在有號網路(signed network)中，鏈結的符號分為正與負；若兩個人中間的鏈結為正，代表這兩人是朋友關係，若兩個人中間的鏈結為負，這兩人便是敵人關係。由平衡定理(balance theorem)可得到：「朋友的朋友即為朋友」、「敵人的敵人即為朋友」、「朋友的敵人即為敵人」等結論。藉此，我們便能根據彼此的鏈結關係，將有號網路的每個人歸類成大大小小的社群。根據Harary's theorem：如果可以將一個圖(graph)分為兩群，則圖中每個迴圈負號的鏈結個數會是偶數。假設在兩個社群中，存在被分錯的節點，則便會有迴圈不符合「擁有偶數個負號鏈結」這個條件。這裡我們引用錯誤更正碼中的奇偶值校驗法，將錯誤的鏈結更正，藉以更正節點的隸屬社群。在此，我們導入了三種錯誤更正的方法：一、位元反向(Bit-Flipping) 二、低密度奇偶檢查碼(Low-densityparity-check code，LDPC code) 三、漢明距離(Hamming distance)，透過以上的方法，我們希望可以正確解出鏈結的正負號。

In this paper, we consider the community detection problem in signed networks, where there are two types of edges: positive edges (friends) and negative edges (enemies). One
renowned theorem of signed networks, known as Harary's theorem, states that structurally balanced signed networks are clusterable. By viewing each cycle in a signed network as a parity-check constraint, we show that the community detection problem in a signed network with two clusters is equivalent to the decoding problem for a parity-check code. We also show how one can use three renowned decoding algorithms in error-correcting codes for community detection in signed networks: the bit-flipping algorithm, the belief propagation algorithm, and the Hamming distance algorithm. In particular, the Hamming distance algorithm is shown to be equivalent to an optimization problem that can be heuristically solved by using the fast unfolding algorithm for community detection in unsigned networks. It can also be extended to signed networks with more than two
clusters. We compare the performance of these three algorithms by conducting various experiments with known ground truth. Our experimental results show that the Hamming distance algorithm outperforms the other two.

1 Introduction 4
2 Signed Networks 7
3 Community Detection 9
3.1 Parity-check codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 basis and parity check codes . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 The bit-
ipping algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 The belief propagation algorithm . . . . . . . . . . . . . . . . . . . . . . 14
3.5 The Hamming distance algorithm . . . . . . . . . . . . . . . . . . . . . . 18
3.6 Extension to more than two clusters . . . . . . . . . . . . . . . . . . . . . 20
4 Experimental Results 22
1
4.1 Community detection with two communities . . . . . . . . . . . . . . . . 22
4.2 Community detection with more than two communities . . . . . . . . . . 25
4.3 Community detection with a real dataset . . . . . . . . . . . . . . . . . . 27
5 Conclusion 29

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