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parallel function working

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Luca Lombardo 2 years ago
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omega_parallel_server.py
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#! /usr/bin/python3
from queue import Empty
import multiprocessing
import networkx as nx
import numpy as np
import argparse
import random
import time
from utils import *
def parallel_omega(G: nx.Graph, k: float, nrand: int = 6, niter: int = 6, n_processes: int = None, seed: int = 42) -> float:
"""
Computes the omega index for a given graph using parallelization.
Parameters
----------
function to compute the omega index of a graph in parallel. This is a much faster approach then the standard omega function. It parallelizes the computation of the random graphs and lattice networks.
Parameters
----------
`G`: nx.Graph
The graph to compute the omega index
`k`: float
The percentage of nodes to sample from the graph.
`niter`: int
Approximate number of rewiring per edge to compute the equivalent random graph. Default is 6.
`nrand`: int
Number of random graphs generated to compute the maximal clustering coefficient (Cr) and average shortest path length (Lr). Default is 6
`n_processes`: int
Number of processes to use. Default is the number of cores of the machine.
`seed`: int
The seed to use to generate the random graphs. Default is 42.
Returns
-------
`omega`: float
"""
if n_processes is None:
n_processes = multiprocessing.cpu_count()
if n_processes > nrand:
n_processes = nrand
random.seed(seed)
if not nx.is_connected(G):
G = G.subgraph(max(nx.connected_components(G), key=len))
if len(G) == 1:
return 0
if k > 0:
G = random_sample(G, k)
def worker(queue_seeds, queue_results): # worker function to be used in parallel
while True:
try:
seed = queue_seeds.get(False)
except Empty:
break
random_graph = nx.random_reference(G, niter, seed=seed)
lattice_graph = nx.lattice_reference(G, niter, seed=seed)
random_shortest_path = nx.average_shortest_path_length(random_graph)
lattice_clustering = nx.average_clustering(lattice_graph)
queue_results.put((random_shortest_path, lattice_clustering))
manager = multiprocessing.Manager() # manager to share the queue
queue_seeds = manager.Queue() # queue to give the seeds to the processes
queue_results = manager.Queue() # queue to share the results
processes = [multiprocessing.Process(target=worker, args=(queue_seeds, queue_results))
for _ in range(n_processes)] # processes to be used
for i in range(nrand): # put the tasks in the queue
queue_seeds.put(i + seed)
for process in processes: # start the processes
process.start()
for process in processes: # wait for the processes to finish
process.join()
# collect the results
shortest_paths = []
clustering_coeffs = []
while not queue_results.empty():
random_shortest_path, lattice_clustering = queue_results.get() # get the results from the queue
shortest_paths.append(random_shortest_path)
clustering_coeffs.append(lattice_clustering)
L = nx.average_shortest_path_length(G)
C = nx.average_clustering(G)
omega = (np.mean(shortest_paths) / L) - (C / np.mean(clustering_coeffs))
return omega
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument("graph", help="Name of the graph to be used.", choices=['checkins-foursquare', 'checkins-gowalla', 'checkins-brightkite', 'friends-foursquare', 'friends-gowalla', 'friends-brightkite'])
parser.add_argument("--k", help="Percentage of nodes to be sampled. Needs to be a float between 0 and 1. Default is 0.", default=0, type=float)
parser.add_argument("--nrand", help="Number of random graphs. Needs to be an integer. Default is 12", default=12, type=int)
parser.add_argument("--niter", help="Approximate number of rewiring per edge to compute the equivalent random graph. Default is 12", default=12, type=int)
parser.add_argument("--processes", help="Number of processes to be used. Needs to be an integer. Default is the number of cores.", default=multiprocessing.cpu_count(), type=int)
parser.add_argument("--seed", help="Seed for the random number generator. Needs to be an integer. Default is 42", default=42, type=int)
parser.add_help = True
args = parser.parse_args()
if args.processes > multiprocessing.cpu_count():
