adjacency_dict[node]
            iteration_nodes.update(connected_nodes_next)

        # Find the next set of yet unseen connected nodes
        connected_nodes = iteration_nodes - community

    # Handle unconnected nodes
    if len(community) == 0:
        community = {root_node}

    return community

# Track the modularity
Q = float('-inf')

# Iteratively remove edges and track the changes in modularity
while remaning_edges > 0:

    # Apply the Girvan Newman algorithm and find communities in the ever-shrinking adjacency dict
    new_graph = sc.parallelize(nodes).map(lambda n: GN(n))

    # Recompute betweenness to be used in this iteration
    B_score = new_graph.flatMap(lambda child_parent_betweennees: [*child_parent_betweennees]).reduceByKey(add).map(lambda row: (row[0], row[1]/2)).sortBy(lambda row: (-row[1], row[0])).collect()

    # Take highest "yet unremoved" betweenness
    curr_betweenness = B_score[0][1]

    # Then remove all pairs whose betweenness matches "curr_betweenness"
    for (left_node, right_node), betweenness in B_score:
        if betweenness >= curr_betweenness:
            adjacency_dict[left_node].remove(right_node)
            adjacency_dict[right_node].remove(left_node)
            remaning_edges -= 1

    # Recompute communities taking into consideration the removed links
    iter_communities = compute_communities(adjacency_dict, nodes)

    # Recompute the modularity score Q
    iter_Q = sum([AM[(left_node, right_node)] - DM[left_node] * DM[right_node] / (2 * m) for comm in iter_communities for left_node in comm for right_node in comm]) / (2  * m)

    # If the modularity score improved, store the current Q and communities as the best thus far
    if iter_Q > Q:
        communities = iter_communities
        Q = iter_Q
        
    print(f'Remaining Edges: {int(remaning_edges)}')
    print(f'Best Modularity: {Q}')
    print()

# Once all edged have been explores, take the sort the best communities found (necessary for proper outputting)
output_communities = sc.parallelize(communities).map(lambda community: sorted(community)).sortBy(lambda community: (len(community), community)).collect()

# Save the communities to a txt
with open(community_output_file_path, "w") as f_out:
    for community in output_communities:
        f_out.write(str(community).replace("[", "").replace("]", "") + "\n")

