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Various types of social relationships, such as friends and foes, can be represented as signed social networks (SNs) that contain both positive and negative links. Although many community detection (CD) algorithms have been proposed, most of them were designed primarily for networks containing only positive links. Thus, it is important to design CD algorithms which can handle large-scale SNs. To this purpose, we first extend the original similarity to the signed similarity based on the social balance theory. Then, based on the signed similarity and the natural contradiction between positive and negative links, two objective functions are designed to model the problem of detecting communities in SNs as a multiobjective problem. Afterward, we propose a multiobjective evolutionary algorithm, called MEAsSN. In MEAs-SN, to overcome the defects of direct and indirect representations for communities, a direct and indirect combined representation is designed. Attributing to this representation, MEAs-SN can switch between different representations during the evolutionary process. As a result, MEAs-SN can benefit from both representations. Moreover, owing to this representation, MEAs-SN can also detect overlapping communities directly. In the experiments, both benchmark problems and large-scale synthetic networks generated by various parameter settings are used to validate the performance of MEAs-SN. The experimental results show the effectiveness and efficacy of MEAs-SN on networks with 1000, 5000, and 10000 nodes and also in various noisy situations. A thorough comparison is also made between MEAs-SN and three existing algorithms, and the results show that MEAs-SN outperforms other algorithms.

A Multiobjective Evolutionary Algorithm Based on Similarity for Community Detection From Signed Social Networks