print("Number of processes is higher than available. Setting it to default value: all available")
args.processes = multiprocessing.cpu_count()
elif args.processes < 1:
raise ValueError("Number of processes needs to be at least 1")
name = args.graph.split('-')[1]
if 'checkins' in args.graph:
G = create_graph_from_checkins(name)
elif 'friends' in args.graph:
G = create_friendships_graph(name)
G.name = str(args.graph) + " Checkins Graph"
print("\nComputing omega for graph {} with {} nodes and {} edges".format(args.graph, len(G), G.number_of_edges()))
print("Number of processes used: ", args.processes)
start = time.time()
omega = parallel_omega(G, k = args.k, nrand=args.nrand, niter=args.niter, n_processes=args.processes, seed=42)
end = time.time()
print("\nOmega: ", omega)
print("Number of random graphs: ", args.nrand)
print("Time: ", round(end - start, 2), " seconds")

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omega_sampled_server.py
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#! /usr/bin/python3
import networkx as nx
from utils import *
import warnings
import time
import random
import argparse
warnings.filterwarnings("ignore")
def random_sample(graph, k):
nodes = list(graph.nodes())
n = int(k*len(nodes))
nodes_sample = random.sample(nodes, n)
G = graph.subgraph(nodes_sample)
if not nx.is_connected(G):
print("Graph is not connected. Taking the largest connected component")
connected = max(nx.connected_components(G), key=len)
G_connected = graph.subgraph(connected)
print(nx.is_connected(G_connected))
print("Number of nodes in the sampled graph: ", G.number_of_nodes())
print("Number of edges in the sampled graph: ", G.number_of_edges())
return G_connected
if __name__ == "__main__":
parser = argparse.ArgumentParser()
parser.add_argument("graph", help="Name of the graph to be used. Options are 'checkins-foursquare', 'checkins-gowalla', 'checkins-brightkite', 'friends-foursquare', 'friends-gowalla', 'friends-brightkite'")
parser.add_argument("k", help="Percentage of nodes to be sampled. Needs to be a float between 0 and 1")
parser.add_argument("--niter", help="Number of rewiring per edge. Needs to be an integer. Default is 5", default=5)
parser.add_argument("--nrand", help="Number of random graphs. Needs to be an integer. Default is 5", default=5)
parser.add_help = True
args = parser.parse_args()
# the name of the graph is the first part of the input string
name = args.graph.split('-')[1]
if 'checkins' in args.graph:
G = create_graph_from_checkins(name)
elif 'friends' in args.graph:
G = create_friendships_graph(name)
G.name = str(args.graph) + " Checkins Graph"
# sample the graph
G_sample = random_sample(G, float(args.k))
# compute omega
start = time.time()
print("\nComputing omega for graph: ", G.name)
omega = nx.omega(G_sample, niter = int(args.niter), nrand = int(args.nrand))
end = time.time()
print("Omega coefficient for graph {}: {}".format(G.name, omega))
print("Time taken: ", round(end-start,2))

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utils.py
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"""
This file is note meant to be run, it's just a collection of functions that are used in the other files. It's just a way to keep the code clean and organized.
"""
import os
import gzip
import wget
import gdown
import shutil
import random
import itertools
import numpy as np
import pandas as pd
import tqdm as tqdm
import networkx as nx
import multiprocessing
import plotly.graph_objects as go
from itertools import combinations
from pyvis.network import Network
from multiprocessing import Pool
from collections import Counter
from subprocess import run
from typing import Literal
from queue import Empty
SCRIPT_DIR = os.path.dirname(os.path.abspath(__file__))
DATA_DIR = os.path.join(SCRIPT_DIR, "data")
# ------------------------------------------------------------------------#
def download_datasets():
"""
Download the datasets from the web and unzip them. The datasets are downloaded from the SNAP website and from a Google Drive folder.
Parameters
----------
None
Returns
-------
None
Notes
-----
The datasets are downloaded in the "data" folder. If the folder doesn't exist, it will be created. If the dataset is already downloaded, it will be skipped. The files are renamed to make them more readable.
