Abstract
The theory of social balance, also called structural balance, is first proposed by Heider in 1940s, which is utilized to describe the potential social dynamics process. This theory is of great importance in sociology, computer science, psychology and other disciplines where social systems can be represented as signed networks. The social balance problem is hard but very interesting. It has attracted many researchers from various fields working on it over the past few years. Many significant theories and approaches have been developed and now exhibit tremendous potential for future applications. A comprehensive review of these existing studies can provide us significant insights into understanding the dynamic patterns of social systems. Yet to our investigation, existing studies have not done this, especially from a dynamical perspective. In this paper, we make an attempt towards conducting a brief survey of these scientific activities on social balance. Our efforts aim to review what has been done so far in this evolving area. We firstly introduce the fundamental concepts and significant properties of social balance. Then we summarize the existing balance measures and present detecting/partitioning algorithms, as well as important empirical investigations in both physical world and cyberspace. We next mainly focus on describing and comparing the fundamental mechanisms of the dynamics models. Several existing problems not yet satisfactorily solved in this area are also discussed.
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References
Abell, P. (1968). Structural balance in dynamic structures. Sociology, 2, 333–352.
Abell, P., & Ludwig, M. (2009). Structural balance: A dynamic perspective. Journal of Mathematical Sociology, 33, 129–155.
Abramson, G., & Kuperman, M. (2001). Social games in a social network. Physical Review E, 63, 030901.
Albert, R., & Barabási, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47.
Altafini, C. (2012). Dynamics of opinion forming in structurally balanced social networks. Preprint.
Antal, T., Krapivsky, P. L., & Redner, S. (2005). Dynamics of social balance on networks. Physical Review E, 72, 036121.
Antal, T., Krapivsky, P. L., & Redner, S. (2006). Social balance on networks: The dynamics of friendship and enmity. Physica D: Nonlinear Phenomena, 224, 130–136.
Aronson, E., & Cope, V. (1968). My enemy’s enemy is my friend. Journal of Personality and Social Psychology, 8, 8–12.
Auster, C. J. (1980). Balance theory and other extra-balance properties: An application to fairy tales. Psychological Reports, 47, 183–188.
Axelrod, R., & Bennett, D. S. (1993). A landscape theory of aggregation. British Journal of Political Science, 23, 211–233.
Axelrod, R., Mitchell, W., Thomas, R. E., Bennett, D. S., & Bruderer, E. (1995). Coalition formation in standard-setting alliances. Management Science, 41, 1493–1508.
Ba, S., Whinston, A., & Zhang, H. (2000). The dynamics of the electronic market: An evolutionary game approach. Information Systems Frontiers, 2, 31–40.
Biha, M. D., & Meurs, M.-J. (2011). An exact algorithm for solving the vertex separator problem. Journal of Global Optimization, 49, 425–434.
Binder, K., & Young, A. P. (1986). Spin glasses: Experimental facts, theoretical concepts, and open questions. Reviews of Modern Physics, 58, 801–976.
Black, P. E. Minimum vertex cut. Dictionary of algorithms and data structures [online]. In V. Pieterse & P. E. Black, (Eds.), 19 April 2004. Available from: http://www.nist.gov/dads/HTML/minvertexcut.html.
Borgatti, S. P., Mehra, A., Brass, D. J., & Labianca, G. (2009). Network analysis in the social sciences. Science, 323, 892–895.
Brzozowski, M.J., Hogg, T., Szabo, G. (2008). Friends and foes: Ideological social networking. Presented at the Proceedings of the twenty-sixth annual SIGCHI conference on Human factors in computing systems, Florence, Italy.
Burke, M., Kraut, R. (2008). Mopping up: Modeling Wikipedia promotion decisions. Presented at the Proceedings of the 2008 ACM conference on Computer supported cooperative work, San Diego, CA, USA.
Carrington, P., Scott, J., & Wasserman, S. (2005). Models and methods in social network analysis. Cambridge: Cambridge University Press.
Cartwright, D., & Gleason, T. C. (1966). The number of paths and cycles in a digraph. Psychometrika, 31, 179–199.
Cartwright, D., & Harary, F. (1956). Structural balance: A generalization of Heider’s theory. Psychological Review, 63, 277–293.
Castellano, C., Fortunato, S., & Loreto, V. (2009). Statistical physics of social dynamics. Reviews of Modern Physics, 81, 591–646.
