Islands of money

[CliffordM]

Given the entire block chain is freely available, has anyone thought of analysing the topology of the currently available coins?

Every time there is a transaction, two addresses get joined, with the coins flowing into the target address.  Transactions form an equivalence relation, so we can compute the resulting equivalence classes AND the total number of coins in each class.  Coins that have been mined but not yet spent would exist in their own class,  whereas coins that have been spent a few times would belong to a much bigger pool.

Pooled mining is going to smear a lot of these classes into what is likely to be a monster central class,  but it would be interesting to know how many tiny satellite classes exist ... Ie how many coins are minted, but not yet entered circulation.

[PrintCoins]

It would make an interesting graphic.

Addresses could be used to pick colors.

[evoorhees]

I wish I were smart enough to know what you're talking about, but it sounds interesting!

[fornit]

since many services and users use a new address for every transaction and there is no indication in the blockchain which addresses belong to the same wallet, you would end up with way to many classes.

[CliffordM]

The maximum number of classes would be the number of blocks mined, but I would guess that a very large amount of these classes would be joined by subsequent transactions.  The entire point of the analysis is to understand this distribution, and how it might change over time.  Completely unspent virgin blocks of course would be quite interesting in themselves as they have yet to enter the commerce foodchain.

There are probably better ways of analysing this data (eg use the directional nature of the transactions as opposed to the symmetric approach outlined), but we need to understand how money is being moved around the system to improve our knowledge of the economy...

[LightRider]

http://www.youtube.com/watch?v=rJN0Hm3srUc

This should interest you. But I wouldn't pay too much attention to their ideas about having to create more bitcoins in the future due to data loss. He apparently doesn't understand the point.

[pharcyde]

Every time there is a transaction, two addresses get joined, with the coins flowing into the target address.  Transactions form an equivalence relation, so we can compute the resulting equivalence classes AND the total number of coins in each class.  Coins that have been mined but not yet spent would exist in their own class,  whereas coins that have been spent a few times would belong to a much bigger pool.

I'm a little confused on your definition or possibly your explanation of why it's an equivalence class. Everyone else, please pardon the jargon. Let X be the set of all addresses. Let's use ~ to denote a relation. I think this is your definition of the relation: Let a,b be in X; a~b if and only if there exists a transaction between a and b. Using this definition, I don't see how it's an equivalence class; specifically, I don't see the reflexive nature or transitive nature of the relation. Let me explain a little. For three addresses, let's assume a~b and b~c. This means that addresses 'a' and 'b' had a transaction and so did addresses 'b' and 'c'. However, this doesn't dictate that addresses 'a' and 'c' had a transaction, so this seems not to be transitive. In addition the relation seems not to be reflexive; I and other's have many addresses that have yet to be used in a transaction. Even if we changed X to be the set of all addresses used in a transaction, not all addresses send coins to themselves (or at least with my understanding of bitcoins, this is not how it works).

This is not a, "you're doing it wrong", type reply. I'm interested in your thoughts, but I think I'm misunderstanding what you're writing. Could you clarify a bit on your definition or how it's and equivalence class? I think it's an interesting idea to involve equivalence classes.

[bg002h]

Every time there is a transaction, two addresses get joined, with the coins flowing into the target address.  Transactions form an equivalence relation, so we can compute the resulting equivalence classes AND the total number of coins in each class.  Coins that have been mined but not yet spent would exist in their own class,  whereas coins that have been spent a few times would belong to a much bigger pool.

I'm a little confused on your definition or possibly your explanation of why it's an equivalence class. Everyone else, please pardon the jargon. Let X be the set of all addresses. Let's use ~ to denote a relation. I think this is your definition of the relation: Let a,b be in X; a~b if and only if there exists a transaction between a and b. Using this definition, I don't see how it's an equivalence class; specifically, I don't see the reflexive nature or transitive nature of the relation. Let me explain a little. For three addresses, let's assume a~b and b~c. This means that addresses 'a' and 'b' had a transaction and so did addresses 'b' and 'c'. However, this doesn't dictate that addresses 'a' and 'c' had a transaction, so this seems not to be transitive. In addition the relation seems not to be reflexive; I and other's have many addresses that have yet to be used in a transaction. Even if we changed X to be the set of all addresses used in a transaction, not all addresses send coins to themselves (or at least with my understanding of bitcoins, this is not how it works).

This is not a, "you're doing it wrong", type reply. I'm interested in your thoughts, but I think I'm misunderstanding what you're writing. Could you clarify a bit on your definition or how it's and equivalence class? I think it's an interesting idea to involve equivalence classes.

...does anyone else hear Simon & Garfunkel playing?

1DrGossc3QidjzgDXzveCAQGiPWsoiDZ8C

[CliffordM]

By my definition if a and b are addresses (public keys),  and coins flow from a to b then a~b and b~a (all I want to capture is that a is linked with b).  a~a in a rather trivial fashion, and also if a~b and b~c then my definition means that a~c .  So 'by definition' it is an equivalence relation.  It's a rather simple one which admittedly doesn't capture the directional nature of coins moving from a to b but  computing the equivalence classes might show up some interesting structure.

My guess is that there is one huge monster class representing most of the addresses, and a lot of singleton classes (unspent mining rewards), but there might be some larger satellite classes too.

One question I have is if there are fees paid in a particular block, are those fees shown as separate from the fixed reward ?

[westkybitcoins]

One question I have is if there are fees paid in a particular block, are those fees shown as separate from the fixed reward ?

Yes.

The fees are yet another relation from one (or more) input addresses, but linking them to the address(es) that the generation block outputs to. A block with 2.5 bitcoins in fees will result in a generation block output that's actually 52.5 bitcoins rather than 50 bitcoins.

Curiously, the link is effectively meaningless, because while it shows money flowing from address to address, the flow is a consequence of the operation of the network rather than an actual transaction (money for good/service) between individuals.

That also has me questioning the utility of this at all. For example, I wonder how many transactions on average, both spends and receipts, one has to engage in before, just by sheer luck, getting back coins that you originally spent. With the existence of exchanges, there's probably no way to show or know this, but it adds a further wrinkle to the plan. If in general the number of transactions is not too large, it suggests that bitcoin analysis may be futile (at least, if the person obscures their transactions through a certain number of "hops".)

There are probably better ways of analysing this data (eg use the directional nature of the transactions as opposed to the symmetric approach outlined), but we need to understand how money is being moved around the system to improve our knowledge of the economy...

Do we? I'm not so sure. I see downsides to attempting this sort of analysis, but apparently, it may not be feasible anyway.

[mc_lovin]

This would be a cool graphic to see once all 21 million coins are out there, and it could be a "complete" island thing.