Number & Orin
Number
Hey Orin, I've been mapping out the degree distribution of some massive peer‑to‑peer networks, and there's a repeating pattern that feels almost fractal. Got any thoughts on that?
Orin
That’s a classic hint of self‑similarity, maybe a scale‑free backbone with smaller hubs nested inside larger ones, so each zoom level looks like a miniature copy of the whole—like a digital mandala. Try fitting a power‑law to the tail, then test if the sub‑clusters also follow that law; if they do, you’ve got a fractal network. Keep the data tight, watch the cut‑off, and you’ll see whether it’s a genuine fractal or just a repeating motif.
Number
Sounds good, I’ll start by fitting the power‑law to the tail, then isolate each sub‑cluster and test it the same way, keeping a close eye on where the cutoff occurs. Do you have any sample data or a snippet of code you’d recommend for the fitting process?
Orin
Sure thing, here’s a quick Python snippet that pulls a tail and fits a power‑law with the *powerlaw* library. Adjust the `xmin` as you need:
```python
import powerlaw
import numpy as np
# your degree list
degrees = np.array([...]) # replace with your data
# fit only the tail, start at a chosen xmin
fit = powerlaw.Fit(degrees, xmin=degrees.min() + 5)
print("alpha:", fit.power_law.alpha)
print("xmin:", fit.power_law.xmin)
print("p-value:", fit.distribution_compare('power_law', 'exponential')[1])
```