Structural balance: a generalization of Heider's theory.

1956/01/01 by Dorwin Cartwright, Frank Harary · 2,572 citations
Health Professions · Mathematics · Psychology · #Balance (ability) #Balance theory #Cognitive psychology #Computer science #Generalization #Mathematical analysis #Mathematical economics #Mathematics #Problem Solving Skills Development #Psychological and Temporal Perspectives Research #Psychology #Resilience and Mental Health #Social psychology

paper · doi:10.1037/h0046049

published in Psychological Review 63(5), 277-293 (American Psychological Association)

openalex publication_date 1956/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Citations

• Attitudes and Cognitive Organization

Cited by

• A model of egoistical relative deprivation.
• Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study
• Herdability of Linear Systems Based on Sign Patterns and Graph\n Structures
• Negative ties highlight hidden extremes in social media polarization
• Endogenous Coalition Formation in Policy Debates
• Erratic Extremism causes Dynamic Consensus (a new model for one-dimensional opinion dynamics)
• The co-evolution of informal social status and gossip in workplace social networks
• How Community Feedback Shapes User Behavior
• Marine insurance firms, business networks, and the modernisation of the financial sector in Southern Italy (1820–1900)
• Negative Link Prediction in Social Media
• Topology-based Conditions for Multiconsensus under the Signed Friedkin-Johnsen Model
• What defines a group of friends? Rethinking community structure in signed, directed networks
• Meso-scale structures in signed networks
• A Survey of Signed Network Mining in Social Media
• Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization
• Local and Global Balance in Financial Correlation Networks: an Application to Investment Decisions
• The index of tC₃^--free signed graphs
• Community detection in heterogeneous signed networks
• On the relationship between Heider links and Ising spins
• Emergent Behaviors over Signed Random Dynamical Networks: Relative-State-Flipping Model
• Heider balance of a square lattice in an external field
• Adversarial Signed Graph Learning with Differential Privacy
• Hyperevent network modelling of partially observed gossip data
• MUSE: Multi-faceted Attention for Signed Network Embedding
• Multi-layer dissolution exponential-family models for weighted signed networks
• Signed Graph Unlearning
• Transitivity Correlation: Measuring Network Transitivity as Comparative Quantity
• Negative social ties as emerging risk factors for accelerated aging, inflammation, and multimorbidity
• Positive, negative, and ambivalent dyads and triads with family and friends: A personal network study on how they are associated with young adults’ well-being
• Liquidity in Credit Networks: A Little Trust Goes a Long Way
• Toward Robust Signed Graph Learning through Joint Input-Target Denoising
• Networks containing negative ties
• The effect of social balance on social fragmentation
• Signed network models for portfolio optimization
• Dynamics of social balance on networks
• Games Real Actors Could Play
• Social Network Theory and Comedy: Insights from NBC’s The Office
• Allies of the Weak: La Résistance and Jews in the Holocaust
• Phase transition in a network model of social balance with Glauber dynamics
• Balance correlations, agentic zeros, and networks: The structure of 192 years of war and peace
• The 1995-2018 Global Evolution of the Network of Amicable and Hostile\n Relations Among Nation-States
• Clustering with Noisy Queries
• Modeling echo chamber effects in signed networks
• Coexistence of balance and hierarchies: An ego perspective to explain empirical networks
• Instability of social network dynamics with stubborn links
• Signed graphs in data sciences via communicability geometry
• A note on the vertex arboricity of signed graphs
• Frustration, glassy behavior and dynamical annealing in societies of Neural Networks
• Gremban Expansion for Signed Networks: Algebraic and Combinatorial Foundations for Community-Faction Detection
• Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment
• Same Stats, Different Graphs (Graph Statistics and Why We Need Graph Drawings)
• Inferring Interpersonal Relations in Narrative Summaries
• GegenNet: Spectral Convolutional Neural Networks for Link Sign Prediction in Signed Bipartite Graphs
• A Generalized Discrete-Time Altafini Model
