<｜begin▁of▁sentence｜>### Instruction:
In the karate club network, a researcher wants to discover which members are most likely to interact with the instructor (node 0) and the president (node 33) of the club. The network consists of 34 members and their interactions. The goal is to use spectral vertex nomination to create a nomination list, ranking all members in order of their likelihood to interact with the seed members based on the structure of their interactions. How does the SpectralVertexNomination class apply to this network to produce a nominee list that ranks members according to their proximity to the instructor and the president?
### Response:
import numpy as np
import networkx as nx
from graspologic.nominate import SpectralVertexNomination
from graspologic.embed import AdjacencySpectralEmbed

# Create a synthetic graph using networkx
G = nx.karate_club_graph()
adjacency_matrix = nx.to_numpy_array(G)

# Assuming we want to rank the vertices in relation to the 'seed' nodes
seed = np.array([0, 33]) # Using node 0 and node 33 as seeds

# Instantiate the SpectralVertexNomination with Adjacency Spectral Embedding
svn = SpectralVertexNomination(input_graph=True, embedder='ASE', n_neighbors=5)

# Fit the model and predict the nomination list
nomination_list, distance_matrix = svn.fit_predict(adjacency_matrix, seed)

print('Nomination List:\n', nomination_list)
print('Distance Matrix:\n', distance_matrix)
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