"""
dict = {
"brightkite": ["https://snap.stanford.edu/data/loc-brightkite_edges.txt.gz", "https://snap.stanford.edu/data/loc-brightkite_totalCheckins.txt.gz"],
"gowalla": ["https://snap.stanford.edu/data/loc-gowalla_edges.txt.gz", "https://snap.stanford.edu/data/loc-gowalla_totalCheckins.txt.gz"],
"foursquare": ["https://drive.google.com/file/d/1PNk3zY8NjLcDiAbzjABzY5FiPAFHq6T8/view?usp=sharing"]
}
if not os.path.exists(DATA_DIR):
os.mkdir(DATA_DIR)
print("Created data folder")
for folder in dict.keys():
if not os.path.exists(os.path.join(DATA_DIR, folder)):
os.mkdir(os.path.join(DATA_DIR, folder))
print("Created {} folder".format(folder))
## DOWNLOADING ##
for folder in dict.keys():
for url in dict[folder]:
if folder == "foursquare":
if not os.path.exists(os.path.join(DATA_DIR, folder, "foursquare_full.zip")):
output = os.path.join(DATA_DIR, folder, "foursquare_full.zip")
gdown.download(url, output, quiet=False, fuzzy=True)
else :
print("{} already downloaded".format(url))
else:
if not os.path.exists(os.path.join(DATA_DIR, folder, url.split("/")[-1])):
print("Downloading {}...".format(url))
wget.download(url, os.path.join(DATA_DIR, folder))
else :
print("{} already downloaded".format(url))
## UNZIPPING ##
for folder in dict.keys():
for file in os.listdir(os.path.join(DATA_DIR, folder)):
if file.endswith(".gz"):
print("Unzipping {}...".format(file))
# os.system("gunzip {}".format(os.path.join(DATA_DIR, folder, file)))
gzip_file_path = os.path.join(DATA_DIR, folder, file)
with gzip.open(gzip_file_path, 'rb') as f_in:
with open(gzip_file_path[:-len(".gz")], 'wb') as f_out:
shutil.copyfileobj(f_in, f_out)
elif file.endswith(".zip"):
print("Unzipping {}...".format(file))
zip_file_path = os.path.join(DATA_DIR, folder, file)
zip_output_dir = os.path.join(DATA_DIR, folder)
if os.name == 'nt':
# Not tested! Require Windows 10+ and Powershell
os.system(f'powershell -command "Expand-Archive -Force \'{zip_file_path}\' \'{zip_output_dir}\'"')
else:
run(["unzip", "-o", zip_file_path, "-d", zip_output_dir])
os.remove(zip_file_path)
## FOURSQUARE CLEANING ##
for file in os.listdir(os.path.join(DATA_DIR, "foursquare", "dataset_WWW2019")):
if file.endswith(".txt"):
os.rename(os.path.join(DATA_DIR, "foursquare", "dataset_WWW2019", file), os.path.join(DATA_DIR, "foursquare", file))
for file in ["dataset_WWW_friendship_old.txt", "dataset_WWW_readme.txt", "raw_Checkins_anonymized.txt"]:
os.remove(os.path.join(DATA_DIR, "foursquare", file))
shutil.rmtree(os.path.join(DATA_DIR, "foursquare", "dataset_WWW2019"))
shutil.rmtree(os.path.join(DATA_DIR, "foursquare", "__MACOSX"))
os.rename(os.path.join(DATA_DIR, "foursquare", "dataset_WWW_friendship_new.txt"), os.path.join(DATA_DIR, "foursquare", "foursquare_friends_edges.txt"))
os.rename(os.path.join(DATA_DIR, "foursquare", "dataset_WWW_Checkins_anonymized.txt"), os.path.join(DATA_DIR, "foursquare", "foursquare_checkins_full.txt"))
## BRIGHTKITE CLEANING ##
os.rename(os.path.join(DATA_DIR, "brightkite", "loc-brightkite_totalCheckins.txt"), os.path.join(DATA_DIR, "brightkite", "brightkite_checkins_full.txt"))
os.rename(os.path.join(DATA_DIR, "brightkite", "loc-brightkite_edges.txt"), os.path.join(DATA_DIR, "brightkite", "brightkite_friends_edges.txt"))
## GOWALLA CLEANING ##
os.rename(os.path.join(DATA_DIR, "gowalla", "loc-gowalla_totalCheckins.txt"), os.path.join(DATA_DIR, "gowalla", "gowalla_checkins_full.txt"))
os.rename(os.path.join(DATA_DIR, "gowalla", "loc-gowalla_edges.txt"), os.path.join(DATA_DIR, "gowalla", "gowalla_friends_edges.txt"))
# ------------------------------------------------------------------------#
def create_graph_from_checkins(dataset: Literal['brightkite', 'gowalla', 'foursquareEU', 'foursquareIT'], create_file = True) -> nx.Graph:
"""
Create a graph from the checkins of the dataset. The graph is undirected and the nodes are the users and the edges are the checkins in common.
