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graph_utils.py
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graph_utils.py
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import copy
import random
import numpy as np
import scipy as sp
import networkx as nx
class EdgeSwapGraph(nx.Graph):
def randomize_by_edge_swaps(self, num_iterations):
newgraph = self.copy()
edge_list = newgraph.edges()
num_edges = len(edge_list)
total_iterations = num_edges * num_iterations
for i in range(total_iterations):
rand_index1 = int(round(random.random() * (num_edges - 1)))
rand_index2 = int(round(random.random() * (num_edges - 1)))
original_edge1 = edge_list[rand_index1]
original_edge2 = edge_list[rand_index2]
head1, tail1 = original_edge1
head2, tail2 = original_edge2
if random.random() >= 0.5:
head1, tail1 = tail1, head1
if head1 == tail2 or head2 == tail1:
continue
if newgraph.has_edge(head1, tail2) or newgraph.has_edge(
head2, tail1):
continue
original_edge1_data = newgraph[head1][tail1]
original_edge2_data = newgraph[head2][tail2]
newgraph.remove_edges_from((original_edge1, original_edge2))
new_edge1 = (head1, tail2, original_edge1_data)
new_edge2 = (head2, tail1, original_edge2_data)
newgraph.add_edges_from((new_edge1, new_edge2))
edge_list[rand_index1] = (head1, tail2)
edge_list[rand_index2] = (head2, tail1)
assert len(newgraph.edges()) == num_edges
return newgraph
def largest_strongly_connected_component(G):
nodes = max(nx.strongly_connected_components(G), key=len)
return G.subgraph(nodes).copy()
def lscc(G): # alias
return largest_strongly_connected_component(G)
def largest_connected_component(G):
nodes = max(nx.connected_components(G), key=len)
return G.subgraph(nodes).copy()
def lcc(G):
return largest_connected_component(G)
def assign_random_weights(array):
x_arr = np.random.random(size=(array.shape[0], array.shape[0]))
w_arr = np.multiply(x_arr, array)
return (w_arr + w_arr.T)/2
def turn_to_directed(mat, directed=0.0, weighted=0):
if not isinstance(mat, np.ndarray):
raise Exception('Wrong input parsed to turn_to_directed function!')
array = copy.deepcopy(mat)
if directed == 0.0:
if not weighted:
a = array.astype(bool)
else:
a = array.astype(float)
return sp.csr_matrix(a)
np.fill_diagonal(array, 0)
rows, cols = array.nonzero()
edgeset = set(zip(rows, cols))
upper = np.array([edge for edge in edgeset if edge[0] < edge[1]])
random_tosses = np.random.random(len(upper))
condition1 = (random_tosses >= directed / 2.0) & (random_tosses < directed)
condition2 = (random_tosses <= directed / 2.0) & (random_tosses < directed)
indices_where_upper_is_removed = np.where(condition1)[0]
indices_where_lower_is_removed = np.where(condition2)[0]
u_xdata = [u[0] for u in upper[indices_where_upper_is_removed]]
u_ydata = [u[1] for u in upper[indices_where_upper_is_removed]]
array[u_xdata, u_ydata] = 0
l_xdata = [u[1] for u in upper[indices_where_lower_is_removed]]
l_ydata = [u[0] for u in upper[indices_where_lower_is_removed]]
array[l_xdata, l_ydata] = 0
a = sp.csr_matrix(array)
return a
def get_symmetry_index(array):
array = array.astype(bool)
symmetrized = array + array.T
difference = symmetrized.astype(int) - array.astype(int)
difference.eliminate_zeros()