# View results
output_communities

[['23y0Nv9FFWn_3UWudpnFMA', 'eqWEgMH-DCP74i82BEAZzw'],
 ['3Vd_ATdvvuVVgn_YCpz8fw', 'jSbXY_rno4hYHQCFftsWXg'],
 ['453V8MlGr8y61PpsDAFjKQ', 'gH0dJQhyKUOVCKQA6sqAnw'],
 ['46HhzhpBfTdTSB5ceTx_Og', 'YVQFzWm0H72mLUh-8gzd5w'],
 ['F47atsRPw-KHmRVk5exBFw', 'JeOHA8tW7gr-FDYOcPJoeA'],
 ['Si3aMsOVGSVlsc54iuiPwA', 'd5WLqmTMvmL7-RmUDVKqqQ'],
 ['_m1ot2zZetDgjerAD2Sidg', 'vENR70IrUsDNTDebbuxyQA'],
 ['gUu0uaiU7UEUVIgCdnqPVQ', 'jJDUCuPwVqwjbth3s92whA'],
 ['98rLDXbloLXekGjieuQSlA',
  'MJ0Wphhko2-LbJ0uZ5XyQA',
  'QYKexxaOJQlseGWmc6soRg'],
 ['9W73B44Iw8WslrTNB2CdCg',
  'UmTMCfPlhA6kJLAsLycSfg',
  'Uo5dPwoDpYBzOnmUnjxJ6A'],
 ['CLbpPUqP6XpeAfoqScGaJQ',
  'drTMOo4p8nL0pnMNEyat2A',
  'tX0r-C9BaHYEolRUfufTsQ',
  'xhlcoVm3FOKcxZ0phkdO6Q'],
 ['Gr-MqCunME2K_KmsAwjpTA',
  'QRsuZ_LqrRU65dTs5CL4Lw',
  '_6Zg4ukwS0kst9UtkfVw3w',
  'lJFBgSAccsMGwIjfD7LMeQ'],
 ['Cf0chERnfd06ltnN45xLNQ',
  'CyrRjt_7iJ8_lSHeH1_TlA',
  'JhFK9D3LYl23Se3x4oPUxA',
  'ZW-XoteNlRuuK-19q1spmw',
  'lL-wNa0TKK6LXrlcVmjYrQ'],
 ['EY8h9IJimXDNbPXVFpYF3A',
  'LiNx18WUre9WFCEQlUhtKA',
  'hilL60vuuh06sMxs6Ckkog',
  'jgoG_hHqnhZvQEoBK0-82w',
  'kwIhn1_cnQeUaLN0CuWWHw',
  'qd16czwFUVHICKF7A4qWsQ'],
 ['2GUjO7NU88cPXpoffYCU8w',
  '6YmRpoIuiq8I19Q8dHKTHw',
  '6xi9tBoZ6r_v41u_XFsSnA',
  'BDmxm7aeWFOLT35gSvkmig',
  'H4EQn0rjFuGRgIm6c9NFLg',
  'H5Asta4LpiKmRhSjWaogIg',
  'XrRLaAeV20MRwdSIGjj2SQ',
  'a48HhwcmjFLApZhiax41IA',
  'angEr2YcXmCl20s8WQu32w',
  'e5sdXDOkCf0sIUAivXVluA',
  'frQs7y5qa-X1pvAM0sJe1w'],
 ['1st2ltGKJ00ZcRsev-Ieew',
  '4ZQq0ozRs-gXSz1z55iIDw',
  'HLY9oDcVBH9D25lU4X_V5Q',
  'Hv_q_ZnSIoZwdcoH0CyV2Q',
  'Ih85YhFRDzOnB09yS__94g',
  'KBoIRjxSW7OWczv8OS9Bew',
  'LaiylSIbrA3aPvOYtl-J4A',
  'Z9a1tDT8fVI75qXYwNhPpw',
  'ZEq0WtRJD9Bl_vYgCsbfOg',
  'e0Jn0ZjqL-dWi7Brs0bbmg',
  'fOut10lknIp64tm3z6UTNg',
  'l-1cva9rA8_ugLrtSdKAqA',
  'oegRUjhGbP62M18WyAL6pQ',
  'wXdrUQg4-VkSZH1FG4Byzw'],
 ['0gZ8E5tBWTEtGEZDuTzhzw',
  '4ONcRRisDZkbV1cviA7nFw',
  '9SWtEX1k9AjRg93BAzMCpg',
  'A-U-K9z9oraMH7eBZW1dOA',
  'B7IvZ26ZUdL2jGbYsFVGxQ',
  'BE4fE4R3TaVn8xy4sYYjbg',
  'DgfsJqg_gozVgaeZ5vjllA',
  'EI9ijI9Wh66LrVW-GmWkOg',
  'FyQrUamokaPLDrBxGmzPnA',
  'Gua5GdTlTWJpovtG7Hdtyg',