Parameters
----------
`dataset` : Literal['brightkite', 'gowalla', 'foursquare']
The dataset to use.
`create_file` : bool, optional
If True, the graph is saved in a file, by default True
Returns
-------
`G` : networkx.Graph
Raises
------
ValueError
If the dataset is not valid.
"""
if dataset not in ['brightkite', 'gowalla', 'foursquare']:
raise ValueError("Dataset not valid. Please choose between brightkite, gowalla, foursquare")
file = os.path.join(DATA_DIR, dataset, dataset + "_checkins.txt")
print("\nCreating the graph for the dataset {}...".format(dataset))
df = pd.read_csv(file, sep="\t", header=None, names=["user_id", "venue_id"], engine='pyarrow')
G = nx.Graph()
venues_users = df.groupby("venue_id")["user_id"].apply(set)
for users in tqdm.tqdm(venues_users):
for user1, user2 in combinations(users, 2):
G.add_edge(user1, user2)
# path to the file where we want to save the graph
edges_path = os.path.join(DATA_DIR, dataset , dataset + "_checkins_edges.tsv")
print("Done! The graph has {} edges".format(G.number_of_edges()), " and {} nodes".format(G.number_of_nodes()))
# delete from memory the dataframe
del df
if create_file:
# save the graph in a file
nx.write_edgelist(G, edges_path, data=True, delimiter="\t", encoding="utf-8")
return G
# ------------------------------------------------------------------------#
def create_friendships_graph(dataset: Literal['brightkite', 'gowalla', 'foursquareEU', 'foursquareIT']) -> nx.Graph:
"""
Create the graph of friendships for the dataset brightkite, gowalla or foursquare.
The graph is saved in a file.
Parameters
----------
`dataset` : str
The dataset for which we want to create the graph of friendships.
Returns
-------
`G` : networkx.Graph
The graph of friendships.
Notes
-----
Since we are taking sub-samples of each check-ins dataset, we are also taking sub-samples of the friendship graph. A user is included in the friendship graph if he has at least one check-in in the sub-sample.
"""
if dataset not in ["brightkite", "gowalla", "foursquare"]:
raise ValueError("The dataset must be brightkite, gowalla or foursquare")
file = os.path.join(DATA_DIR, dataset, dataset + "_friends_edges.txt")
# read the file with the edges of the friendship graph and get the unique users
df_friends_all = pd.read_csv(file, sep="\t", header=None, names=["node1", "node2"], engine='pyarrow')
unique_friends = set(df_friends_all["node1"].unique()).union(set(df_friends_all["node2"].unique()))
# read the file with the edges of the check-ins graph and get the unique users
df_checkins = pd.read_csv(os.path.join(DATA_DIR, dataset, dataset + "_checkins_edges.tsv"), sep="\t", header=None, names=["node1", "node2"])
unique_checkins = set(df_checkins["node1"].unique()).union(set(df_checkins["node2"].unique()))
# get the intersection of the two sets and filter the friendship graph
unique_users = unique_friends.intersection(unique_checkins)
df = df_friends_all[df_friends_all["node1"].isin(unique_users) & df_friends_all["node2"].isin(unique_users)]
df.to_csv(os.path.join(DATA_DIR, dataset, dataset + "_friends_edges_filtered.tsv"), sep="\t", header=False, index=False)
G = nx.from_pandas_edgelist(df, "node1", "node2", create_using=nx.Graph())
del df_friends_all, df_checkins, df # delete from memory the dataframes
return G
# ------------------------------------------------------------------------#
def degree_distribution(G: nx.Graph, log: bool = True, save: bool = False) -> None:
"""
This function takes in input a networkx graph object and plots the degree distribution of the graph.
