<｜begin▁of▁sentence｜>### Instruction:
Suppose you're working with a trio of property networks, each connecting four different real estate assets, akin to the way banking institutions might share mortgage lending opportunities. Each network is neatly catalogued in a table-like structure, reflecting the shared interests or partnerships between the properties, much like the shared clientele or agreements between lenders. If you're interested in finding a combined perspective of these networks to better understand the overarching relationships, similar to comparing different loan options across various lenders, you might consider leveraging the OmnibusEmbed function from the graspologic toolkit. This tool is designed to assimilate the separate networks, akin to merging client lists from different lenders, into a unified two-dimensional representation while preserving their unique interconnections. How might one engage this function to visually map out the interconnected landscape shared by these property networks, providing a bird's-eye view similar to a comparative market analysis that aids in recognizing the prime areas for brokerage?
### Response:
import numpy as np
import networkx as nx
from graspologic.embed import OmnibusEmbed
from graspologic.plot import heatmap
import matplotlib.pyplot as plt

# Generate synthetic adjacency matrices for the demonstration
n_vertices = 4
n_graphs = 3

# Generate random adjacency matrices for 3 graphs
graphs = [np.random.binomial(1, 0.5, size=(n_vertices, n_vertices)) for _ in range(n_graphs)]
# Since the graphs are undirected, we make the matrices symmetric
graphs = [np.triu(g) + np.triu(g, 1).T for g in graphs]

# Instantiate OmnibusEmbed with 2 components
omni = OmnibusEmbed(n_components=2)

# Fit and transform the graphs
embedded = omni.fit_transform(graphs)

for i, latent in enumerate(embedded):
    # Plot the latent positions as heatmap
    heatmap(latent, title=f'Graph {i+1}')
    plt.show()
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