Hello, folks! I've made one more step in further BCN/CN research.
I've analyzed two years old bulk of transactions in Bytecoin and here's the result.
Full text (.pdf):
http://www.filehosting.org/file/details/451593/txan.pdfInitial Data- 500k of blocks from 2012-07-04 to 2014-06-10
- 210k of transactions
- 4m inputs
- 2.7m outputs
Glossary- blockId - number of the block
- amount - total inputs (defined as transfer+change)
- mixinCount - size of the ring signature, level of anonymity (1 - min)
- transfer - estimated amount of transaction
- change - estimated amount of change
Note: normally the transfer is half as much as the amount (the reason for this is a simplistic algorithm of change calculation), therefore majority of transfer charts will be looking very similar to amount charts
(with coefficient 2 on one of the scales). Most of the times when transaction is mentioned the reader should perceive the notion as amount, although a few exceptions may occur.
All the figures are expressed as 10
12 of BCN atomic units. The reward amount for the early blocks if calculated in such units equals 70.
Amount of funds in transactions
Firstly, let's look how the amounts are distributed over the periods of time. The first chart shows the number of amounts below 300. There are approximately
198k of those (93.4%)The highest points represent the round amounts, those are sent and received more frequently. The rest of the amounts form a Chi-squared distribution with 5-8 degrees of freedom. It's hard to say whether this
distribution is normal or not. However seeing the straight horizontal line on this chart would have been more surprising.
It is worth mentioning that we are looking at input amounts as opposed to transfer amounts i.e. the available funds that are used to form a transaction. The most popular sizes of amounts are residing within
30-60 region, which corresponds to the average block size for the first 1.5 years. Based on these figures we may conclude that either users transferred freshly mined coins to the wallets for safekeeping (e.g. cold
storage) or spent them right away - it is clear that
the majority of the blocks were spent entirely in the first 1.5 years.Now let's take a look at the tail distribution (amounts from 500 to 1000)
Here we can observe an interesting pattern that goes by the name
Benford's Law : in decimal fraction of a number, 1 will be more persistent than 2, 2 more persistent than 3 and so on. Perhaps there's some sort of mystery since we are not seeing the same pattern on the previous chart. The number of large transactions is marginal; perhaps they were executed by different type of users? It is also clear that the same pattern will be present for large amount transfers distribution.
And this is an almost complete distribution of all amounts.
Here we can see that the large amounts distribution does not t the overall pattern. If there was one unifying principle, the Benford's law pattern would have been applicable to smaller round amounts, which is not the case. It can therefore be deduced that
the large transactions belong to a separate class of users whereas smallish transactions are random and may have resulted as online purchases of goods or debt settlements or whatever.
Here is the distribution of transaction amounts
Analysis of the transactions that were executed in the first 1.5 years showed that
the most frequently spent amounts are ranging from 1 to 3 blocks in size. The tail contains 21K of transactions namely 10% (nearly all of them below 1500).
Now let's look at the distribution of transfers below 300. There the picture is not clear and distribution is not even. It becomes more obvious if you look closely at amounts below 120:
It seems that if the amount of change could be more precisely calculated it would have been easier to draw a conclusion on the types of expenditures that had taken place. So far we can see a signifi cant increase
in low volume transactions (with amounts around 5). It resembles the one-time transfers to friends to try out the new coin while the larger chunk of transactions is concentrated far back on the time line.
Timeline Intervals
Here is 4 charts with 10K, 50K, 100K and 150K transactions. And here is one more: all of them below 300.
It is clear that preceding transactions are more evenly distributed. One possible explanation is that they were conducted as testing transactions to provide sufficient amount of outputs for future ring signatures. After that the final distribution has started to grow.
One can draw a conclusion that as the first chart shows
the number of users has started to grow steadily. There is no need for transfers chart since the idea there is similar. Although certain increase in low volume transactions (5) is visible.
Now we'll try to compare the increase in transactions for different time periods. The oldest 30K transactions are the first to be examined.
Familiar pattern. Let's call it 'the first wave users'. And here is a chunk of recent 30K transactions:
Here we can see a significant change. Input compilation has become chaotic as it were. What is the reason for it? Could be a source code alteration or perhaps an increase in number of users:
emergence of 'the second wave users' or possibly new services with automated remittance processing. The number of transactions is also increased and that is what we are going to look into.
Trends
This is the number of transactions that simply grew with time.
Obviously at the beginning a lot of transactions were made to create enough ring signatures for future transactions. Eventually this number has dropped leaving only the transactions created by users. Leaving out the two consecutive surges of transactional activity it is clear that
the number of transactions indicates that the number of real users grew.
Here is one more interesting detail: the way the average transaction amount changes with time
It seems pretty even but recently the average has dropped sharply. On the other hand a lot of larger transactions reappeared.
And surprisingly, there used to be very few larger transactions before. It could have been an imposed limitation on transaction size that subsequently was withdrawn. Then it makes sense why at some point the number of larger transactions soared. So why impose a limit in the first place? It might have been due security considerations. And the reason to pull it back is growing popularity and users' demands.
Here is a chart for change in the average transaction amount.
Decrease is insignificant but worth mentioning. It looks like part of the transactions with smallish amounts has grown to be the size of the larger ones. It also happened at the time of 'the second wave users' emergence.
In conclusion let's see how anonymous the transactions were.
This chart shows AD values that were normally used. The tail is very short. Now let's look at the changes.
This chart shows the volatility of average amounts and possible limitations and also
proves the theory of new users influx.
Conclusions1. At the very beginning (the first 10 transactions) the circle of users was very small and some of the transactions were made deliberately (manually or automatically, doesn't matter) to increase the number of ring signatures.
2. Subsequently we can see all sorts of dynamics: increase in number of transactions, amounts distribution, level of anonymity variations and so on. Three stages can be singled out or perhaps even more. The beginning of each stage can be linked with the influx of new users. These users break down to classes of users with specific patterns of behavior.
3. The most common input amounts coincide with average reward for mining a new block. Therefore it is likely that the coins had been in circulation from the very beginning and not stored in coinbase.
4. Expenditure analysis is hardly possible because of the imperfection of change calculation algorithm as well as ambiguous transaction amounts. New heuristic must be put in place to help unveil the new
facts about the early transactions.
5. The other hindering aspect for conducting successful analysis is the fact that we don't know how many changes have been introduced to the source code over the last 2 years. If the source code alterations indeed took place in the past then perhaps we are missing even more details than we can think of.
6. Overall, Bytecoin's blockchain provides some data to analyze users' behavior, but still doesn't reveal anything in particular except for very general patterns.
What do you think about it?
