<｜begin▁of▁sentence｜>### Instruction:
How can you generate a soft random geometric graph with 100 nodes, where the nodes are joined with a given probability following an exponential distribution based on their Euclidean distance, which must be at most 0.2, and output the graph as a JSON object containing the nodes and edges with labels?
### Response:
import networkx as nx
import numpy as np
from scipy.stats import expon

# Define the number of nodes, probability radius, and dimension
n = 100
radius = 0.2
dim = 2

# Define the exponential distribution function
rate_lambda = 1
p_dist = lambda dist: expon.pdf(dist, scale=1/rate_lambda)

# Generate the graph
G = nx.soft_random_geometric_graph(n, radius, dim=dim, p=0.5, p_dist=p_dist)

# Assign positions to nodes for visualization
pos = nx.get_node_attributes(G, 'pos')

# Optionally, visualize the graph using matplotlib
# import matplotlib.pyplot as plt
# nx.draw(G, pos, node_size=50)
# plt.show()

# Create a JSON object for the graph nodes and edges
nodes = [{'id': node, 'label': str(node)} for node in G]
edges = [{'source': u, 'target': v, 'label': str(u) + '-' + str(v)} for u, v in G.edges()]
graph_json = {'graph nodes': nodes, 'graph edges': edges}

# Print the JSON object
print(graph_json)
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