This topic examines how social tension and harmony are formally represented, measured, and simulated through the theory of structural balance. Signed networks are introduced as mathematical models of sentiment, where edges represent positive or negative relationships. Heider’s Balance Theory (1946) is computationally operationalized through triad enumeration, allowing the classification of configurations as balanced or imbalanced based on sign products. The computational complexity of this process is acknowledged, and matrix-based optimizations are described as practical means of scaling triad analysis.

The extension of balance theory by Cartwright and Harary (1956) to global structural balance introduces the notion of partitioning the network into internally friendly and externally hostile subgroups. Simulations of polarization and conflict demonstrate how local instabilities cascade into macroscopic social divisions, forming echo chambers and filter bubbles. Quantitative indices, such as the Balance Index and Signed Clustering Coefficient, are presented as numerical indicators of social equilibrium, while agent-based models illustrate the emergence of conflict cascades and fragmentation. The topic concludes that computational models of balance provide both a predictive and diagnostic framework for understanding the dynamics of polarization in social systems.

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