Parameters
----------
`G` : networkx graph object
The graph object
`log` : bool, optional
If True, the plot will be in log-log scale, by default True
`save` : bool, optional
If True, the plot will be saved in the folder "plots", by default False
Returns
-------
None
Notes
-----
Due to the characteristics of datasets, not using a log log scale will lead to a un-useful plot. Even if using a log scales alters the power-law distribution, it is still clearly visible and distinguishable from a poisson distribution (witch is what we are interested in in this case)
"""
degrees = [G.degree(n) for n in G.nodes()]
degreeCount = Counter(degrees)
fig = go.Figure()
fig.add_trace(go.Bar(x=list(degreeCount.keys()), y=list(degreeCount.values()), name='Degree Distribution'))
if log:
fig.update_layout(
title='Degree Distribution (log-log scale) of {}' .format(G.name),
xaxis_title='Degree',
yaxis_title='Number of Nodes',
xaxis_type='log',
yaxis_type='log',
width=800,
height=600,
template='plotly_white'
)
else:
fig.update_layout(
title='Degree Distribution of {}' .format(G.name),
xaxis_title='Degree',
yaxis_title='Number of Nodes',
width=800,
height=600,
template='plotly_white'
)
fig.show()
if save:
fig.write_image("plots/degree_distribution_{}.png".format(G.name))
# ------------------------------------------------------------------------#
def chunks(l, n):
"""
Auxiliary function to divide a list of nodes `l` in `n` chunks
Parameters
----------
`l` : list
List of nodes
`n` : int
Number of 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, k =None) -> dict:
"""
Compute the betweenness centrality for nodes in a graph using multiprocessing.
Parameters
----------
G : graph
A networkx graph
processes : int, optional
The number of processes to use for computation.
If `None`, then it sets processes = 1
k : int, optional
Percent of nodes to sample. If `None`, then all nodes are used.
seed : int, optional
Seed for random number generator (default=None).
Returns
-------
dict
Notes
-----
Do not use more then 6 process for big graphs, otherwise the memory will be full. Do it only if you have more at least 32 GB of RAM. For small graphs, you can use more processes.
"""
# if process is None or 1, run the standard algorithm with one process
if processes is None or processes == 1:
print("\tRunning the networkx approximated algorithm with just one process")
G_copy = G.copy()
sample = int((k)*G_copy.number_of_nodes())
print("\tNumber of nodes after removing {} % of nodes: {}" .format((k)*100, G_copy.number_of_nodes()))
return np.mean(nx.betweenness_centrality(G, k=sample, seed=42).values())
if processes > os.cpu_count():
raise ValueError("The number of processes must be less than the number of cores in the system.")
if k is not None:
if (k < 0 or k > 1):
raise ValueError("k must be between 0 and 1.")
else:
G_copy = G.copy()
G_copy.remove_nodes_from(random.sample(G_copy.nodes(), int((k)*G_copy.number_of_nodes())))
print("\tNumber of nodes after removing {}% of nodes: {}" .format((k)*100, G_copy.number_of_nodes()))
print("\tNumber of edges after removing {}% of nodes: {}" .format((k)*100, G_copy.number_of_edges()))
if k is None:
G_copy = G.copy()
p = Pool(processes=processes)
node_divisor = len(p._pool) * 4
node_chunks = list(chunks(G_copy.nodes(), G_copy.order() // node_divisor))
num_chunks = len(node_chunks)
bt_sc = p.starmap(
nx.betweenness_centrality_subset,
zip(
[G_copy] * num_chunks, # this returns a list of Gs
node_chunks,
[list(G_copy)] * num_chunks, # this returns a list of lists of nodes
[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
# ------------------------------------------------------------------------#
def average_shortest_path(G: nx.Graph, k=None) -> float:
"""
This function takes in input a networkx graph and returns the average shortest path length of the graph. This works also for disconnected graphs.
Parameters
----------
`G` : networkx graph
The graph to compute the average shortest path length of.
`k` : float
percentage of nodes to remove from the graph. If `k` is None, the average shortest path length of each connected component is computed using all the nodes of the connected component.