  'LKP0Yq9T7Ss6oiDZnVtQwQ',
  'LgFDWZTLi1w9OGi5BtKORg',
  'Nf_Jw_W_CwOz5WJ7ApSMxg',
  'ORJnGXXkS9tQBTNyPQJF9A',
  'QUYbGl1DL-9faG150MQ7zA',
  'QvLg2kxqHHahxxOlHlEIZw',
  'S1cjSFKcS5NVc3o1MkfpwA',
  'SVC0CajvmYfH5uAq4JnGvg',
  'SX_SMrddkDU5dySbsZMu9A',
  'WXlxViTwXHPBvhioljN9PQ',
  'YA-caxALI4C-eCiSM97new',
  'ZXyGw3Z1DyhK1sfNtpcyYA',
  'ZZvfGGLnAkSBSUduV7KN-w',
  'ae7zi8F0B6l_JCITh1mXDg',
  'cyuDrrG5eEK-TZI867MUPA',
  'h-ajC_UHD0QAyAzySN6g2A',
  'jnn504CkjtfbYIwBquWmBw',
  'k24kSTpZHUdEd-QYXLy3fQ',
  'k58KNO8Rya-q8njKq8-uBQ',
  'mm9WYrFhiNqvHCyhQKw3Mg',
  'o-t-i7nbT5N_cmkCXs5oDQ',
  'pDNeS1nbkKS7mJmhRQJPig',
  'tcWnoX_IfuDmlDl6o6y3_g'],
 ['0KhRPd66BZGHCtsb9mGh_g',
  '2k8OVAPxlXHsA5X6EIoQpQ',
  '2xVrxhQJUBmOyG4ML77XKw',
  '37HswRimgBEf7_US-c3CDA',
  '5DgFmyjW6hkBtXtTMKl4tA',
  '5fQ9P6kbQM_E0dx8DL6JWA',
  '750rhwO7D_Cul7_GtO9Jsg',
  '7G8w2SnaC-qDVQ7_GqTxMg',
  '8oYMqhC5fhqAK_yxRjE7dQ',
  '903YwVSoAKyzudc8LH_HMA',
  '9S52XHEyrvOv4OZxU6pCLw',
  'DPtOaWemjBPvFiZJBi0m8A',
  'DjcRgZ0cJbf6-W2TxvFlBA',
  'IuaAfrkirlfzY3f4PkgSmw',
  'JM0GL6Dx4EuZ1mprLk5Gyg',
  'JRqMFKGxx6DnTGZrxwQZaA',
  'JqjAthJThuVYgTh4iWDZ2A',
  'MrsRJa4SWLq8XLU1RtPdlw',
  'MtdSCXtmrSxj_uZOJ5ZycQ',
  'MwpK7PqQX7fgTFM2Pfy61w',
  'NUtVG7jNPLJR2cxMXMH2-A',
  'NlNlyQynkyEU3l7TR3LXdg',
  'PKEzKWv_FktMm2mGPjwd0Q',
  'SsOiVav4V5_NjTl21Lj92w',
  'TZ974xcbw2kqjYxAhDUYVg',
  'UYcmGbelzRa0Q6JqzLoguw',
  'UwV6jBuTR1S9acT6bPTBPw',
  'VdoTNYWuoXo01umgannw8A',
  'WaAOt_eG0_-yLpG3fI--3g',
  'XEqQG61fetXhuEV9RPslIA',
  'Y0-lLNc2Y7gUGXPzSsMueQ',
  'ZA1OT-PIZwz2kdHDA6mShw',
  'Zk95TMXDx0zMUhYq5u8pxw',
  'ajxohdcsKhRGFlEvHZDyTw',
  'cIbbfJEGLB3B-c8Po4AL5g',
  'dzJDCQ5vubQBJTfYTEmcbg',
  'e5kg9bLvlJz-MEUrGjIeVQ',
  'fLnkI1uHtXEsjtF6KoBHbQ',
  'fcWM-oqjgS94yi1INhZa0g',
  'hLVq7VSJBHZwqurwWoCmpg',
  'jcriwcTidug0fK8sgAloHA',
  'm1IVpXClMox1VGw5hO2LhQ',
  'mu4XvWvJOb3XpG1C_CHCWA',
  'nOTl4aPC4tKHK35T3bNauQ',
  'tekHDsd0fskYG3tqu4sHQw',
  'xrvyW1ruKS0uz9RtFewC0Q'],
 ['0FMte0z-repSVWSJ_BaQTg',
  '0FVcoJko1kfZCrJRfssfIA',
  '0QREkWHGO8-Z_70qx1BIWw',
  '1KQi8Ymatd4ySAd4fhSfaw',
  '23o7tyUGlC6FCDVcyqLeFA',
  '2XYdguaaZ7dgi6fAlddujg',
  '2quguRdKBzul3GpRi9e1mA',
  '39FT2Ui8KUXwmUt6hnwy-g',
  '4PQhC-zTQ4ACEN0-r39JuQ',
