def nx_graph_nbrw(G):
import networkx as nx
A = nx.to_scipy_sparse_matrix(G)
P = mkm.graph_nbrw_transition_matrix(A)
mc = mkm.MarkovChain(P)
mc.set_stationary_distribution(mkm.uniform_distribution(mc.get_n()))
return mc
def nx_graph_nbrw(G): import networkx as nx A = nx.to_scipy_sparse_matrix(G) P = mkm.graph_nbrw_transition_matrix(A) mc = mkm.MarkovChain(P) mc.set_stationary_distribution(mkm.uniform_distribution(mc.get_n())) return mc
def nx_graph_nbrw(G): """Returns the Markov chain for the NBRW on the graph G. """ import networkx as nx A = nx.to_scipy_sparse_matrix(G) P = mkm.graph_nbrw_transition_matrix(A) mc = mkm.MarkovChain(P) mc.set_stationary(mkm.uniform_distribution(mc.get_n())) return mc
def nx_graph_nbrw(G):
"""Returns the Markov chain for the NBRW on the graph G.
"""
import networkx as nx
A = nx.to_scipy_sparse_matrix(G)
P = mkm.graph_nbrw_transition_matrix(A)
mc = mkm.MarkovChain(P)
mc.set_stationary(mkm.uniform_distribution(mc.get_n()))
return mc
import matplotlib.pyplot as plt
# load a 6-regular graph with 50.000 nodes from file
G_6_regular = nx.read_sparse6('6_regular.s6')
# get the adjacency matrix
A = nx.to_scipy_sparse_matrix(G_6_regular)
# transition matrix for NBRW on the graph from the adjacency matrix
P = mkm.graph_nbrw_transition_matrix(A)
# Markov chain with the transition marix
mc = mkm.MarkovChain(P)
# the stationary distribution is uniform
mc.set_stationary(mkm.uniform_distribution(mc.get_n()))
# add a random starting position to the Markov chain
mc.add_random_delta_distributions(1)
# determine the mixing
mc.compute_tv_mixing()
# plot the mixing
(x,tv) = mc.distribution_tv_mixing(0)
plt.plot(x, tv, marker='o', linestyle='dashed')
plt.title("Mixing of NBRW on a 6-regular graph")
plt.xlabel("t")
plt.ylabel("Toal variation distance to stationarity")
plt.show()