Returns
-------
float
The average shortest path length of the graph.
Raises
------
ValueError
If `k` is not between 0 and 1
"""
if k is not None and (k < 0 or k > 1):
raise ValueError("k must be between 0 and 1")
elif k is None:
G_copy = G.copy()
connected_components = list(nx.connected_components(G))
else:
G_copy = G.copy()
# remove the k% of nodes from G
G_copy.remove_nodes_from(random.sample(G_copy.nodes(), int((k)*G_copy.number_of_nodes())))
print("\tNumber of nodes after removing {}% of nodes: {}" .format((k)*100, G_copy.number_of_nodes()))
print("\tNumber of edges after removing {}% of nodes: {}" .format((k)*100, G_copy.number_of_edges()))
tmp = 0
connected_components = list(nx.connected_components(G_copy))
# remove all the connected components with less than 10 nodes
connected_components = [c for c in connected_components if len(c) > 10]
print("\tNumber of connected components with more then 10 nodes: {}" .format(len(connected_components)), "\r")
for C in (G_copy.subgraph(c).copy() for c in connected_components):
print("\tComputing average shortest path length of connected component with {} nodes and {} edges" .format(C.number_of_nodes(), C.number_of_edges()), "\r", end="")
tmp += nx.average_shortest_path_length(C)
return np.mean(tmp)
# ------------------------------------------------------------------------#
def average_clustering_coefficient(G: nx.Graph, k=None) -> float:
"""
This function takes in input a networkx graph and returns the average clustering coefficient of the graph. This works also for disconnected graphs.
Parameters
----------
`G` : networkx graph
The graph to compute the average clustering coefficient of.
`k` : int
percentage of nodes to remove from the graph. If `k` is None, the average clustering coefficient of each connected component is computed using all the nodes of the connected component.
Returns
-------
float
The average clustering coefficient of the graph.
Raises
------
ValueError
If `k` is not between 0 and 1
"""
if k is not None and (k < 0 or k > 1):
raise ValueError("k must be between 0 and 1")
elif k is None:
return nx.average_clustering(G)
else:
G_copy = G.copy()
G_copy.remove_nodes_from(random.sample(list(G_copy.nodes()), int((k)*G_copy.number_of_nodes())))
print("\tNumber of nodes after removing {}% of nodes: {}" .format((k)*100, G_copy.number_of_nodes()))
return nx.average_clustering(G_copy)
def generalized_average_clustering_coefficient(G: nx.Graph) -> float:
"""
Generalized definition of the average clustering coefficient of a graph. It better applies to small world networks and it's way more efficient than the average_clustering_coefficient function with the standard definition of the clustering coefficient.
Parameters
----------
`G` : networkx graph
The graph to compute the generalized average clustering coefficient of.
Returns
-------
float
The generalized average clustering coefficient of the graph.
"""
C = 0
for node in G.nodes():
k = G.degree(node)
C += (3*(k-1))/(2*(2*k - 1))
return C/G.number_of_nodes()
# ------------------------------------------------------------------------#
def create_random_graphs(G: nx.Graph, model = None, save = True) -> nx.Graph:
"""Create a random graphs with about the same number of nodes and edges of the original graph.
Parameters
----------
`G` : nx.Graph
The original graph.