# symm_index is 1 for a symmetrix matrix and 0 for an asymmetric one
symm_index = 1 - difference.nnz / symmetrized.nnz * 2
return symm_index
def symmetric_component(array, is_weighted):
a = array.astype(bool).A
symm_mask = np.bitwise_and(a, a.T)
if not is_weighted:
return symm_mask
return np.multiply(symm_mask, array.A)
def non_symmetric_component(array, is_weighted):
return array.astype(float) - symmetric_component(array, is_weighted).astype(float)
def adj_random_rewiring_iom_preserving(a, is_weighted, r=10):
s = symmetric_component(a, is_weighted)
rs = turn_to_directed(s, directed=1.0, weighted=is_weighted)
rows, cols = rs.A.nonzero()
edgeset = set(zip(rows, cols))
upper = [edge for edge in edgeset]
source_nodes = [e[0] for e in upper]
target_nodes = [e[1] for e in upper]
double_edges = len(upper)
i = 0
while i < double_edges * r:
good_choice = 0
n1, n2, n3, n4, ind1, ind2 = [None] * 6
while not good_choice:
ind1, ind2 = np.random.choice(double_edges, 2)
n1, n3 = source_nodes[ind1], source_nodes[ind2]
n2, n4 = target_nodes[ind1], target_nodes[ind2]
if len({n1, n2, n3, n4}) == 4:
good_choice = 1
w1 = s[n1, n2]
w2 = s[n2, n1]
w3 = s[n3, n4]
w4 = s[n4, n3]
if s[n1, n3] + s[n1, n4] + s[n2, n3] + s[n2, n4] == 0:
s[n1, n4] = w1
s[n4, n1] = w2
s[n2, n3] = w3
s[n3, n2] = w4
s[n1, n2] = 0
s[n2, n1] = 0
s[n3, n4] = 0
s[n4, n3] = 0
target_nodes[ind1], target_nodes[ind2] = n4, n2
i += 1
# plt.matshow(s)
# print ('Rewiring single connections...')
ns = non_symmetric_component(a, is_weighted)
# plt.matshow(ns)
rows, cols = ns.nonzero()
edges = list((set(zip(rows, cols))))
source_nodes = [e[0] for e in edges]
target_nodes = [e[1] for e in edges]
single_edges = len(edges)
i = 0
while i < single_edges * r:
good_choice = 0
n1, n2, n3, n4, ind1, ind2 = [None] * 6
while not good_choice:
ind1, ind2 = np.random.choice(single_edges, 2)
n1, n3 = source_nodes[ind1], source_nodes[ind2]
n2, n4 = target_nodes[ind1], target_nodes[ind2]
if len({n1, n2, n3, n4}) == 4:
good_choice = 1
w1 = ns[n1, n2]
w2 = ns[n3, n4]
checklist = [ns[n1, n3], ns[n1, n4], ns[n2, n3], ns[n2, n4],
ns[n3, n1], ns[n4, n1], ns[n3, n2], ns[n4, n2],
s[n3, n1], s[n4, n1], s[n3, n2], s[n4, n2]]
if checklist.count(0) == 12:
ns[n1, n4] = w1
ns[n3, n2] = w2
ns[n1, n2] = 0
ns[n3, n4] = 0
i += 1
target_nodes[ind1], target_nodes[ind2] = n4, n2
res = s + ns
if not is_weighted:
res = res.astype(bool)
return sp.csr_matrix(res)
def create_sbm(n, q, w_in=100, w_out=0.01, random_sizes=0, weighted=1):
if not weighted:
raise Exception('Unweighted sbm is not implemented')
a = np.zeros((n, n))
if random_sizes:
sizes_do_not_fit = 1
starts = None
while sizes_do_not_fit:
starts = [0] + list(np.sort(np.random.randint(0, high=n, size=q)))
sz = [starts[i+1] - starts[i] for i in range(len(starts)-1)]
if sum(np.array([s > n//(2*q) for s in sz]).astype(int)) == q:
sizes_do_not_fit = 0
else:
sz = int(n/q)
starts = [i*sz for i in range(q)]
ends = np.r_[[starts[i] - 1 for i in range(1, q)], [n-1]]
for i in range(q):
for j in range(i, q):
if i == j:
lm = w_in
else:
lm = w_out
a[starts[i]:ends[i]+1, starts[j]:ends[j]+1] = np.random.poisson(lm, size=np.shape(a[starts[i]:ends[i]+1, starts[j]:ends[j]+1]))
