def nx_graph_srw(G):
"""Returns the srw on the graph G
"""
import networkx as nx
A = nx.to_scipy_sparse_matrix(G)
P = mkm.graph_srw_transition_matrix(A)
mc = mkm.MarkovChain(P)
mc.set_stationary_distribution(mkm.graph_srw_stationary_distribution(A))
return mc
def nx_graph_srw(G): """Returns the srw on the graph G """ import networkx as nx A = nx.to_scipy_sparse_matrix(G) P = mkm.graph_srw_transition_matrix(A) mc = mkm.MarkovChain(P) mc.set_stationary_distribution(mkm.graph_srw_stationary_distribution(A)) return mc
import markovmixing as mkm
import networkx as nx
import matplotlib.pyplot as plt
# load a random 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 SRW on the graph from the adjacency matrix
P = mkm.graph_srw_transition_matrix(A)
# Markov chain with the transition marix
mc = mkm.MarkovChain(P)
# stationary distribution of SRW on a graph is deg(x)/2*|E|
mc.set_stationary_distribution(mkm.graph_srw_stationary_distribution(A))
# add a random starting position to the Markov chain
mc.add_distributions(mkm.random_delta_distributions(mc.get_n(),1))
# determine the mixing in total variation
mc.compute_tv_mixing()
# plot the mixing
(x,tv) = mc.distribution_tv_mixing(0)
plt.plot(x, tv)
plt.xlabel("t")
plt.ylabel("Distance to stationary distribution in total variation")
plt.show()