`model` : str
The model to use to generate the random graphs. It can be one of the following: "erdos", "watts_strogatz"
`save`: bool
If True, the random graph is saved in the folder data/random/model
Returns
-------
`G_random` : nx.Graph
"""
if model is None:
model = "erdos_renyi"
if model == "erdos_renyi":
G_random = nx.erdos_renyi_graph(G.number_of_nodes(), nx.density(G))
print("Creating a random graph with the Erdos-Renyi model {}" .format(G.name))
# print("Number of edges in the original graph: {}" .format(G.number_of_edges()))
# print("Number of edges in the random graph: {}" .format(G_random.number_of_edges()))
G_random.name = G.name + " Erdos-Renyi"
if save:
# check if the folder exists, otherwise create it
if not os.path.exists(os.path.join(DATA_DIR, 'random', 'erdos')):
os.makedirs(os.path.join(DATA_DIR, 'random', 'erdos'))
nx.write_gpickle(G_random, os.path.join(DATA_DIR, 'random', 'erdos', "erdos_" + str(G.number_of_nodes()) + "_" + str(G_random.number_of_edges()) + ".gpickle"))
print("\tThe file graph has been saved in the folder data/random/erdos with the syntax erdos_n_nodes_n_edges.gpickle")
return G_random
elif model == "watts_strogatz":
p = G.number_of_edges() / (G.number_of_nodes())
avg_degree = int(np.mean([d for n, d in G.degree()]))
G_random = nx.watts_strogatz_graph(G.number_of_nodes(), avg_degree, p)
# print("Number of edges in the original graph: {}" .format(G.number_of_edges()))
# print("Number of edges in the random graph: {}" .format(G_random.number_of_edges()))
G_random.name = G.name + " Watts-Strogatz"
if save:
# check if the folder exists, otherwise create it
if not os.path.exists(os.path.join(DATA_DIR, 'random', 'watts_strogatz')):
os.makedirs(os.path.join(DATA_DIR, 'random', 'watts_strogatz'))
nx.write_gpickle(G_random, os.path.join(DATA_DIR, 'random', 'watts_strogatz', "watts_strogatz_" + str(G.number_of_nodes()) + "_" + str(G_random.number_of_edges()) + ".gpickle"))
print("\tThe file graph has been saved in the folder data/random/watts_strogatz with the syntax watts_strogatz_n_nodes_n_edges.gpickle")
return G_random
# ------------------------------------------------------------------------#
def visualize_graphs(G: nx.Graph, k: float, connected = True):
"""
Function to visualize the graph in a HTML page using pyvis
Parameters
----------
`G`: nx.Graph
The graph to visualize
`k`: float
The percentage of nodes to remove from the graph. Default is None, in which case it will be chosen such that there are about 1000 nodes in the sampled graph. I strongly suggest to use the default value, other wise the visualization will be very slow.
`connected`: bool
If True, we will consider only the largest connected component of the graph
Returns
-------
`html file`
The html file containing the visualization of the graph
Notes:
------
This is of course an approximation, it's nice to have an idea of the graph, but it's not a good idea trying to understand the graph in details from this sampled visualization.
"""
if k is None:
if len(G.nodes) > 1500:
k = 1 - 1500/len(G.nodes)
else:
k = 0
# remove a percentage of the nodes
nodes_to_remove = np.random.choice(list(G.nodes), size=int(k*len(G.nodes)), replace=False)
G.remove_nodes_from(nodes_to_remove)
if connected:
# take only the largest connected component
connected_components = list(nx.connected_components(G))
largest_connected_component = max(connected_components, key=len)
G = G.subgraph(largest_connected_component)
# create a networkx graph
net = net = Network(directed=False, bgcolor='#1e1f29', font_color='white')
# for some reasons, if I put % values, the graph is not displayed correctly. So I use pixels, sorry non FHD users
net.width = '1920px'
net.height = '1080px'
# add nodes and edges
net.add_nodes(list(G.nodes))
net.add_edges(list(G.edges))
# set the physics layout of the network
net.set_options("""
var options = {
"edges": {
"color": {
"inherit": true
},
"smooth": false
},
"physics": {
"repulsion": {
"centralGravity": 0.25,
"nodeDistance": 500,
"damping": 0.67
},
"maxVelocity": 48,
"minVelocity": 0.39,
"solver": "repulsion"
}
}
""")
name = G.name.replace(" ", "_").lower()
if not os.path.exists("html_graphs"):
os.mkdir("html_graphs")
# save the graph in a html file
net.show("html_graphs/{}.html".format(name))
print("The graph has been saved in the folder html_graphs with the name {}.html" .format(name))
# ------------------------------------------------------------------------#
def random_sample(graph: nx.Graph, k: float) -> nx.Graph:
"""
Function to take a random sample of a graph
Parameters
----------
`graph`: nx.Graph
The graph to sample
`k`: float
The percentage of nodes to remove from the graph
Returns
-------
`G`: nx.Graph
"""
if not 0 <= k <= 1:
raise ValueError("Percentage of nodes needs to be between 0 and 1")
nodes = list(graph.nodes())
nodes_sample = np.random.choice(nodes, size=int((1-k)*len(nodes)), replace=False)
G = graph.subgraph(nodes_sample)
if not nx.is_connected(G):
print("Graph is not connected. Taking the largest connected component")
connected = max(nx.connected_components(G), key=len)
G_connected = graph.subgraph(connected)
print("Number of nodes in the sampled graph: ", G.number_of_nodes())
print("Number of edges in the sampled graph: ", G.number_of_edges())
return G_connected
# ------------------------------------------------------------------------#
def omega_sampled(G: nx.Graph, k: float, niter: int, nrand: int) -> float:
"""
Function to compute the omega index of a graph
Parameters
----------
`G`: nx.Graph
The graph to compute the omega index
`k`: float
The percentage of nodes to sample from the graph.
