Extended Structural Balance Theory and Method for Cooperative–Antagonistic Networks

For the behavior analysis of cooperative–antagonistic networks (CANs), the structural balance theory has been adopted widely since it can be developed to accommodate the simultaneous existence of competitive interactions. This advantage of structural balance is further explored in this paper by aiming at the local nodes instead of the global CAN, and a notion of structurally balanced nodes is proposed. It is shown that structurally balanced nodes play a dominant role in determining the dynamic behaviors of CANs. Furthermore, such an extension of structural balance is applied to distinguish the roles of all nodes to create a hierarchical structure decomposition of CANs. Particularly, regarding interval bipartite consensus of quasi-strongly connected CANs, the impact index of root nodes can be calculated directly through counting the number of structurally balanced nodes.

[1]  Tamer Basar,et al.  Exponential Convergence of the Discrete- and Continuous-Time Altafini Models , 2017, IEEE Transactions on Automatic Control.

[2]  Julien M. Hendrickx,et al.  A lifting approach to models of opinion dynamics with antagonisms , 2014, 53rd IEEE Conference on Decision and Control.

[3]  Noah E. Friedkin,et al.  A Structural Theory of Social Influence: List of Tables and Figures , 1998 .

[4]  Hongwei Zhang,et al.  Bipartite consensus of multi‐agent systems over signed graphs: State feedback and output feedback control approaches , 2017 .

[5]  Deyuan Meng,et al.  Convergence analysis of directed signed networks via an M-matrix approach , 2018, Int. J. Control.

[6]  Claudio Altafini,et al.  Dynamics of Opinion Forming in Structurally Balanced Social Networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  Mikolaj Morzy,et al.  Signed Graphs , 2014, Encyclopedia of Social Network Analysis and Mining.

[8]  Roberto Tempo,et al.  A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II , 2018, Annu. Rev. Control..

[9]  Roy M. Howard,et al.  Linear System Theory , 1992 .

[10]  Yingmin Jia,et al.  Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions , 2017, Syst. Control. Lett..

[11]  Giancarlo Ferrari-Trecate,et al.  Containment Control in Mobile Networks , 2008, IEEE Transactions on Automatic Control.

[12]  F. Harary,et al.  STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 , 1977 .

[13]  C. Altafini,et al.  Computing global structural balance in large-scale signed social networks , 2011, Proceedings of the National Academy of Sciences.

[14]  Deyuan Meng,et al.  Bipartite containment tracking of signed networks , 2017, Autom..

[15]  Karl Henrik Johansson,et al.  Structural Balance and Opinion Separation in Trust–Mistrust Social Networks , 2016, IEEE Transactions on Control of Network Systems.

[16]  W. Zheng,et al.  Emergent collective behaviors on coopetition networks , 2014 .

[17]  Guanghui Wen,et al.  Bipartite Tracking Consensus of Linear Multi-Agent Systems With a Dynamic Leader , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Ziyang Meng,et al.  Behaviors of networks with antagonistic interactions and switching topologies , 2016, Autom..

[19]  Claudio Altafini,et al.  Consensus Problems on Networks With Antagonistic Interactions , 2013, IEEE Transactions on Automatic Control.

[20]  Warren E. Dixon,et al.  Containment control for a social network with state-dependent connectivity , 2014, Autom..

[21]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[22]  Jie Chen,et al.  Sign-Consensus of Linear Multi-Agent Systems Over Signed Directed Graphs , 2017, IEEE Transactions on Industrial Electronics.

[23]  Magnus Egerstedt,et al.  Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks , 2012, Autom..

[24]  Ziyang Meng,et al.  Uniform convergence for signed networks under directed switching topologies , 2018, Autom..

[25]  Mingjun Du,et al.  Interval Bipartite Consensus of Networked Agents Associated With Signed Digraphs , 2016, IEEE Transactions on Automatic Control.

[26]  Maria Elena Valcher,et al.  On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions , 2014, Syst. Control. Lett..

[27]  Francesco Bullo,et al.  The Coevolution of Appraisal and Influence Networks Leads to Structural Balance , 2016, IEEE Transactions on Network Science and Engineering.

[28]  Roberto Tempo,et al.  A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II , 2018, Annu. Rev. Control..

[29]  F. Harary.  On the notion of balance of a signed graph. , 1953 .

[30]  Ziyang Meng,et al.  Disagreement of Hierarchical Opinion Dynamics with Changing Antagonisms , 2019, SIAM J. Control. Optim..

[31]  Ziyang Meng,et al.  Multiagent Systems with Compasses , 2015, SIAM J. Control. Optim..

[32]  Alexey S. Matveev,et al.  Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization , 2015, IEEE Transactions on Automatic Control.