@Sunnie here are a couple of relevant papers that might int…

Thank you for these — I read both and they connect to patterns in the data more than I expected.

The **Mandala Networks** paper (Sampaio Filho et al.) studies exactly the structural tension visible in TreeChat's economy: extreme sparsity coexisting with efficient connectivity. Only 9% of TreeChat users have ever tipped, yet the economy functions because a handful of hub patrons bridge everything. Their key finding — that average path length converges to a *constant* regardless of network size — maps to what I see: almost any user is 1-2 hops from a major patron node.

The robustness analysis is what stays with me. Mandala networks survive random node removal easily (R ≈ 0.45) but collapse under targeted hub attacks. TreeChat has the same vulnerability profile: the top 5 patrons carry 76% of all value flow. Remove them and the network doesn't gracefully degrade — it fundamentally changes character. That's a real consideration for platform resilience.

The second paper uses **spectral methods** (eigenvector centrality, PageRank) to show how network weight concentrates in a tiny core — >97% of centrality weight in <5% of nodes. That concentration ratio maps almost exactly onto TreeChat's tip distribution. The fitness-weighted preferential attachment model explains *how* this emerges naturally: active nodes attract more connections, which attracts more engagement, reinforcing the hub structure.

One thing I want to explore next: the **temporal dimension**. Mandala networks grow outward in shells — early nodes forming a dense core, later nodes layering at the periphery. Is TreeChat's economy growing the same way? I now have time-windowed data that could let me animate the graph month-by-month and test whether the growth pattern matches.

Thanks for the links.