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erdos_renyi_default_poisson.py
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erdos_renyi_default_poisson.py
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#!/usr/bin/env python3
import random as rnd
import numpy as np
import matplotlib.pyplot as plt
import graph_tool as gt
from graph_tool.all import *
import pandas as pd
import time
import scipy.special
import collections
#The script contains an Erdos-Renyi graph class, that has functions to simulate the process, do the time reshuffling and count different motifs
def subgraph_num(subgraph,graph):
i = 0
gen = gt.topology.subgraph_isomorphism(subgraph, graph, generator=True)
for iter in gen:
i += 1
return i
class Erdos_Renyi():
def __init__(self,N_vertices,exp_deg,p):
self.g = gt.Graph()
for i in range(0,N_vertices):
self.g.add_vertex()
for j in range(0,i):
if(rnd.uniform(0,1) < p):
self.g.add_edge(i,j)
if(rnd.uniform(0,1) < p):
self.g.add_edge(j,i)
self.g.vp.stecaj = self.g.new_vertex_property("bool")
self.g.vp.known = self.g.new_vertex_property("bool")
self.g.vp.time = self.g.new_vertex_property("double")
self.g.ep.time = self.g.new_edge_property("double")
self.g.vp.t_part = self.g.new_vertex_property("bool")
self.g.ep.causal = self.g.new_edge_property("bool")
samci = []
self.g_c = self.g.copy()
def set_directedness(self,directedness):
self.g_c.set_directed(directedness)
def initial_properties(self, zeta, dynamics):
self.g_c = self.g.copy()
N = self.g_c.num_vertices()
vert_times = self.poisson_interevent(N,zeta)
rnd.shuffle(vert_times)
self.index_time = dict()
for v in self.g_c.vertices():
self.index_time[vert_times[-1]] = [self.g_c.vertex_index[v],"alpha"]
self.g_c.vp.known[v] = True
vert_times = vert_times[:-1]
edge_interevent = self.poisson_interevent(self.g_c.num_edges(),1)
for e in self.g_c.edges():
if(dynamics == "VM"):
s,t = e
kin = t.in_degree()
self.g_c.ep.time[e] = edge_interevent[-1]*kin
elif(dynamics == "SI"):
self.g_c.ep.time[e] = edge_interevent[-1]
edge_interevent = edge_interevent[:-1]
for e in self.g_c.edges():
self.g_c.ep.causal[e] = False
def process(self,exp_deg,zeta,N_vertices,frac_def):
index_time_sorted = collections.OrderedDict(sorted(self.index_time.items()))
self.g_c.set_vertex_filter(self.g_c.vp.stecaj, inverted = True)
nondefault = self.g_c.get_vertices()
self.g_c.clear_filters()
pot = []
N_pot = 0
pot.append([0,0])
while((N_vertices - len(nondefault)) < frac_def*N_vertices):
vert_time_list = list(index_time_sorted.keys())
vert_time = vert_time_list[0]
vert = index_time_sorted[vert_time][0]
prcs = index_time_sorted[vert_time][1]
while(self.g_c.vp.stecaj[vert] == True):
del index_time_sorted[vert_time]
index_time_list = list(index_time_sorted.items())
vert_time, vert_process = index_time_list[0]
vert,prcs = vert_process
del index_time_sorted[vert_time]
self.g_c.set_vertex_filter(self.g_c.vp.stecaj, inverted = False)
in_edges = self.g_c.get_in_edges(vert)
self.g_c.clear_filters()
self.g_c.set_vertex_filter(self.g_c.vp.stecaj, inverted = True)
out_edges = self.g_c.get_out_edges(vert)
N_pot = N_pot + len(out_edges) - len(in_edges)
for edge in out_edges:
s,t,i = edge
