<｜begin▁of▁sentence｜>### Instruction:
While conducting investigative work in the realm of neurological responses, a squad has gathered a trio of functional MRI scans for a set of individuals, each illustrating the cerebral network infrastructure. Here, the nodes mark various significant cerebral regions, and the edges trace the pathways of connectivity between these areas. The scans are segregated into two categories, correlating with distinct cognitive conditions.

The task at hand for our team is akin to piecing together clues from different scenes to determine which specific pathways—in our case, the connections between these cerebral regions—are crucial in distinguishing between the two cognitive states. We have connectivity intel for 5 key brain regions sourced from 3 separate scans, accompanied by binary indicators that denote the cognitive state linked with each scan.

Our objective, as if seeking to uncover the defining characteristics of two separate incidents, is to utilize graspologic's SignalSubgraph estimator in pinpointing the signal subgraph—essentially, the critical subset of connections—that sets these cognitive states apart. We are also mandated to work within specific limits concerning the number of connections and regions in our subgraph.

This is a methodical approach, much like examining a case where one must discern the key evidence that separates two linked yet distinct scenarios. How can we, with the constraint on the number of edges and vertices, employ the SignalSubgraph estimator effectively to detect this differential subgraph?
### Response:
import numpy as np
from graspologic.subgraph import SignalSubgraph

# Generate synthetic graph data
n_vertices = 5
s_samples = 3
np.random.seed(42)
graphs = np.random.rand(n_vertices, n_vertices, s_samples)
graphs = np.triu(graphs, k=1)  # Using only the upper triangle for undirected graphs
labels = np.array([0, 1, 1])  # Binary class labels for the samples

# Instantiate and fit the SignalSubgraph estimator
sg_estimator = SignalSubgraph()
constraints = (7, 3)  # Number of edges in sig subgraph and number of vertices the subgraph must be incident to
sg_estimator.fit(graphs, labels, constraints)

# Extract the signal subgraph
sigsub = sg_estimator.fit_transform(graphs, labels, constraints)

# Print the results
print('Signal subgraph indices (row, col):', sigsub)
print('Signal subgraph mask:\n', sg_estimator.mask_)
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