结构平衡与人际评价动态：超越所有对所有和两派网络
Structural Balance and Interpersonal Appraisals Dynamics: Beyond All-to-All and Two-Faction Networks
摘要：
结构平衡理论描述了符号人际评价网络的稳定拓扑结构。现有的模型解释收敛的评价网络的结构平衡，要么在有限的时间内发散，或可能陷入堵塞状态，或收敛到只有完整的图形。在本文中，我们研究了开放的问题，如何稳定的非所有对所有的结构平衡出现通过本地动态的人际评价。我们首先比较了一般非全对全图的结构平衡的两个合理定义，即，三元结构平衡和二元结构平衡，并深入研究它们之间的关系。其次，基于三种广泛采用的社会学机制：对称机制、影响机制和同质性机制，我们提出了两个简单的类八卦评价动力学模型：同质性-影响-同质性（SIH）动力学和同质性-影响-意见-同质性（SIOH）动力学。在这些模型中，从任意初始条件出发的评价网络几乎必然分别在有限时间内达到非全对全的三元结构平衡和二元结构平衡。此外，SIOH动态捕捉到了人际评价和个人意见的共同演变。关于理论贡献，我们表明，SIH（SIOH resp.）动力学对应于所有可能的三元组（两个派别分别）的集合。评价网络的结构平衡配置。此外，我们还证明了对于任意初始条件，SIH（SIOH resp.）动力学几乎肯定会实现三合会明智的（两个派别分别）。在有限的时间内实现结构平衡。对SIH动态的数值研究也暗示了一些关于多边关系是减少还是加剧冲突的有见地的信息。
英文摘要：
Structural balance theory describes stable configurations of topologies of signed interpersonal appraisal networks. Existing models explaining the convergence of appraisal networks to structural balance either diverge in finite time, or could get stuck in jammed states, or converge to only complete graphs. In this paper, we study the open problem how steady non-all-to-all structural balance emerges via local dynamics of interpersonal appraisals. We first compare two well-justified definitions of structural balance for general non-all-to-all graphs, i.e., the triad-wise structural balance and the two-faction structural balance, and thoroughly study their relations. Secondly, based on three widely adopted sociological mechanisms: the symmetry mechanism, the influence mechanism, and the homophily mechanism, we propose two simple models of gossip-like appraisal dynamics, the symmetry-influence-homophily (SIH) dynamics and the symmetry-influence-opinion-homophily (SIOH) dynamics. In these models, the appraisal network starting from any initial condition almost surely achieves non-all-to-all triad-wise and two-faction structural balance in finite time respectively. Moreover, the SIOH dynamics capture the co-evolution of interpersonal appraisals and individuals' opinions. Regarding the theoretical contributions, we show that the equilibrium set of the SIH (SIOH resp.) dynamics corresponds to the set of all the possible triad-wise (two-faction resp.) structural balance configurations of the appraisal networks. Moreover, we prove that, for any initial condition, the appraisal networks in the SIH (SIOH resp.) dynamics almost surely achieve triad-wise (two-faction resp.) structural balance in finite time. Numerical studies of the SIH dynamics also imply some insightful take-home messages on whether multilateral relations reduce or exacerbate conflicts.
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