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# Licensed under the Apache License, Version 2.0 (the "License");
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import networkx as nx
import torch
[docs]
def doubly_stochastic_adjacency(graph: nx.Graph) -> torch.Tensor:
"""Using Metropolis-Hastings algorithm to compute a doubly stochastic adjacency matrix."""
num_agents = len(graph.nodes())
binary_adjacency_matrix = torch.from_numpy(nx.to_numpy_array(graph)).float()
degree = torch.sum(binary_adjacency_matrix, dim=0)
W = torch.zeros((num_agents, num_agents))
for i in range(num_agents):
N_i = torch.nonzero(binary_adjacency_matrix[i, :])
for j in N_i:
W[i, j] = 1 / (1 + max(degree[i], degree[j]))
W[i, i] = 1 - torch.sum(W[i, :])
return W
[docs]
def get_matrix_steady_state(A: torch.Tensor):
"""Get the steady state of a matrix via eigendecomposition"""
eigenvalues, eigenvectors = torch.linalg.eig(A) # unnormalized and unordered eigenvalues and eigenvectors
idx = eigenvalues.float().argsort(descending=True)
eigenvectors = eigenvectors.float()[:, idx]
steady_state = eigenvectors[:, 0] / torch.sum(eigenvectors[:, 0])
return steady_state