<｜begin▁of▁sentence｜>### Instruction:
Given a simple unweighted graph represented by an adjacency matrix `A`, and a list of seed vertices represented by `seed_indices`, how would you use the SpectralVertexNomination API to rank all vertices in the graph in order of relation to the seed vertices using Spectral Graph Theory?
### Response:
import numpy as np
from graspologic.nominate import SpectralVertexNomination
from graspologic.embed import AdjacencySpectralEmbed

# Assume we have an adjacency matrix `A` which represents our graph.
A = np.array([[0, 1, 0, 0, 1],
              [1, 0, 1, 0, 0],
              [0, 1, 0, 1, 0],
              [0, 0, 1, 0, 1],
              [1, 0, 0, 1, 0]])

# List of seed vertex indices
seed_indices = np.array([1, 2])

# Instantiate and run SpectralVertexNomination
svn = SpectralVertexNomination(input_graph=True, embedder='ASE', n_neighbors=None, metric='euclidean', metric_params=None)
fit_predict_result = svn.fit_predict(A, seed_indices)

# Get nomination list and distance matrix
distance_matrix = fit_predict_result[1]
nomination_list = fit_predict_result[0]

# Print results
print('Nomination List:\n', nomination_list)
print('Distance Matrix:\n', distance_matrix)
<|EOT|>
