<｜begin▁of▁sentence｜>### Instruction:
A team of network scientists is analyzing a series of temporally evolving graphs to understand patterns of connectivity change over time within a particular network system. Each graph represents the network at a given time point, with nodes remaining consistent across the series but edges changing to reflect evolving interactions. The team is interested in embedding these graphs in a lower-dimensional space to compare and contrast their structural similarities and differences over time using Multiple Adjacency Spectral Embedding (MASE). How can they use MASE to achieve this, and what insights might the embedded representations reveal about the temporal evolution of the network?
### Response:
import numpy as np
import networkx as nx
from graspologic.embed import MultipleASE
from graspologic.plot import heatmap

# Define three simple graphs with the same set of nodes but different edges
g1 = nx.Graph([(0, 1), (1, 2)])
g2 = nx.Graph([(1, 2), (2, 3)])
g3 = nx.Graph([(1, 3), (3, 4)])

# Collect the graphs into a list
gs = [g1, g2, g3]

# Use Multiple Adjacency Spectral Embedding (MASE) to embed the graphs
mase = MultipleASE(n_components=2)
mase_embedding = mase.fit_transform(gs)

# Plot the embedding of the first graph for visualization
heatmap(mase_embedding[0], title='MASE Embedding of Graph 1')
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