Cheng, H., Zhou, Y., & Yu, J. X. (2011). Clustering large attributed graphs: A balance between structural and attribute similarities. ACM Transactions on Knowledge Discovery from Data, 5, 1–33.
Costa, L. D. F., Oliveira, O., Travieso, G., Rodrigues, F. A., Villas Boas, P., Antiqueira, L., et al. (2011). Analyzing and modeling real-world phenomena with complex networks: A survey of applications. Advances in Physics, 60, 329–412.
Cui, K., Zheng, X., Zeng, D.D., Zhang, Z., Luo, C., He, S. (2013). An empirical study of information diffusion in micro-blogging systems during emergency events. In: Web-age information management (pp. 140–151). Qinhuangdao, China.
Cui, K., Zheng, X., Wen, D., & Zhao, X. (2013b). Researches and applications of computational experiments. Acta Automatica Sinica, 39, 1157–1169.
Daniel, G., Enrique, G.-A., Conrado, M., Guillermo, O., del Mónica, P., & Martha, S. (2008). The cohesiveness of subgroups in social networks: A view from game theory. Annals of Operations Research, 158, 33–46.
Davis, J. A. (1963). Structural balance, mechanical solidarity, and interpersonal relations. American Journal of Sociology, 68, 444–462.
Davis, J. A. (1967). Clustering and structural balance in graphs. Human Relations, 20, 181–187.
Davis, J. A. (1977). Sociometric triads as multi-variate systems. Journal of Mathematical Sociology, 5, 41–59.
Davis, J. A. (1979). The Davis/Holland/Leinhardt studies: An overview. New York: Academic Press.
Davol, S. H. (1959). An empirical test of structural balance in sociometric triads. Journal of Abnormal and Social Psychology, 59, 393–398.
Doreian, P., & Krackhardt, D. (2001). Pre-transitive balance mechanisms for signed networks. Journal of Mathematical Sociology, 25, 43–67.
Doreian, P., & Mrvar, A. (1996). A partitioning approach to structural balance. Social Networks, 18, 149–168.
Doreian, P., & Mrvar, A. (2009). Partitioning signed social networks. Social Networks, 31, 1–11.
DuBois, T., Golbeck, J., Srinivasan, A. (2011). Predicting trust and distrust in social networks. In: Privacy, security, risk and trust (passat), 2011 I.E. Third International Conference on and 2011 I.E. Third International Conference on Social Computing (Socialcom) (pp. 418–424.
Eagle, N., Pentland, A., & Lazer, D. (2009). Inferring friendship network structure by using mobile phone data. Proceedings of the National Academy of Sciences, 106, 15274–15278.
Easley, D., & Kleinberg, J. (2010). Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge: Cambridge University Press.
Facchetti, G., Iacono, G., & Altafini, C. (2011). Computing global structural balance in large-scale signed social networks. Proceedings of the National Academy of Sciences, 108, 20953–20958.
Fang, S., Xu, L., Zhu, Y., Liu, Y., Liu, Z., Pei, H., et al. (2013). An integrated information system for snowmelt flood early-warning based on internet of things. Information Systems Frontiers 1–15.
Feige, U., Hajiaghayi, M., Lee, J.R. (2005) Improved approximation algorithms for minimum-weight vertex separators. Presented at the Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, Baltimore, MD, USA.
Fei-Yue, W. (2010). The emergence of intelligent enterprises: From CPS to CPSS. IEEE Intelligent Systems, 25, 85–88.
Fowler, J. H., & Christakis, N. A. (2010). Cooperative behavior cascades in human social networks. Proceedings of the National Academy of Sciences, 107, 5334–5338.
Frank, O., & Harary, F. (1979). Balance in stochastic signed graphs. Social Networks, 2, 155–163.
Friedkin, N. E. (2004). Social cohesion. Annual Review of Sociology, 30, 409–425.
Galeotti, A., Goyal, S., Jackson, M. O., Vega-Redondo, F., & Yariv, L. (2010). Network games. The Review of Economic Studies, 77, 218–244.
Gill, M. (1981). A note concerning Acharya’s conjecture on a spectral measure of structural balance in a social system. In S. Rao (Ed.), Combinatorics and graph theory (Vol. 885, pp. 266–271). Berlin: Springer.
Glauber, R. J. (1963). Time-dependent statistics of the Ising model. Journal of Mathematical Physics, 4, 294–307.
Gnyawali, D. R., & Madhavan, R. (2001). Cooperative networks and competitive dynamics: A structural embeddedness perspective. The Academy of Management Review, 26, 431–445.
