<｜begin▁of▁sentence｜>### Instruction:
As a fraud investigator examining the communication network of a karate club to uncover fraudulent activity, we have a potential lead on two key members - the instructor (node 0) and the president (node 33). Given the structure of the network, which encompasses 34 members and records of their interactions, our objective is to determine which members are most likely to engage with these two key figures.

To tackle this task, we're considering the use of Spectral Vertex Nomination, a tool renowned for its ability to produce a nomination list, effectively ranking all members by the estimated probability of their interaction with particular seeds, in this case, the instructor and the president.

How can we adapt and implement the SpectralVertexNomination class in such a way that it aligns with this network? Specifically, we want to generate a nominee list that orders members according to their anticipated proximity to the nominated seeds: the instructor and the president. Keep in mind that our objective is not to modify the semantics but to creatively integrate the data into the practical application of the API.
### 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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