# How to Create a Bitcoin Graph

In this article I will discuss the use of Bitcoin Graphs as an application for private key cryptography. Private key cryptography is a security measure used to prevent attackers from intercepting or reading any other users private keys. A private key is a number, code or address that is used to sign an encrypted transaction. The value of a private key can be derived from its discrete log (a mathematical concept used to calculate the discrete log of a number over time). An attacker would be unable to intercept such transactions because their private keys would have been recorded and kept secret.

Let us imagine that we want to send some transaction data from one computer to another. First we create a network (we could call it a ‘brick’) and then we make a number of single entity addresses. When we then send the transaction data from one computer to the other, we are passing through each brick only once. We can then encrypt the data we are passing through each block with our private key. The data that we are passing through each block (the transaction data) would only be able to be read by the single entity that was passing through that particular block.

Let us now try to reconstruct the Bitcoin Graph using our address data. We need to construct a graph that is constrained between two discrete points. This means that there are at most countable vertices between the two points and the nodes can be thought of as a set of ‘points’. In our example we may have four nodes and our address data will be passed through seven address cells.

To get a good approximation we will want to model time periods as points. By default each time period will be assigned a unique interval. We can model the time period of the transaction by connecting the starting point of the node to every existing edge that is in the graph. We can also model the transac-tion data by connecting the ending point of every outgoing edge to the starting point of the node. This gives us our new graph. Let us addcles to our new directed graph and observe the behavior of a juryman. We can see that the most common way to transfer money from one user to another (the so called ‘offslots’) takes place during the interval when the MTD is above the average value of the currency flows that occur in the previous period. During these periods, most of the trading activity is done in the direction of the current price and the trades are usually successful.

Let us now remove the outliers and focus on the central figures. The range of activities during the period of time when the MTD is above the average can be represented by a curved line representing the range of trading activity. This gives us our central figure, which is the ratio of the number of transactions done during the trading session to the number of currency exchanges carried out during the period. Finally we can add our private key and a smoothed variable that represent the balances between users. hotgraph This completes our first bitcoin example or visualization.