## 1 Introduction  
Bitcoin is a decentralized cryptographic currency system, proposed by [PERSON] [1]. Based on a peer-to-peer (P2P) architecture, Bitcoin users are able to issue transactions carrying payments in bitcoins. To provide some form of anonymity, direct personally identifiable information are omitted from any transaction; instead, source and destination are encoded in the form of public keys, which serve as pseudonyms. Every party can generate as many public keys as he wishes; the corresponding private keysare used to authenticate (sign) transactions and are stored in private wallets either locally on a user's computer or in cloud-storage providers. In order to use Bitcoin, one must run a client software that is able to communicate with other nodes (peers) based on a standardized protocol. The official client is the [PERSON] client [2], but several other clients have been developed since Bitcoin emerged. Transactions are broadcast by the Bitcoin client into the peer-to-peer system and get definite (confirmed) once they are added to the \"block chain\"--a hash chain containing blocks of all (signed) transactions since the existence of Bitcoin. Peer discovery takes place either through a private database of known peers or through a public IRC channel. By design, there is no central instance that could check all transactions for validity (such as looking for traces of double spending attacks); every node in the network is required to do so once its Bitcoin client receives new incoming transactions. Indeed, the possibility of double-spending attacks against Bitcoin has been shown in [3] for fast payments. For verification purposes, the block chain is public knowledge and stored in all Bitcoin clients today. Generating a new block is a computationally expensive operation, requiring a \"proof of work\" based on the concept of Hashcash [4], initially proposed to limit e-mail spam by requiring the sender to spend some CPU time in order for the mail to be accepted by the receiver. The central idea of a proof of work is to make it expensive for a single peer to rewrite the history of transactions once it has been accepted as definite. The proof of work system requires choosing a nonce for each block in a way that the hash of the block together with the nonce contains a number of preceding zeros. The number of zeros (and thus the complexity of finding such a nonce through brute force) varies and is adapted periodically. Peers who devote computation resources to block generation are issued a reward; block generation is called bitcoin mining. Only limited information is available on the graph structure of the Bitcoin P2P network, as it is formed dynamically and a client only has knowledge of the peers to which its client is connected to. In contrast, the graph of all transactions can be re-constructed accurately from the publicly available block chain: the nodes of the graph correspond to Bitcoin addresses and the edges to transactions performed between these addresses. Some basic facts on the structure of this graph were published by [PERSON] and [PERSON] [5] and recently by [PERSON] and [PERSON] [6]. The structure and the dynamics of the graph play a key role to assess the level of anonymity each Bitcoin user enjoys. Two studies investigated the complexity of de-anonymizing a Bitcoin user: [PERSON] and [PERSON] [5] focused on an exemplary case study and [PERSON] _et al_. [7] relied on simulations that faithfully mimic the usage of Bitcoin in a closed community. In this paper, we empirically study important global properties of the Bitcoin transaction graph. For our analysis, we used the data of the Bitcoin block chain up to block number 215,399, which was created on 6 January 2013. In contrast to existing works, we focus on the time evolution of these properties since the emergence of Bitcoin in order to capture the dynamics of the transaction network.