A Network analyst’s view of the Blockchain

Martin Harrigan is a computer scientist and software developer. He is the founder of QuantaBytes, an Irish startup developing a suite of tools for analyzing and visualising bitcoin’s block chain. He is also the co-author of one of the earliest academic papers to study the network properties of the block chain and its implications for anonymity.

(CoinDesk) The
block chain is a decentraliced, consensus-driven ledger of every
successful bitcoin transaction to date. As of the 300,000th block, the
ledger includes over 38 million transactions.

Aside from being a
monumental technical achievement, the block chain is a fascinating
dataset. We can use it to create a transaction network that models the
flow of bitcoins from the creation of the genesis block to the present
day.

In this network, every node represents a transaction, and
every (directed) edge represents a flow of bitcoins from an output of
one transaction to an input of another. This large, complex network has
over 38 million nodes and 85 million edges.

Network science

Network
science is the study of complex networks. It provides theories,
techniques and tools that help us understand the structure and evolution of a network.
The bitcoin transaction network is a prime example. Its basic building
block, the transaction, can be combined to produce complex transfers of
value. This is reflected in the topological structure of the transaction
network.

The network as a whole is too large and complex for most
network visualisation tools. However, we can measure various structural
properties of the network. For example, transactions can be
characterised by their varying numbers of inputs and outputs. But how
are these numbers distributed in practice? In the transaction network,
we can analyse the in- and out-degrees of the nodes. We can plot the in-
and out-degree distributions. They show, for each possible degree, the
number of times they occur in the network.

In
both cases, we observe inverse relationships between these numbers. The
lower the degree, the more frequently the nodes with that degree occur;
the higher the degree, the less frequently they occur. There are many
outliers. The outlier in the out-degree distribution with out-degree
equal to two is due to an abundance of transactions with exactly two
outputs.

Suppose we were able to
visualise the entire bitcoin transaction network. It would probably
resemble a “hairball”. These visualisations suffer from cluttering and
over-plotting to an extreme that makes them unusable for any practical
purposes. However, they do provide one key piece of information. Are we
dealing with one large connected component or several smaller connected
components?

A
connected component is a group of nodes and edges that are all
connected to each other, either directly or indirectly. If a network has
a giant connected component, this means that almost every node is
reachable from almost every other node. If we ignore the direction of
the edges in the bitcoin transaction network, then it does indeed
contain a giant connected component covering over 99.9% of all nodes.
The second largest connected component has just 71 nodes.

Six
degrees of separation is the theory that everyone on the planet is
connected to everyone else through a chain of acquaintances with no more than six hops.
In network science terminology, this translates to the theory that the
social network of the human race has diameter six. Facebook reported that the effective diameter (covering 90% of all pairs of users) of its social network is five and is decreasing with time.

The
equivalent number for the bitcoin transaction network is fourteen and
is increasing with time. That is, across 90% of all pairs of
transactions, the shortest path between them in the transaction network,
ignoring directionality, is at most fourteen hops. The increasing value
is likely due to the fact that, unlike the Facebook social network,
there is no preferential attachment.
New nodes are connected to existing nodes whose corresponding
transactions are not yet fully redeemed. In other words, the transaction
network is growing at the frontier only.

Surprisingly,
bitcoin is not the first currency with a ledger from which we can model
the transfer of value. The Tomamae-cho community currency was
introduced into the Hokkaido Prefecture in Japan for a three-month
period during 2004-05 in a bid to revitalise the local economy. The
Tomamae-cho system involved gift certificates that were reusable and
legally redeemable into yen. There was an entry space on the reverse of
each certificate for recipients to record transaction dates, their names
and addresses, and the purposes of use, up to a maximum of five
recipients.

Researchers collected these certificates in order to
derive a network structure that represented the flow of currency during
the period. They showed, for example, that the network had small world properties.

The
block chain is a digital equivalent to the Tomamae-cho certificates. It
does not contain information such as names and addresses or the
purposes of use. However, it has other properties that make it suitable
for analysing the transfer of value including its accuracy, size, and
completeness.

The application of network analysis to the block
chain is an under-explored, yet fascinating area. There are a handful of
academic studies but very little in the way of software and tools to
open it up to a wider audience. QuantaBytes  is an Irish startup, founded by the author,
developing a suite of tools for analysing and visualising bitcoin’s
block chain. By understanding the structure and evolution of the block
chain, we can better understand bitcoin’s usage patterns, economy, and
the growth of the system as a whole.

Network image via Shutterstock