Guha, R., Kumar, R., Raghavan, P., Tomkins, A. (2004). Propagation of trust and distrust. Presented at the Proceedings of the 13th international conference on World Wide Web, New York, NY, USA.
Hanaki, N., Peterhansl, A., Dodds, P. S., & Watts, D. J. (2007). Cooperation in evolving social networks. Management Science, 53, 1036–1050.
Harary, F. (1953). On the notion of balance of a signed graph. Michigan Mathematical Journal, 2, 143–146.
Harary, F. (1955). On local balance and N-balance in signed graphs. Michigan Mathematical Journal, 3, 37–41.
Harary, F. (1959). On the measurement of structural balance. Behavioral Science, 4, 316–323.
Harary, F. (1960). A matrix criterion for structural balance. Naval Research Logistics Quarterly, 7, 195–199.
Harary, F. (1961). A structural analysis of the situation in the Middle East in 1956. Journal of Conflict Resolution, 5, 167–178.
Harary, F. (1966). Structural study of ‘a severed head’. Psychological Reports, 19, 473–474.
Harary, F., & Kabell, J. A. (1980). A simple algorithm to detect balance in signed graphs. Mathematical Social Sciences, 1, 131–136.
Harary, F., & Kommel, H. J. (1979). Matrix measures for transitivity and balance. Journal of Mathematical Sociology, 6, 199–210.
He, S., Zheng, X., Zeng, D., Cui, K., Zhang, Z., Luo, C. (2013). Identifying peer influence in online social networks using transfer entropy. In: Pacific Asia Workshop on Intelligence and Security Informatics (PAISI 2013) (pp. 47–61).
Heider, F. (1944). Social perception and phenomenal causality. Psychological Review, 51, 358–374.
Heider, F. (1946). Attitudes and cognitive organization. The Journal of Psychology, 21, 107–112.
Heider, F. (1958). The psychology of interpersonal relations. New York: Wiley.
Henley, N. M., Horsfall, R. B., & De Soto, C. B. (1969). Goodness of figure and social structure. Psychological Review, 76, 194–204.
Hummon, N. P., & Doreian, P. (2003). Some dynamics of social balance processes: Bringing Heider back into balance theory. Social Networks, 25, 17–49.
Iacono, G., Ramezani, F., Soranzo, N., & Altafini, C. (2010). Determining the distance to monotonicity of a biological network: A graph-theoretical approach. IET Systems Biology, 4, 223–235.
Istrate, G. (2008). On the dynamics of social balance on general networks (with an application to XOR-SAT). arXiv:0811.0381.
Istrate, G. (2009). On the dynamics of social balance on general networks (with an application to XOR-SAT). Fundamenta Informaticae, 91, 341–356.
Jackson, M. O. (1996). A strategic model of social and economic networks. Journal of Economic Theory, 71, 44–74.
Jackson, M. O. (2008). Social and economic networks. Princeton: Princeton University Press.
Jackson, M. O., & Zenou, Y. (2014). Games on networks (Vol. 4). Amsterdam: Elsevier Science.
Jung, J., Chang, Y.-S., Liu, Y., & Wu, C.-C. (2012). Advances in intelligent grid and cloud computing. Information Systems Frontiers, 14, 823–825.
Kakade, S., Kearns, M., Ortiz, L., Pemantle, R., & Suri, S. (2005). Economic properties of social networks. Advances in Neural Information Processing Systems, 17, 633–640.
Katai, O., & Iwai, S. (1978). On the characterization of balancing processes of social systems and the derivation of the minimal balancing processes. IEEE Transactions on Systems, Man, and Cybernetics, 8, 337–348.
Kim, C.-H. (2007). Explaining interstate trust/distrust in triadic relations. International Interactions, 33, 423–439.
Kim, M., & Candan, K. S. (2012). SBV-cut: Vertex-cut based graph partitioning using structural balance vertices. Data & Knowledge Engineering, 72, 285–303.
King, M. G. (1964). Structural balance tension, and segregation in a university group. Human Relations, 17, 221–225.
Kogan, N., & Tagiuri, R. (1958). Interpersonal preference and cognitive organization. Journal of Abnormal and Social Psychology, 56, 113–116.
Kulakowski, K. (2007). Some recent attempts to simulate the Heider balance problem. Computing in Science and Engineering, 9, 80–85.
