<｜begin▁of▁sentence｜>### Instruction:
Imagine we are illustrating a detailed map of a human body's neural network, where each neuron (node) is connected to others, illustrating the pathway of neural signals (edges). For a specific educational purpose, we need to create an accurate depiction showing the signal path from a particular neuron labeled '3' to all reachable neurons within three synapses (levels).

To accurately capture this scenario, we must limit our illustration to show only the connections (edges) that would be activated if a signal started at neuron '3' and traveled no further than three synapses away. Can you provide the connections list for this specific signal propagation pathway, considering our neural map has the following known synapses defined in the dataset: [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (2, 7), (7, 8), (8, 9), (9, 10)]? Let's ensure we convey this neural activity clearly and precisely in our next medical illustration.
### Response:
import networkx as nx

# Create a graph
H = nx.Graph()
nx.add_path(H, [0, 1, 2, 3, 4, 5, 6])
nx.add_path(H, [2, 7, 8, 9, 10])

# Use bfs_tree with a source node and a depth limit
bfs_tree = nx.bfs_tree(H, source=3, depth_limit=3)

# Print the edges of the tree
print(sorted(list(bfs_tree.edges())))
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