Google matrix of Bitcoin network

TL;DR

This paper constructs and analyzes the Google matrix of Bitcoin transactions from 2009 to 2013, revealing community structures and wealth concentration among users.

Contribution

It introduces the Google matrix analysis of Bitcoin network, highlighting its spectral properties, community structures, and wealth distribution characteristics.

Findings

Spectrum exhibits an unusual circle-type structure.

Hidden communities of nodes are identified.

Wealth is concentrated in a small fraction of users.

Abstract

We construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics including the PageRank and CheiRank probability distributions, the spectrum of eigenvalues of Google matrix and related eigenvectors. We find that the spectrum has an unusual circle-type structure which we attribute to existing hidden communities of nodes linked between their members. We show that the Gini coefficient of the transactions for the whole period is close to unity showing that the main part of wealth of the network is captured by a small fraction of users.