The Rich Still Get Richer

Dynamics of Bitcoin & Ethereum Networks

"Considering the scale of Bitcoin and the many factors influencing transaction dynamics, it is remarkable how well preferential attachment describes its evolution."

Cryptocurrencies present some of the largest real-world complex networks available for study. While much attention is paid to their price volatility, the underlying network structure—who transacts with whom—reveals a surprisingly stable mathematical order.

In our comparative analysis of Bitcoin and Ethereum, we revisited the "Rich Get Richer" phenomenon (Preferential Attachment) using a dataset that covers an almost 100-fold growth period in these networks. We sought to determine if the chaotic market forces disrupted the fundamental laws of network growth.

Universal Scaling Laws

Our results confirm that Preferential Attachment continues to be the key factor driving the evolution of both Bitcoin and Ethereum. New nodes do not connect randomly; they connect with a probability proportional to the existing connectivity of the target.

Graph showing preferential attachment scaling — Fig 1. Empirical proof of Preferential Attachment. The straight lines indicate that the "transformed rank" of connections follows a uniform distribution, confirming that connection probability scales with node degree.

The 100-Fold Robustness:
Despite massive market fluctuations, regulatory changes, and a 100-fold increase in network size, the underlying mechanism of attachment remained constant. The network topology is resilient to external market shocks.

Bitcoin vs. Ethereum

While both networks exhibit power-law degree distributions, we found intriguing nuances in Ethereum's Smart Contracts. Unlike regular user addresses, Smart Contracts show a slightly different attachment exponent.

This suggests that while human behavior (represented by regular addresses) follows the classic "Rich Get Richer" dynamic, automated agents and decentralized applications (Smart Contracts) may follow a "Recency" model, where recent activity is as important as total accumulated connectivity.

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Reference: Kondor, D., Bulatovic, N., Stéger, J., Csabai, I. & Vattay, G. (2021). The Rich Still Get Richer: Empirical Comparison of Preferential Attachment via Linking Statistics in Bitcoin and Ethereum. Frontiers in Blockchain, 4:668510.