This work was supported by National Cryptography Development Fund (GrantNo.MMJJ20180412).
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Figure 1
Bitcoin transaction. (a) Bitcoin transaction diagram; (b) multi-input transaction diagram; (c) coinbase transaction diagram; (d) change address diagram.
Figure 2
(Color online) System model of transaction analysis.
Figure 3
(Color online) Address transaction relationship diagram.
Figure 4
(Color online) The user incidence relation diagram (different colored addresses belonging to different subcommunities).
Figure 5
(Color online) Different data group results.
Figure 6
(Color online) Different iteration results.
Figure 7
(Color online) Different heuristic method results.
Figure 8
(Color online) Runtime comparison between the Louvain and improved Louvain algorithms.
Figure 9
(Color online) Increase of $\triangle~Q$ with the improved Louvain algorithm.
Initialize $S=\{s_{1},~s_{2},~\ldots,~s_{n}\}$; |
Acquire $s_{k}$ page data; |
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Store the addresses; |
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Find the associated URL from the user's URL; |
Save URL of page to $S$; |
Initialize address set $A=\{a_{1},~a_{2},~\ldots,~a_{n}\}$, $k\leq~n$; |
Initialize transaction set $T=\{t_{1},~t_{2},~\ldots,~t_{n}\}$; |
Acquire data of the address transaction to save to $A$; |
Acquire $s_{k}$ page data; |
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Addresses outputted to save to $A$;ELSIFone of Output$(t)$ belongs to a known mining pool and number of Output$(t)~\geq~100$ |
Addresses outputted to save to $A$; |
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Addresses inputted to save to $A$; |
Judge change address to save to $A$; |
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Initialize transaction data set txLsit; |
Initialize a mapping set of address and cluster labels ${\rm~addr}\_{\rm~label}$; |
Initialize temporary address set tempList and temporary label ${\rm~tempLabel}=0$; |
Take the transaction ${\rm~TX}_{n}$ out of txList; |
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Extract all output addresses from ${\rm~TX}_{n}$ and add them to the collection tempList; |
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Take an undetected address from tempList; |
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The label corresponding to this address is written to tempLabel; |
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The address is written back to tempList; |
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Write all the addresses in tempList to ${\rm~addr}\_{\rm~label}$ and assign the same label to those addresses; |
${\rm~addr}\_{\rm~label}$+; |
Initialize $G$; |
Calculate the module value $Q_{1},~Q_{0}~=~Q_{1}$; |
$Q_{2}~=~Q_{1}$; |
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Put vertex $V_{i}$ to the community connected with it; |
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Take vertex $V_{i}$ out of original community; |
Put $V_{i}$ to community with largest $\Delta~Q$; |
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Calculate the module value $Q_{1}$; |
Go to step 2; |
Combine the various communities into one hyperdot. |
Initialize $G$; |
Check node $V_{i}$ of every community connecting outside; |
Check node $V_{j}$ with highest degree in every community; |
Adopt K-medoids algorithm; |
Calculate distance value $D_{ij}$ of every $V_{i}$ and every $V_{j}$; |
Calculate minimum value of $D_{ij}$; |
$V_{i}$ save to community of $V_{j}$. |