<｜begin▁of▁sentence｜>### Instruction:
Given a simple cycle graph with 4 nodes, can you use a placeholder function '_layout_mapping' to generate a layout mapping of the nodes and then convert this mapping to a JSON string?
### Response:
import networkx as nx
import json

# Create a simple graph
G = nx.cycle_graph(4)

# Assuming '_layout_mapping' is a placeholder function that maps nodes to positions
# We'll create a dummy function to represent it. Note that in actual use, '_layout_mapping'
# would be an internal function provided by a library such as NetworkX or igraph.
def _layout_mapping(G):
    # This is a dummy implementation using the circular layout for demonstration.
    return nx.circular_layout(G)

# Get the layout mapping
layout = _layout_mapping(G)

# Convert to JSON
layout_json = json.dumps(layout)
print(layout_json)
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