  '4pc_EyanaC3ARh0MZZyouA',
  '79yaBDbLASfIdB-C2c8DzA',
  '7RCz4Ln_FaTvNrdwe251Dg',
  '7Vfy39A_totC-w70qZi0MA',
  '97j2wkFU46OOgm6ErRAb7w',
  '9xM8upr_n9jchUDKxqSGHw',
  'Ams0iLRd0AhZZectGKA8fw',
  'B0ENvYKQdNNr1Izd2r-BAA',
  'BDjiEmXljD2ZHT61Iv9rrQ',
  'CebjpVd3PsofCgotWp60pg',
  'ChshgCKJTdIDg17JKtFuJw',
  'DKolrsBSwMTpTJL22dqJRQ',
  'DkLSyxogCcJXY5DbTZ-f2A',
  'ELfzWgdf64VBLi5z1ECItw',
  'EiwxlbR8fb68lMgEXhcWKA',
  'IXD-jdycm7m34b_Nliy82g',
  'JLv2Dmfj73-I0d9N41tz1A',
  'JteQGisqOf_pklq7GA0Rww',
  'KHjroLTG6Ah8LyItTyB2yw',
  'KLB3wIYUwKDPMbijIE92vg',
  'KgJdBWS3ReP6TVhYWJRKmg',
  'KtE55izPs1ubJn3ofF2IrA',
  'LcCRMIDz1JgshpPGYfLDcA',
  'O9pMFJSPg80YVzpMfNikxw',
  'OoyQYSeYNyRVOmdO3tsxYA',
  'PE8s8ACYABRNANI-T_WmzA',
  'R4l3ONHzGBakKKNo4TN9iQ',
  'S9dDf0JqSMAvusp5f-9bGw',
  'SdXxLZQQnQNUEL1rGMOQ6w',
  'T88y73qdOSutuvzLlhWtqQ',
  'TjsBbWAfwxWEXPxaLNv5SQ',
  'Tk_FWXueutKii3f9yJFsdw',
  'UAB1Zyg6Q0oEpXeYRf5K_g',
  'WoKCLSctS7G2547xKcED-Q',
  'XPAJ2KHkCwBA0vafF-2Zcg',
  'XUEwSGOGARxW-3gPiGJKUg',
  '_Pn-EmWO-pFPFg81ZIEiDw',
  '_VTEyUzzH92X3w-IpGaXVA',
  'ay4M5J28kBUf0odOQct0BA',
  'bE7Yd0jI_P6g27MWEKKalA',
  'bHufZ2OTlC-OUxBDRXxViw',
  'bJguBxPlnTW29tRTAF0nkQ',
  'bSUS0YcvS7UelmHvCzNWBA',
  'bbK1mL-AyYCHZncDQ_4RgA',
  'cm3_8c_NDhPcpwJQ96Aixw',
  'dTeSvET2SR5LDF_J07wJAQ',
  'dW6bAWM1HbPdk_cGS_a2HA',
  'e8uzNcSC5tQMD22GNAQEQA',
  'hd343st7cOIUSfAd5r0U7A',
  'hqmnMdDS-Opjp3BfBJA8qA',
  'j8Dts8irvVBwEhEEae_-wA',
  'jPcrABeWgWlTPi-E0Op_aA',
  'kKTcYPz47sCDH1_ylnE4ZQ',
  'ma6206bmu-a_Ja7Iv-yRCw',
  'mnoe2vwouRADn97dTDkw4A',
  'p9942XebvxZ9ubHm4SXmMQ',
  'qtOCfMTrozmUSHWIcohc6Q',
  'sBqCpEUn0qYdpSF4DbWlAQ',
  'sO6iNKgv_ToVfof-aQWgXg',
  'sdLns7062kz3Ur_b8wgeYw',
  'tAcY4S3vIuNlAoRlCcz5VA',
  'tL2pS5UOmN6aAOi3Z-qFGg',
  'tRZAC_H5RHrjvyvtufcNXQ',
  'voXU5A3FfOcXZ2VNsJ0q4w',
  'waN6iwcphiVEoCews4f4CA',
  'y6jsaAXFstAJkf53R4_y4Q',
  'yCaDISH0R8e5U376zDWTpQ',
  'zBi_JWB5uUdVuz3JLoAxGQ']]

# Close spark context
sc.stop()

# Measure the total time taken and report it
time_elapsed = time.time() - start_time
print(f'Duration: {time_elapsed:.0f} seconds')

Duration: 3206 seconds

End

Matheus Schmitz
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