Bitcoin system (or Bitcoin) is a peer-to-peer and decentralized payment system that uses cryptocurrency named bitcoins (BTCs) and was released as open-source software in 2009. Unlike fiat currencies, there is no centralized authority or any statutory recognition, backing, or regulation for Bitcoin. All transactions are confirmed for validity by a network of volunteer nodes (miners) and after collective agreement is subsequently recorded into a distributed ledger “Blockchain”. Bitcoin platform has attracted both social and anti-social elements. On the one hand, it is social as it ensures the exchange of value, maintaining trust in a cooperative, community-driven manner without the need for a trusted third party. At the same time, it is anti-social as it creates hurdles for law enforcement to trace suspicious transactions due to anonymity and privacy. To understand how the social and anti-social tendencies in the user base of Bitcoin affect its evolution, there is a need to analyze the Bitcoin system as a network. The current paper aims to explore the local topology and geometry of the Bitcoin network during its first decade of existence. Bitcoin transaction data from 03 Jan 2009 12:45:05 GMT to 08 May 2020 13:21:33 GMT was processed for this purpose to build a Bitcoin user graph. The characteristics, local and global network properties of the user’s graph were analyzed at ten intervals between 2009 and 2020 with a gap of one year. Small diameter, skewed distribution of transactions, power-law distributed in and out degrees, disconnected graph, and presence of large connected components were the observations from network analysis. Thus, it could be inferred that despite anti-social tendencies, Bitcoin network shared similarities with other complex networks. Network analysis also uncovered twenty types of legal and anti-social entities operating on Bitcoin and provided a path for uncovering these anti-social entities.

۱٫ Introduction

Originally proposed in 2008 by an unknown individual (or a group of individuals) who used a pseudonym ”Santoshi Nakamoto”, Bitcoin cryp tocurrency has since then emerged as the most successful cryptocurrency amongst its peers, reaching an adoption level unrealized by older digital currencies [1, 2, 3]. As on 19th March 2020, Bitcoin has a market cap of USD$98,584,789,143 with 18,277,112 bitcoins (BTC’s) in circulation each with a value of USD$5,393.89. Bitcoin differs from its traditional online banking peers by relying on a decentralized consensus scheme for verifying the correctness and authentic nature of currency transfers between users [4, 5, 6]. The decentralized consensus scheme is made possible by an ganized collective of nodes in the Bitcoin system known as “miners”. The miners confirm each transaction for authenticity. This increases security in the Bitcoin system and ensures the core philosophy of Bitcoin ”Maintain trust in an untrusted environment” without the need for a trusted third party as a reward miners collect transaction fees for the transactions that they confirm. Illustrating the transaction fundamentals of bitcoin transfers, consider that user i wants to transfer n bitcoins to user j. Then i will need a bitcoin wallet, which holds all his private keys and the wallet address of j (Figure 1). Also, the transaction is valid only if user i signs it using his cryptographic key.