ELTE Bitcoin Project website and resources


In this project, we download and analyze the list of transactions from the Bitcoin digital currency system. Bitcoin is an innovative system based on a peer-to-peer network of users connected over the Internet. You can read more about it and the technical background on its website or in the original paper. The most radical difference from traditional financial systems (e.g. banks) is that in Bitcoin, every transaction is made public to anyone who participates in it. You can access the complete history of transactions with any of the several available Bitcoin clients. Or as a simpler alternative, you can obtain it from third-parties, including us, or from the blockchain.info website, where you can browse it online. To provide some privacy to users, the sender and recipient are identified by their Bitcoin addresses (a seemingly random string of about 35 characters, e.g. 1KQZ2mvcZMLmJA6mBNv8QvkhD5vtYPavg1), of which anyone can create any number for themselves on their computer. This way, it is very hard to infer who is behind a specific address. Even with this limitation, the Bitcoin transaction history provides a unique opportunity for network scientists and econophysicists to study the movement of money in detail.

When scientists make models of the economy, they usually start from interacting "agents", who correspond to the people participating in financial activities. The behavior of these agents is determined by the parameters of the model; usually, modelers prefer simple rules and hope that the interactions can then lead to the complex behavior observed in the real world. With the model at hand, the next step is to investigate its behavior by performing computations and simulations. Ultimately, the model's predictions need to be checked on real-world data. However, this validation is limited by the available data; while general statistics, e.g. the distribution of wealth or incomes can be compiled for the real society (think e.g. about the 99% protests against inequality), more detailed, "microscopic" mechanisms cannot be directly checked due to most financial data being regarded as confidential. E.g. it is very hard to obtain realistic large-scale datasets about everyday monetary transactions, as you would expect your bank not to share your account's history with anyone. We believe that the Bitcoin transaction network is the only dataset that contains detailed information about monetary transactions and is publicly available for anyone to analyze. Of course it is different from a traditional currency (actually, the analysis of similarities and differences to traditional currencies is an ongoing research project in our group), but yet it presents a unique opportunity to test and improve econophysics models on a very detailed level. In the following we introduce two research projects which we believe are only the very beginning of exploring the new possibilities.

Do the rich get richer?

The short answer is: yes! At least that's what the history of Bitcoin suggests. The results presented here appeared in PLOS ONE:
Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network. Kondor D, Pósfai M, Csabai I, Vattay G (2014). PLOS ONE, 9(5): e97205.
An extended version based on updated data is available as Chapter 4 in Daniel Kondor's PhD thesis, "Empirical analysis of complex social and financial networks"

The perception that the "rich get richer", also sometimes referred to as the Matthew-effect after a biblical verse seems to be well established in society. From a modeling point of view it can thought as that someone who is already better established has more and better opportunities to gain more wealth, thus the total inequality increases. In the context of networks, this was the motivation of the preferential attachment model. In this case, instead of wealth, the participants of a network gain new connections with a rate proportional to their number of previous connections; this results in that already better connected nodes gain more links over time than others. The outcome of this process is the so called power-law distribution of degrees (the number of connections each node has), with a few nodes with very high number of connections ("rich club") and most nodes with only a relatively limited number of connections.

In the case of Bitcoin, we can keep track of participants' (represented by their Bitcoin addresses) balance and also their network degree (i.e. how many distinct transaction partners they had previously). We can ask the question how these quantities change over time, and test if preferential attachment is present in either the network dynamics or wealth accumulation. Since we have the details of each transaction, we can analyze the statistics of new link formation, and test the hypothesis if nodes with larger wealth or degrees are favored as transaction recipients. We found that this is indeed true, preferential attachment holds for both network degrees and balances. Note that initiators of the transactions generally do not base their decisions on the network degree or the wealth of their potential transaction partners (even though in the case of Bitcoin they could compute these measures themselves), rather on other, more relevant factors (e.g. they want to buy goods or services). In spite of this, through possibly nontrivial mechanisms, already larger players in the Bitcoin system are chosen to receive bitcoins more commonly, i.e. they are more attractive in common terms.

This is complemented by a simple statistic of the growth of address balances: in the figure on the left the growth in one month is displayed as a function of the balance at the start of the given month. While the points are scattered, we can see a clear correlation. Apart from these "microscopic" properties, the macroscopic properties of the Bitcoin system agree with the hypothesis of preferential attachment: both the distribution of degrees and that of balances show high inequality and can be modeled by power-law and stretched exponential mathematical functions, respectively. Also, the degrees and balances of Bitcoin addresses are correlated; addresses with high degree also tend to have a lot of bitcoins.

Exchange price and network structure
The work presented here appeared in the New Journal of Physics:
Inferring the interplay between network structure and market effects in Bitcoin. Kondor D, Csabai I, Szüle J, Pósfai M, Vattay G (2014). New J. Phys. 16 125003.

A topic of high theoretical and practical interest is the analysis of prices of goods and methods to forecast them. Especially exciting is the price of bitcoins, which has shown great fluctuations since people first started trading bitcoins for conventional money. Just over the course of a year, in 2013, the price experienced an almost 100-fold increase (from around $10 to $1000), to drop back to a few hundred dollars per Bitcoin in 2014. While similarly exciting as any other highly volatile asset, Bitcoin offers a unique opportunity here as well. Since the complete history of Bitcoin transactions is public, we can analyze the network of transactions together with the time series of the price, and test if the two are related. This means that we not only include transactions where bitcoins are traded for conventional currencies, but we look at the general activity in the network. To overcome the limitation presented by the fact that most Bitcoin addresses are short-lived, we use a heuristic approach to aggregate some the addresses which belong to the same user with high probability and select users who are highly active for longer time periods for our analysis. We are currently working on possible ways to improve this method so that we can include a larger portion of Bitcoin transactions in our analyses. We decompose the transaction history among these selected users into a sum of activities of 'base networks' varying over time by a mathematical method called principal component analysis applied on the network time series. This way, we get time series of the contribution of these base network, whose correlation with the exchange price time series is tested easily. The above figure displays the time series of the price and of the contribution of the first 'base network' to the whole, showing high degree of similarity. Also, the price time series is well approximated as a combination of the activity of only a few base networks. This means that the dynamics of the exchange price have a clear fingerprint in the network dynamics. We are now working on improving these methods to gain understanding of the significance of the base networks identified. Also, we are interested if causality can be established between the network dynamics and exchange price, i.e. whether the network activity follows the changes in the price or the other way. Also, we are working on extending models for price forecasting to include information about the network dynamics.

Contact us

Dániel Kondor

dkondor at complex dot elte dot hu Scholar

Márton Pósfai

posfaim at gmail dot com Scholar

János Szüle

szule at complex dot elte dot hu website

István Csabai DSc

csabai at complex dot elte dot hu website Scholar

Gábor Vattay DSc

vattay at elte dot hu Twitter Scholar

All authors currently work at the Eötvös Loránd University, Budapest, Hungary. DK, MP and JS are PhD students aiming to earn their degrees very soon, IC and GV are full professors. All authors' research interests include data mining and modeling on large network datasets including the analysis of the navigability of the network of Twitter users and other large-scale studies using Twitter messages. DK is also currently doing an internship at Ericsson Research in Budapest, where he is involved in the Signature of Humanity project. MP's research is mainly focused on network controllability with a focus on temporal networks. IC is also interested in bioinformatics with a focus on large-scale analysis of next genome sequencing data.