<｜begin▁of▁sentence｜>### Instruction:
Imagine you're overseeing a swim class and each of your 10 swimmers could potentially pair up with any other to practice relay races. The likelihood of any two swimmers pairing up is much like the way water flows, uneven and influenced by various factors—consider this like a "kernel function." I'd like you to create a buddy system based on this principle where, on average, every swimmer ends up with about 5 partners, just as in a well-coordinated swim team where each swimmer practices with a few others. Picture this as a network of swimmers, and let's sketch out this buddy system visually, using something similar to a pool lane diagram, but in our case, it'll be done with NetworkX, a tool that helps us draw out these intricate connections. How does that sound?
### Response:
import networkx as nx
import scipy.optimize

# Define the kernel integral function
def integral(u, w, z):
    c = 5 # mean expected degree
    return c * (z - w)

# Define the kernel root function
def root(u, w, r):
    c = 5
    return r / c + w

# Generate a random graph using the specified kernel
n = 10 # number of nodes
graph = nx.random_kernel_graph(n, integral, root)

# Draw the graph
nx.draw(graph, with_labels=True)
<|EOT|>
