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import numpy as np
import numpy.random as nr
from six.moves import range
def create_random_graph(n_nodes, p=.5):
graph = .5 * np.random.binomial(2, p=.5, size=(n_nodes, n_nodes))
for k in range(len(graph)):
graph[k, k] = 0
return np.log(1. / (1 - p * graph))
def create_wheel(n_nodes, p=.5):
graph = np.zeros((n_nodes, n_nodes))
graph[0] = np.ones(n_nodes)
graph[0, 0] = 0
for i in range(1, n_nodes-1):
graph[i, i + 1] = 1
graph[n_nodes-1, 1] = 1
return np.log(1. / (1 - p * graph))
def simulate_cascade(x, graph):
"""
Simulate an IC cascade given a graph and initial state.
For each time step we yield:
- susc: the nodes susceptible at the beginning of this time step
- x: the subset of susc who became infected
"""
yield x, np.zeros(graph.shape[0], dtype=bool)
susc = np.ones(graph.shape[0], dtype=bool)
while np.any(x):
susc = susc ^ x # nodes infected at previous step are now inactive
if not np.any(susc):
break
x = 1 - np.exp(-np.dot(graph.T, x))
y = nr.random(x.shape[0])
x = (x >= y) & susc
yield x, susc
def random_source(graph, node_p=None):
n_nodes = graph.shape[0]
if node_p is None:
node_p = np.ones(n_nodes) / n_nodes
x0 = np.zeros(graph.shape[0], dtype=bool)
x0[nr.choice(n_nodes, p=node_p)] = True
return x0
def simulate_cascades(n_obs, graph, source=random_source):
n_nodes = graph.shape[0]
x_obs = np.zeros((n_obs, n_nodes), dtype=bool)
s_obs = np.zeros((n_obs, n_nodes), dtype=bool)
i = 0
while i < n_obs:
for x, s in simulate_cascade(source(graph), graph):
x_obs[i] = x
s_obs[i] = s
i += 1
if i >= n_obs:
break
return x_obs, s_obs
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