a[starts[j]:ends[j]+1, starts[i]:ends[i]+1] = a[starts[i]:ends[i]+1, starts[j]:ends[j]+1].T
if i == j:
a[starts[i]:ends[i]+1, starts[j]:ends[j]+1] = (a[starts[i]:ends[i]+1, starts[j]:ends[j]+1]+a[starts[i]:ends[i]+1, starts[j]:ends[j]+1].T)/2
return a
def get_single_double_edges_lists(g):
list_single = []
list_double = []
h = nx.to_undirected(g).copy()
for e in h.edges():
if g.has_edge(e[1], e[0]):
if g.has_edge(e[0], e[1]):
list_double.append((e[0], e[1]))
else:
list_single.append((e[1], e[0]))
else:
list_single.append((e[0], e[1]))
return [list_single, list_double]
def random_rewiring_iom_preserving_undirected_unweighted(graph, r=10):
[list_single, list_double] = get_single_double_edges_lists(graph)
number_of_single_edges = len(list_single)
number_of_double_edges = len(list_double)
number_of_rewired_1_edge_pairs = number_of_single_edges * r
number_of_rewired_2_edge_pairs = number_of_double_edges * r
print(f"number_of_rewired_1_edge_pairs: {number_of_rewired_1_edge_pairs}")
print(f"number_of_rewired_2_edge_pairs: {number_of_rewired_2_edge_pairs}")
i = 0
previous_text = ""
print('Rewiring double connections...')
while i < number_of_rewired_2_edge_pairs:
edge_index_1 = random.randrange(0, number_of_double_edges)
edge_index_2 = random.randrange(0, number_of_double_edges)
edge_1 = list_double[edge_index_1]
edge_2 = list_double[edge_index_2]
[node_a, node_b] = edge_1
[node_c, node_d] = edge_2
while (node_a == node_c) or (node_a == node_d) or (node_b == node_c) or (node_b == node_d):
edge_index_1 = random.randrange(0, number_of_double_edges)
edge_index_2 = random.randrange(0, number_of_double_edges)
edge_1 = list_double[edge_index_1]
edge_2 = list_double[edge_index_2]
[node_a, node_b] = edge_1
[node_c, node_d] = edge_2
if graph.has_edge(node_a, node_d) == 0 and graph.has_edge(node_c, node_b) == 0:
graph.remove_edge(node_a, node_b)
graph.remove_edge(node_c, node_d)
graph.add_edge(node_a, node_d)
graph.add_edge(node_c, node_b)
list_double[edge_index_1] = (node_a, node_d)
list_double[edge_index_2] = (node_c, node_b)
i += 1
if (i != 0) and (i % (number_of_double_edges // 1)) == 0:
text = str(round(100.0 * i / number_of_rewired_2_edge_pairs, 0)) + "%"
if text != previous_text:
pass
previous_text = text
i = 0
print('Rewiring single connections...')
while i < number_of_rewired_1_edge_pairs:
edge_index_1 = random.randrange(0, number_of_single_edges)
edge_index_2 = random.randrange(0, number_of_single_edges)
edge_1 = list_single[edge_index_1]
edge_2 = list_single[edge_index_2]
[node_a, node_b] = edge_1
[node_c, node_d] = edge_2
while (node_a == node_c) or (node_a == node_d) or (node_b == node_c) or (node_b == node_d):
edge_index_1 = random.randint(0, number_of_single_edges-1)
edge_index_2 = random.randint(0, number_of_single_edges-1)
edge_1 = list_single[edge_index_1]
edge_2 = list_single[edge_index_2]
[node_a, node_b] = edge_1
[node_c, node_d] = edge_2
if graph.has_edge(node_a, node_d) == 0 and graph.has_edge(node_c, node_b) == 0:
graph.remove_edge(node_a, node_b)
graph.remove_edge(node_c, node_d)
graph.add_edge(node_a, node_d)
graph.add_edge(node_c, node_b)
list_single[edge_index_1] = (node_a, node_d)
list_single[edge_index_2] = (node_c, node_b)
i += 1
graph_rewired = copy.deepcopy(graph)
return graph_rewired