Theoretical studies of signed social networks based on null models
XU Xiaoke1,2, GENG Xuena1, WANG Xue3
1. College of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, China;
2. Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China;
3. Library of Dalian Minzu University, Dalian 116600, China
Abstract:The structural balance and the status are important issues in social network fields, which can be used to analyze signed social networks with a mixture of positive and negative interactions. In this study firstly three novel random link-mixing null models are proposed. Then the status and structural balance theories of signed social networks are studied based on the random link-mixing null models as well as the random sign-mixing null models. It is shown that, based on null models, not only the accuracy obtained based on both theories can be verified in the study of empirical networks, but also the impacts of the positive and negative edge topologies and the edge signed correlation on the whole network properties can be revealed. Finally, a new framework is proposed to study whether the directed signed networks can be transformed into the undirected signed networks. It is confirmed that the common methods for transforming the directed signed networks into the undirected signed networks are not suitable for studying social network theories, and the potential theory in unsigned directed networks is also studied.
[1] 程苏琦, 沈华伟, 张国清, 等. 符号网络研究综述[J]. 软件学报, 2014, 25(1):1-15. Cheng Suqi, Shen Huawei, Zhang Guoqing, et al. Survey of signed network research[J]. Journal of Software, 2014, 25(1):1-15
[2] Guha R, Kumar R, Raghavan P, et al. Propagation of trust and distrust[C]//Proceedings of Thirteenth International Conference on World Wide Web (WWW2004). New York, USA:ACM Press, 2004:403-412.
[3] Kunegis J, Lommatzsch A, Bauckhage C. The slashdot zoo (mining a social network with negative edges)[C]//Proceedings of Eighteenth International Conference on World Wide Web (WWW2009). Madrid, Spain:ACM Press, 2009:741-750.
[4] 伍杰华. 异构符号网络中正负社交关系的分类预测研究[J]. 情报科学, 2016, 34(1):81-86. Wu Jiehua. Positive and negative social relation classification prediction in heterogeneous signed network[J]. Information Science, 2016, 34(1):81-86.
[5] 胡心专, 郭景峰, 贺释千, 等一种节点相似度和参与度符号网络社区发现算法[J]. 小型微型计算机系统, 2017, 38(10):2275-2280. Hu Xinzhuan, Guo Jingfeng, He Shiqian, et al. Community detection algorithm of node similarity and node participation degree in signed networks[J]. Journal of Chinese Computer Systems, 2017, 38(10):2275-2280.
[6] Heider F. Attitudes and cognitive organization[J]. The Journal of Psychology, 1946, 21(1):107-112.
[7] Leskovec J, Huttenlocher D, Kleinberg J. Signed networks in social media[J]. Human Factors in Computing Systems, 2010:1361-1370.
[8] Davis J A. Clustering and structural balance in graphs[J]. Human Relations, 1967, 20(2):181-187.
[9] Milo R, Itzkovitz S, Kashtan N, et al. Superfamilies of evolved and designed networks[J]. Science, 2004, 303(5663):1538-1542.
[10] Foeter J G, Foster D V, Grassberger P, et al. Edge direction and the structure of networks[J]. Proceedings of the National Academy of Sciences, 2010, 107(24):10815-10820.
[11] Costa L F, Rodrigues F A, Travieso G, et al. Characterization of complex networks:A survey of measurements[J]. Advances in Physics, 2010, 56(1):167-242.
[12] Newman M. The physics of networks[J]. Physics Today, 2008, 61(11):33-38.
[13] Amarll A N, Guimera R. Complex networks:Lies, damned lies and statistics[J]. Nature Physics, 2006, 2(2):75-76.
[14] 陈泉, 杨建梅, 曾进群. 零模型及其在复杂网络研究中的应用[J]. 复杂系统与复杂性科学, 2013(1):8-17. Chen Quan, Yang Jianmei, Zeng Jinqun. Null model and its application in the research of complex networks[J]. Complex Systems and Complexity Science, 2013(1):8-17.
[15] 尚可可, 许小可. 基于置乱算法的复杂网络零模型构造及其应用[J]. 电子科技大学学报, 2014, 43(1):7-20. Shang Keke, Xu Xiaoke. Construction and application for null models of complex networks based on randomized algorithms[J]. Journal of University of Electronic Science and Technology of China, 2014, 43(1):7-20.
[16] 崔丽艳, 许小可. 参照零模型的双层网络结构相关性检测[J]. 科技导报, 2017, 35(14):63-74. Cui Liyan, Xu Xiaoke. Correlation detection of double-layer network based on null models[J]. Science & Technology Review, 2017, 35(14):63-74.
[17] 陈关荣, 汪小帆, 李翔. 复杂网络引论:模型、结构与动力学[M]. 北京:高等教育出版社, 2012:217-218. Chen Guanrong, Wang Xiaofan, Li Xiang. Introduction to complex networks:Models, structures and dynamics[M]. Beijing:Higher Education Press. 2012:217-218.
[18] Zhao M, Zhou T, Wang B, et al. Relations between average distance, heterogeneity and network synchronizability[J]. Physica A-statistical Mechanics and Its Applications, 2006, 371(2):773-780.
[19] Colizza V, Flammini A, Serrano M A, et al. Detecting richclub ordering in complex networks[J]. Nature Physics, 2006, 2(2):110-115.
[20] 李欢, 卢罡, 郭俊霞. 复杂网络零模型的量化评估[J]. 计算机应用, 2015, 35(6):1560-1563, 1572. Li Huan, Lu Gang, Guo Junxia. Quantitative evaluation for null models of complex networks[J]. Journal of Computer Applications. 2015, 35(6):1560-1563, 1572.
[21] Cartwright D, Harary F. Structural balance:A generalization of heider's theory[J]. Psychological Review, 1956, 63(5):277-293.
[22] Zhang Q, Lu L, Wang W, et al. Potential theory for directed networks[J]. PLoS One, 2013, 8(2):e55437.
[23] Leskovec J, Huttenlocher D, Kleinberg J. Predicting positive and negative links in online social networks[C]//Proceedings of Nineteenth International Conference on World Wide Web (WWW2010). Raleigh, USA:ACM Press, 2010:641-650.