Kulakowski, K., Gawronski, P., & Gronek, P. (2005). The Heider balance-a continuous approach. International Journal of Modern Physics C, 16, 707–716.
Kunegis, J., Lommatzsch, A., Bauckhage, C. (2009). The slashdot zoo: Mining a social network with negative edges. Presented at the Proceedings of the 18th international conference on World wide web, Madrid, Spain.
Kunegis, J., Schmidt, S., Lommatzsch, A., Lerner, J., De Luca, E.W., Albayrak, L.S. (2010). Spectral analysis of signed graphs for clustering, prediction and visualization. In: Proceedings of the SIAM International Conference on Data Mining, Columbus, Ohio, USA (pp. 559–570).
Labianca, G., Brass, D. J., & Gray, B. (1998). Social networks and perceptions of intergroup conflict: The role of negative relationships and third parties. The Academy of Management Journal, 41, 55–67.
Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabási, A.-L., Brewer, D., et al. (2009). Computational social science. Science, 323, 721–723.
Lerner, S. (2008). The enemy of my enemy: The alarming convergence of militant Islam and the extreme right. Shofar: An Interdisciplinary Journal of Jewish Studies, 27, 138–141.
Leskovec, J., Huttenlocher, D., Kleinberg, J. (2010). Signed networks in social media. Presented at the Proceedings of the 28th international conference on Human factors in computing systems, Atlanta, Georgia, USA.
Leskovec, J., Huttenlocher, D., Kleinberg, J. (2010) Predicting positive and negative links in online social networks. Presented at the Proceedings of the 19th international conference on World Wide Web, Raleigh, North Carolina, USA.
Li, Y., Chen, W., Wang, Y., Zhang, Z.-L. (2013). Influence diffusion dynamics and influence maximization in social networks with friend and foe relationships. Presented at the Proceedings of the sixth ACM international conference on Web search and data mining, Rome, Italy
Liang, Y., Zheng, X., Zeng, D.D., Zhou, X., Leischow, S. (2013). An Empirical analysis of social interaction on tobacco-oriented social networks. In: International Conference for Smart Health (ICSH) (pp. 19–24).
Ludwig, M., & Abell, P. (2007). An evolutionary model of social networks. The European Physical Journal B - Condensed Matter and Complex Systems, 58, 97–105.
Malekzadeh, M., Fazli, M., Khalilabadi, P.J., Rabiee, H.R., Safari, M. (2011). Social balance and signed network formation games. Presented at the SNA-KDD Workshop ‘11, San Diego CA, USA.
Martens, B., & Teuteberg, F. (2012). Decision-making in cloud computing environments: A cost and risk based approach. Information Systems Frontiers, 14, 871–893.
Marvel, S. A., Strogatz, S. H., & Kleinberg, J. M. (2009). Energy landscape of social balance. Physical Review Letters, 103, 198701.
Marvel, S. A., Kleinberg, J., Kleinberg, R. D., & Strogatz, S. H. (2011). Continuous-time model of structural balance. Proceedings of the National Academy of Sciences, 108, 1771–1776.
Mazhelis, O., & Tyrväinen, P. (2012). Economic aspects of hybrid cloud infrastructure: User organization perspective. Information Systems Frontiers, 14, 845–869.
McDonald, H. B., & Rosecrance, R. (1985). Alliance and structural balance in the international system. Journal of Conflict Resolution, 29, 57–82.
McPherson, J. M., Popielarz, P. A., & Drobnic, S. (1992). Social networks and organizational dynamics. American Sociological Review, 57, 153–170.
Miller, H., & Geller, D. (1972). Structural balance in dyads. Journal of Personality and Social Psychology, 21, 135–138.
Moore, M. (1978). An international application of Heider’s balance theory. European Journal of Social Psychology, 8, 401–405.
Moore, M. (1979). Structural balance and international relations. European Journal of Social Psychology, 9, 323–326.
Morrissette, J. O. (1958). An experimental study of the theory of structural balance. Human Relations, 11, 239–254.
Morrissette, J. O., Jahnke, J. C., & Baker, K. (1966). Structural balance: A test of the completeness hypothesis. Behavioral Science, 11, 121–125.
Morrissette, J. O., Jahnke, J. C., Baker, K., & Rohrman, N. (1967). Degree of structural balance and group effectiveness. Organizational Behavior and Human Performance, 2, 383–393.
Newcomb, T. M. (1956). The prediction of interpersonal attraction. American Psychologist, 11, 575–586.
Newcomb, T. M. (1961). The acquaintance process. New York: Holt, Rinehart & Winston.