• From Factors to Actors: Computational Sociology and Agent-Based Modeling
• Dimensions of social networks: A taxonomy and operationalization
• Bias-Resistant Social News Aggregator Based on Blockchain
• Higher-order interactions shape collective human behaviour
• Visualizing structural balance in signed networks
• Spectral Turán problem for K_3,3^--free signed graphs
• Finding Core Balanced Modules in Statistically Validated Stock Networks
• Structural equivalence of individuals in social networks
• Inter-organisational patent opposition network: How companies form adversarial relationships
• Patterns of imbalance states between sub-brain regimes during development in the resting state
• Seating Assignment Using Constrained Signed Spectral Clustering
• The Heider balance and the looking-glass self
• Structural Stability of a Family of Group Formation Games
• Harnack Inequality for Magnetic Graphs
• Towards a class of complex networks models for conflict dynamics
• Signed Network Modeling Based on Structural Balance Theory
• Historical and Comparative Research on Social Diffusion: Mechanisms, Methods, and Data
• Sitting closer to friends than enemies, revisited
• The Power Allocation Game on A Network: Balanced Equilibrium
• Signed Graph Convolutional Network
• A modeling and computational study of the frustration index in signed networks
• Contending Parties: A Logistic Choice Analysis of Inter- and Intra-group Blog Citation Dynamics in the 2004 US Presidential Election
• Coevolutionary balance of resting-state brain networks in autism
• Implication Avoiding Dynamics for Externally Observed Networks
• A Latent Variable Model for Relational Events with Multiple Receivers
• A Survey on Network Embedding
• Exploring Quantum Heider Balance Theory
• Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model
• A Correlation Clustering Approach to Link Classification in Signed Networks -- Full Version --
• How trust networks shape students' opinions about the proficiency of artificially intelligent assistants
• Can Selfish Groups be Self-Enforcing?
• Xenophobia based on a few attributes can impede society's cohesiveness
• Repelling curvature via ε-repelling Laplacian on positive connected signed graphs
• Signed Node Relevance Measurements
• Network organization of coopetitive genetic influences on cortical morphologies
• Leveraging Sociological Models for Predictive Analytics
• Modeling temporal hypergraphs
• SOC-DGL: Social Interaction Behavior Inspired Dual Graph Learning Framework for Drug-Target Interaction Identification
• The Evolution of Beliefs over Signed Social Networks
• Balance in Signed Bipartite Networks
• Eigenvalues of weakly balanced signed graphs and graphs with negative cliques
• Synergistic Motifs in Gaussian Systems
• Structural balance in signed digraphs: considering transitivity to\n measure balance in graphs constructed by using different link signing methods
• From Signed Networks to Group Graphs
• Generalized Dynamics in Social Networks With Antagonistic Interactions
• Decoupled Variational Embedding for Signed Directed Networks
• 寻求现代意识：汪曾祺《聊斋新义》的立意根柢
• Signatures, lifts, and eigenvalues of graphs
• Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms
• On Signed Network Coordination Games
• The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is K_2,2-minor free
• From populations to networks: Relating diversity indices and frustration in signed graphs
• Signed Bipartite Graph Neural Networks
• Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment
• Separable models for dynamic signed networks
• Friendships, Rivalries, and Trysts: Characterizing Relations between Ideas in Texts
• Frustration of signed networks: How does it affect the thermodynamic properties of a system?
• Randomized Consensus with Attractive and Repulsive Links
• Web Science: Understanding the Emergence of Macro-Level Features on the World Wide Web
• Homo Entropicus, the emotional agent and societies of Neural Networks
• Truth and distortion in complex networks: a global consistency approach
• Voltage Graphs and Cluster Consensus with Point Group Symmetries
• Romantic Involvement and Social Network Involvement
• Community Detection in Signed Networks: an Error-Correcting Code Approach
• Balanced and fragmented phases in societies with homophily and social balance
• Social balance as a satisfiability problem of computer science
• Universality class of triad dynamics on a triangular lattice
• Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs
• Positional Analysis and Blockmodeling
• On Balanced Clustering (Indices, Models, Examples)
• The physics of custody
• High-order Graph Neural Networks with Common Neighbor Awareness for Link Prediction
• Gain and loss of esteem, direct reciprocity and Heider balance
• Motifs in triadic random graphs based on Steiner triple systems
• Relational Priors as Convergence Pressure in LLM-Based Multi-Agent Systems
• Quartic balance theory: Global minimum with imbalanced triangles
• Beyond Dyads and Triads: A Comparison of Tetrads in Twenty Social Networks
• Relevance of Negative Links in Graph Partitioning: A Case Study Using Votes from the European Parliament
• Extracting the signed backbone of intrinsically dense weighted networks
• 7. Very Local Structure in Social Networks
• Dissonance induction and reduction: A possible principle and connectionist mechanism for why therapies are effective
• Leader-following consensus of nonlinear singular multi-agent systems under signed digraph
• Complex ordering in spin networks: Critical role of adaptation rate for dynamically evolving interactions
• Competing effects of social balance and influence
• Towards the Heider balance: Cellular automaton with a global neighborhood
• Balance in signed networks
• Subgraphs and network motifs in geometric networks
• Reconciling Conflict and Cooperation in Environmental Governance: A Social Network Perspective
• Measuring partial balance in signed networks
• A modelling and computational study of the frustration index in signed networks
• Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
• Energy Landscape of Social Balance
• Ambiguous Weighting and Nonsensical Sense: The Problems of “Balance” and “Common Sense” as Commonplace Concepts and Decision-making Heuristics in Environmental Rhetoric
• Suicide and Friendships Among American Adolescents
• Fundamental Principles of Network Formation among Preschool Children. [europepmc]
• Popularity Trajectories and Substance Use in early Adolescence. [europepmc]
• Generalization of clustering coefficients to signed correlation networks. [europepmc]
• Macrostructure from Microstructure: Generating Whole Systems from Ego Networks. [europepmc]
• The Embeddedness of Adolescent Friendship Nominations: The Formation of Social Capital in Emergent Network Structures. [europepmc]
• Network Ecology and Adolescent Social Structure. [europepmc]
• Investigating cellular network heterogeneity and modularity in cancer: a network entropy and unbalanced motif approach. [europepmc]
• Graph partitions and cluster synchronization in networks of oscillators. [europepmc]
• Collective Dynamics of Belief Evolution under Cognitive Coherence and Social Conformity. [europepmc]
• Markov Networks of Collateral Resistance: National Antimicrobial Resistance Monitoring System Surveillance Results from Escherichia coli Isolates, 2004-2012. [europepmc]
• The Unresponsive Partner: Roles of Social Status, Auditory Feedback, and Animacy in Coordination of Joint Music Performance. [europepmc]
• Statistical physics of balance theory. [europepmc]
• Automated methods to test connectedness and quantify indirectness of evidence in network meta-analysis. [europepmc]
• Social Network Characteristics and Their Associations With Stress in Older Adults: Closure and Balance in a Population-Based Sample. [europepmc]
• Learning relationships in community-based service-learning: a social network analysis. [europepmc]
• Social-ecological alignment and ecological conditions in coral reefs. [europepmc]
• The effect of social balance on social fragmentation. [europepmc]
• Topological impact of negative links on the stability of resting-state brain network. [europepmc]
• Integrating social and cognitive aspects of belief dynamics: towards a unifying framework. [europepmc]
• Topological analysis of interaction patterns in cancer-specific gene regulatory network: persistent homology approach. [europepmc]
• Revealing semantic and emotional structure of suicide notes with cognitive network science. [europepmc]
• Multi-Scale Graph Representation Learning for Autism Identification With Functional MRI. [europepmc]
• Empirical social triad statistics can be explained with dyadic homophylic interactions. [europepmc]
• Omnipresence of the sensorimotor-association axis topography in the human connectome. [europepmc]
• BISoN: A Bayesian Framework for Inference of Social Networks. [europepmc]