`niter`: int
Approximate number of rewiring per edge to compute the equivalent random graph.
`nrand`: int
Number of random graphs generated to compute the maximal clustering coefficient (Cr) and average shortest path length (Lr).
Returns
-------
`omega`: float
The omega index of the graph
"""
# sample the graph
G_sampled = random_sample(G, k)
# compute the omega index
omega = nx.omega(G_sampled, nrand, niter)
return omega
# ------------------------------------------------------------------------#
def parallel_omega(G: nx.Graph, k: float, nrand: int = 6, niter: int = 6, n_processes: int = None, seed: int = 42) -> float:
"""
function to compute the omega index of a graph in parallel. This is a much faster approach then the standard omega function. It parallelizes the computation of the random graphs and lattice networks.
Parameters
----------
`G`: nx.Graph
The graph to compute the omega index
`k`: float
The percentage of nodes to sample from the graph.
`niter`: int
Approximate number of rewiring per edge to compute the equivalent random graph. Default is 6.
`nrand`: int
Number of random graphs generated to compute the maximal clustering coefficient (Cr) and average shortest path length (Lr). Default is 6
`n_processes`: int
Number of processes to use. Default is the number of cores of the machine.
`seed`: int
The seed to use to generate the random graphs. Default is 42.
Returns
-------
`omega`: float
Notes
-----
This is just a notebook version of the program omega_parallel_server.py that you can find in the repository. This is supposed to be used just fo testing on small graphs.
"""
if n_processes is None:
n_processes = multiprocessing.cpu_count()
if n_processes > nrand:
n_processes = nrand
random.seed(seed)
if not nx.is_connected(G):
G = G.subgraph(max(nx.connected_components(G), key=len))
if len(G) == 1:
return 0
# sample the graph
G = random_sample(G, k)
def worker(queue_seeds, queue_results): # worker function to be used in parallel
while True:
try:
seed = queue_seeds.get(False)
except Empty:
break
random_graph = nx.random_reference(G, niter, seed=seed)
lattice_graph = nx.lattice_reference(G, niter, seed=seed)
random_shortest_path = nx.average_shortest_path_length(random_graph)
lattice_clustering = nx.average_clustering(lattice_graph)
queue_results.put((random_shortest_path, lattice_clustering))
manager = multiprocessing.Manager() # manager to share the queue
queue_seeds = manager.Queue() # queue to give the seeds to the processes
queue_results = manager.Queue() # queue to share the results
processes = [multiprocessing.Process(target=worker, args=(queue_seeds, queue_results))
for _ in range(n_processes)] # processes to be used
for i in range(nrand): # put the tasks in the queue
queue_seeds.put(i + seed)
for process in processes: # start the processes
process.start()
for process in processes: # wait for the processes to finish
process.join()
# collect the results
shortest_paths = []
clustering_coeffs = []
while not queue_results.empty():
random_shortest_path, lattice_clustering = queue_results.get() # get the results from the queue
shortest_paths.append(random_shortest_path)
clustering_coeffs.append(lattice_clustering)
L = nx.average_shortest_path_length(G)
C = nx.average_clustering(G)
omega = (np.mean(shortest_paths) / L) - (C / np.mean(clustering_coeffs))
return omega
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