Newcomb, T. M. (1981). Heiderian balance as a group phenomenon. Journal of Personality and Social Psychology, 40, 862–867.
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45, 167.
Nooy, W. D. (1999). The sign of affection: Balance-theoretic models and incomplete signed digraphs. Social Networks, 21, 269–286.
Norman, R. Z., & Roberts, F. S. (1972). A derivation of a measure of relative balance for social structures and a characterization of extensive ratio systems. Journal of Mathematical Psychology, 9, 66–91.
Notsu, A., Ichihashi, H., & Honda, K. (2006). Agent simulation based on perceptual balance. IJCSNS International Journal of Computer Science and Network Security, 6, 50–54.
Notsu, A., Honda, K., Ichihashi, H. (2010). Social simulation based on perceptual balance on the influence of communication styles. Presented at the Proceedings of SICE Annual Conference.
Osborne, M. J. (2003). An introduction to game theory. Oxford: Oxford University Press.
Pelino, V., Maimone, F. (2012). Towards a class of complex networks models for conflict dynamics. Available at: arXiv:1203.1394.
Radicchi, F., Vilone, D., Yoon, S., & Meyer-Ortmanns, H. (2007). Social balance as a satisfiability problem of computer science. Physical Review E, 75, 026106.
Romero, D.M., Meeder, B., Barash, V., Kleinberg, J. (2011). Maintaining ties on social media sites: The competing effects of balance, exchange, and betweenness. In: Proceedings of the Fifth International AAAI Conference on Weblogs and Social Media (pp. 606–609).
Sampson, S.F. (1968). A novitiate in a period of change: An experimental and case study of social relationships. Ph.D., Department of Sociology, Cornell University.
Schilling, M. A., & Phelps, C. C. (2007). Interfirm collaboration networks: The impact of large-scale network structure on firm innovation. Management Science, 53, 1113–1126.
Sheth, A., Anantharam, P., & Henson, C. (2013). Hysical-cyber-social computing: An early 21st century approach. IEEE Intelligent Systems, 28, 78–82.
Singh, R., Dasgupta, S., Sinha, S. (2013). Extreme variability in convergence to structural balance in frustrated dynamical systems. arXiv, preprint arXiv:1307.8018.
Smith, J. M., & Price, G. R. (1973). The logic of animal conflict. Nature, 246, 15–18.
Srinivasan, A. (2011). Local balancing influences global structure in social networks. Proceedings of the National Academy of Sciences, 108, 1751–1752.
Stix, A. H. (1974). An improved measure of structural balance. Human Relations, 27, 439–455.
Summers, T. H., & Shames, I. (2013). Active influence in dynamical models of structural balance in social networks. Europhysics Letters, 103, 18001.
Szabó, G., & Fáth, G. (2007). Evolutionary games on graphs. Physics Reports, 446, 97–216.
Szell, M., & Thurner, S. (2010). Measuring social dynamics in a massive multiplayer online game. Social Networks, 32, 313–329.
Szell, M., Lambiotte, R., & Thurner, S. (2010). Multirelational organization of large-scale social networks in an online world. Proceedings of the National Academy of Sciences, 107, 13636–13641.
Tang, J., Zhang, Y., Sun, J., Rao, J., Yu, W., Chen, Y., et al. (2012). Quantitative study of individual emotional states in social networks. IEEE Transactions on Affective Computing, 3, 132–144.
Taylor, H. F. (1970). Balance in small groups. New York: Van Nostrand Reinhold.
Terzi, E., & Winkler, M. (2011). A spectral algorithm for computing social balance. In A. Frieze, P. Horn, & P. Pralat (Eds.), Algorithms and models for the web graph (Vol. 6732, pp. 1–13). Berlin: Springer.
Thomas, S. (2010). The friend of my enemy is my enemy, the enemy of my enemy is my friend: Axioms for structural balance and bi-polarity. Mathematical Social Sciences, 60, 39–45.
Toulouse, G. (1977). Theory of the frustration effect in spin glasses I. Communications on Physics, 2, 115.
Traag, V. A., Van Dooren, P., & De Leenheer, P. (2013). Dynamical models explaining social balance and evolution of cooperation. PLoS ONE, 8, e60063.
Van De Rijt, A. (2011). The micro–macro link for the theory of structural balance. Journal of Mathematical Sociology, 35, 94–113.
Viktorov, T. (2007). Social and culture dynamics. Sotsiologicheskie issledovaniia 155–155.
