<｜begin▁of▁sentence｜>### Instruction:
Imagine we're working on a community health project and we've designed a square city block (let's say it's perfectly one unit by one unit for simplicity) within which we want to model a network of community members. Our goal is to simulate a network of 100 residents distributed evenly across this block.

Now, we want to understand how information about health services spreads among these residents. To do this, we'll think of residents as being 'connected' if they're close enough, within a distance we'll call the 'radius of communication'. But not every pair of neighbors will actually share information; the likelihood that two residents connect and share health information depends on how far apart they are, following a rule that's similar to how likely you are to catch a cold if someone sneezes near you - it drops off the further away you get.

This likelihood isn't just random; it follows a precise mathematical pattern called an exponential probability density function. To visualize this, we want to create a map showing all our residents as points, and draw lines between them that get fainter as this sharing likelihood decreases. 

Think of it as a map overlaid with a web of potential conversations, where the strongest connections - the most probable ones for information exchange - are the boldest. This map won't be a static image; it'll reflect the dynamic, probabilistic nature of communication we see in real communities.

If we'd like to keep this network for further study, we can store it in a GML file named 'community_health_network.gml'. Now, how could we go about creating this visual representation of our urban health network and save it for ongoing analysis?
### Response:
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import expon

# Define a custom probability density function
def custom_p_dist(dist):
    """Exponential distribution function with rate parameter lambda=1."""
    return expon.pdf(dist, scale=1)

# Generate a soft random geometric graph with a custom distance function
G = nx.soft_random_geometric_graph(100, radius=0.2, dim=2, p_dist=custom_p_dist)

# Get positions
pos = nx.get_node_attributes(G, 'pos')

# Draw the graph
plt.figure(figsize=(8, 8))
nx.draw_networkx_edges(G, pos, alpha=0.4)
nx.draw_networkx_nodes(G, pos, node_size=10)
plt.title('Soft Random Geometric Graph')
plt.show()
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