# Evaluating Methods for the Identification of Off-Chain Transactions in the Lightning Network
## 5 Results
### Linking  
The linking of channels was done, both on the set of channel graphs found on the blockchain during the LN collection intervals, and the sets of channels found when doing complete runs as described in Section 5.4. In Table 3 we can see the findings in regards to the key reuse when checking the channels graphs for testnet and mainnet found during the complete runs. Using the 3809 channels we found on the mainnet, we extracted a total of 26,824 unique keys from the transactions in the graphs, with 1370 or 5.1% of these being found multiple times. These keys combined where reused 2850 times, which if the key reuse was evenly distributed in the channel graphs, each channel graph would have 0.75 keys used in another channel graph. For the 8047 channels found on the testnet, we got 50,050 unique keys. The results here are very similar to the mainnet, with 6.5% of the keys found were reused, and 0.9 reused keys per channel graph if they were equally distributed. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Mainnet** & **LN Mainnet** & **Testnet** & **LN testnet** \\ \hline Sample size (channels) & 3809 & 715 & 8047 & 251 \\ Average Channel value & 0.00439556 & 0.0023375 & 0.07086336 & 0.07758942 \\ Median channel value & 0.001 & 0.0005 & 0.005 & 0.06 \\ Standard Deviation Channel value & 0.01384113 & 0.00586706 & 0.07067473 & 0.07191958 \\ Average channel lifetime & 1600 & 1940 & 2441 & 1269 \\ Median channel lifetime & 693 & 1836 & 433 & 312 \\ Standard Deviation channel lifetime & 2183 & 1791 & 5631 & 4059 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Value and lifetime for channels. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Mainnet** & **Testnet** \\ \hline Channels with one input & 69.3 & 76.4 \\ Channels with two inputs & 23.2 & 16.8 \\ Channels with three inputs & 4.5 & 3.8 \\ Channels with more than three inputs & 2.8 & 2.9 \\ Channels with one output & 69.2 & 50.5 \\ Channels with two outputs & 29.6 & 46.3 \\ Channels with three outputs & 0.8 & 2.1 \\ Channels with more than three outputs & 0.2 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentages of input-output count for channels. Our two other heuristics were also used on these channel sets, allowing us to determine how many channels we were able to link. The results of this are shown in Table 4. For heuristic one, where we found directly connected graphs trough outputs-inputs, we have separate results for each possible output which can be the source of such a relationship. We discovered a clear difference between the different outputs: the outputs from the funding transactions make up over 65% of the connections found using heuristic one, both on the testnet and mainnet, compared to 2.1% or less for the outputs from the closing transactions. The outputs from the timelocked transactions make up 30% and 33% of the connections on the mainnet and testnet, respectively. One possible explanation for this difference has to do with the value of the outputs: closing timelocked outputs are used to give one party their value from the channel, meaning the value of these outputs is limited to the channel balance of the participant owning them; outputs from the funding transaction, on the other hand, are used to transfer change resulting from the output spent to fund the channel, which has no size limit, meaning an output many times the value of the channel can be used. Unless multiple inputs are used to fund a channel, creating a new channel using the outputs from another channel, limits the value of the funding input to the balance in the previous channel. A possible reason for the difference between closing and timelocked outputs could be the recommendation to spend timelocked outputs discussed in Section 4.3.