Wang, F. (2004). Computational experiments for behavior analysis and decision evaluation in complex systems. Journal of System Simulation, 16, 893–897.
Wang, F.-Y. (2007). Toward a paradigm shift in social computing: The ACP approach. IEEE Intelligent Systems, 22, 65–67.
Wang, Z., & Thorngate, W. (2003). Sentiment and social mitosis: Implications of Heider’s balance theory. Journal of Artificial Societies and Social, Simulation, 6.
Wang, F.-Y., Carley, K. M., Zeng, D., & Mao, W. (2007). Social computing: From social informatics to social intelligence. IEEE Intelligent Systems, 22, 79–83.
Wang, Y., Zeng, D., Cao, Z., Wang, Y., Song, H., Zheng, X. (2011). The impact of community structure of social contact network on epidemic outbreak and effectiveness of non-pharmaceutical interventions. In: Intelligence and security informatics (pp. 108–120). Springer.
Wang, Y., Zeng, D., Zhu, B., Zheng, X., Wang, F. (2012). Patterns of news dissemination through online news media: A case study in China. Information Systems Frontiers. 1–14
Wasserman, S., & Faust, K. (1994). Social networks analysis: Methods and applications. Cambridge: Cambridge University Press.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440.
Wu, L., Ying, X., Wu, X., Lu, A., & Z–H, Z. (2011). Spectral analysis of k-balanced signed graphs. In J. Huang, L. Cao, & J. Srivastava (Eds.), Advances in knowledge discovery and data mining (Vol. 6635, pp. 1–12). Berlin: Springer.
Yang, B., Cheung, W., & Liu, J. (2007). Community mining from signed social networks. IEEE Transactions on Knowledge and Data Engineering, 19, 1333–1348.
Young, H. P. (2011). The dynamics of social innovation. Proceedings of the National Academy of Sciences, 108, 21285–21291.
Zajonc, R. B., & Sherman, S. J. (1967). Structural balance and the induction of relations. Journal of Personality, 35, 635–650.
Zenou, Y. (2012). Networks in economics. In: International encyclopedia of social and behavioral sciences, 2nd Edn. Amsterdam: Elsevier.
Zheng, X., Zeng, D., Sun, A., Luo, Y., Wang, Q., Wang, F. (2008). Network-based analysis of Beijing SARS data. Presented at the BioSecure.
Zheng, X., Zeng, D., Cao, Z., Wang, Q., Wang, F.-Y. (2009). Evolutionary patterns on SARS networks. In: Biosurveillance and Biosecurity.
Zheng, X., Zeng, D., Sun, A., Luo, Y., Wang, Q., Wang, F.-Y. (2009). The prediction of missing infectious links in Beijing SARS. In: Biosurveillance and Biosecurity.
Zheng, X., Zhong, Y., Wang, F., Zeng, D., Zhang, Q., & Cui, K. (2011a). Social dynamics research based on web information. Complex Systems and Complexity Science, 8, 1–12.
Zheng, X., Ke, G., Zeng, D. D., Ram, S., & Lu, H. (2011b). Next-generation team-science platform for scientific collaboration. IEEE Intelligent Systems, 26, 72–76.
Zheng, X., Zhong, Y., Zeng, D., & Wang, F.-Y. (2012). Social influence and spread dynamics in social networks. Frontiers of Computer Science, 6, 611–620.
Ziegler, C.-N., & Lausen, G. (2005). Propagation models for trust and distrust in social networks. Information Systems Frontiers, 7, 337–358.
Acknowledgments
We greatly appreciate the valuable comments provided by anonymous reviewers. By responding to those significant comments, we were able to further improve the content and presentation of this paper. We would thank for each member of SMILES group in Institute of Automation, Chinese Academy of Sciences. Especially, we would thank for Kainan Cui, Saike He, Chuan Luo, Yunji Liang and Zhu Zhang for useful discussions. This work was supported in part by the following grants: The National Natural Science Foundation of China, Grant No. 71103180, 91124001 and 91024030, the Early Career Development Award of SKLMCCS, and The Ministry of Health, Grant No. 2012ZX10004801 and 2013ZX10004218.
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Zheng, X., Zeng, D. & Wang, FY. Social balance in signed networks. Inf Syst Front 17, 1077–1095 (2015). https://doi.org/10.1007/s10796-014-9483-8
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DOI: https://doi.org/10.1007/s10796-014-9483-8