edge_time = self.g_c.ep.time[edge]
cascade_time = vert_time + edge_time
index_time_sorted[cascade_time] = [t,"beta"]
pot.append([vert_time,N_pot])
self.g_c.vp.time[vert] = vert_time
self.g_c.vp.stecaj[vert] = True
nondefault = self.g_c.get_vertices()
self.g_c.clear_filters()
index_time_sorted = collections.OrderedDict(sorted(index_time_sorted.items()))
time_list = self.g_c.vp.time.get_array()
pot = np.asarray(pot)
return pot
def network_part(self,time_frac_tot,l):
time_list_p = list(self.g_c.vp.time.get_array())
time_list_p.sort()
last = time_list_p[int((l+1)/time_frac_tot*self.g_c.num_vertices())-1]
for v in self.g_c.vertices():
if(self.g_c.vp.time[v] <= last):
self.g_c.vp.t_part[v] = True
self.g_c.set_vertex_filter(self.g_c.vp.t_part)
return last
def clear_graph(self):
for i in self.g_c.vertices():
self.g_c.vp.stecaj[i] = False
def largest_component(self):
l = gt.topology.label_largest_component(self.g_c, directed = False)
u = gt.GraphView(self.g_c, vfilt=l)
return u.num_vertices()
def one_path(self):
self.g_c.set_directed(False)
onepath = 0
onepath = self.g_c.num_edges()
self.g_c.set_directed(True)
return onepath
def two_path(self):
sub_twoI = gt.Graph(directed =True)
sub_twoV = gt.Graph(directed =True)
sub_twoΛ = gt.Graph(directed =True)
for n in range(0,3):
sub_twoI.add_vertex()
sub_twoV.add_vertex()
sub_twoΛ.add_vertex()
edgesI = [[0,1],[1,2]]
edgesV= [[1,0],[1,2]]
edgesΛ = [[0,1],[2,1]]
sub_twoI.add_edge_list(edgesI)
sub_twoV.add_edge_list(edgesV)
sub_twoΛ.add_edge_list(edgesΛ)
sub_isoI= subgraph_num(sub_twoI,self.g_c)
sub_isoV= subgraph_num(sub_twoV,self.g_c)
sub_isoΛ= subgraph_num(sub_twoΛ,self.g_c)
numI = int(sub_isoI)
numV = int(sub_isoV)
numΛ = int(sub_isoΛ)
return numI, numV, numΛ
def three_path(self):
self.g_c.set_directed(False)
sub_three1 = gt.Graph(directed = False)
sub_three2 = gt.Graph(directed = False)
sub_three3 = gt.Graph(directed = False)
for n in range(0,4):
sub_three1.add_vertex()
sub_three2.add_vertex()
for n in range(0,3):
sub_three3.add_vertex()
edges1 = [[0,1],[1,2],[2,3]]
edges2 = [[0,1],[1,2],[1,3]]
edges3 = [[0,1],[1,2],[2,0]]
sub_three1.add_edge_list(edges1)
sub_three2.add_edge_list(edges2)
sub_three3.add_edge_list(edges3)
sub_iso1 = subgraph_num(sub_three1,self.g_c)
sub_iso2 = subgraph_num(sub_three2,self.g_c)
sub_iso3 = subgraph_num(sub_three3 ,self.g_c)
num = int(sub_iso1)/2 + int(sub_iso2)/6 + int(sub_iso3)/6
self.g_c.set_directed(True)
return num
def reset_edges(self):
for i in self.g_c.edges():
self.g_c.ep.causal[i] = False
def only_causal(self):
for i in self.g_c.edges():
first,second = i
first_time = self.g_c.vp.time[self.g_c.vertex(first)]
second_time = self.g_c.vp.time[self.g_c.vertex(second)]
if(first_time < second_time):
self.g_c.ep.causal[i] = True
self.g_c.set_edge_filter(self.g_c.ep.causal)
def poisson_interevent(self,N,lam):
uniform = np.random.rand(N)
interevent = [-np.log(x)/lam for x in uniform]
return interevent
def shuffle_time(self):
time_list = self.g_c.vp.time.get_array()
rnd.shuffle(time_list)
gt.map_property_values(self.g_c.vertex_index, self.g_c.vp.time, lambda x: time_list[x])
def remember_time(self):
original_time = self.g_c.vp.time.get_array()
return original_time