Social balance theory

Last updated January 05, 2025

Social balance theory is a class of theories about balance or imbalance of sentiment relation in dyadic or triadic relations with social network theory.^[1] Sentiments can result in the emergence of two groups. Disliking exists between the two subgroups within liking agents.

Development of the theory

This theory evolved over time to produce models more closely resembling real-world social networks. It uses a balance index to measure the effect of local balance on that of a global level and also on a more intimate level, like in interpersonal relationships. Dorwin Cartwright and Frank Harary introduced clustering to account for multiple social cliques. Davis introduced hierarchical clustering to account for asymmetric relations.

The topology and hubness of positive and negative links have been shown to significantly affect the structural balance of real-world signed networks.^[2] This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph.^[3]

The dynamics of relationships have been modeled to explore the finite states of social networks, ranging from an idealized "paradise," where all links represent friendships, to social bipolarity.^[4]^[5] The energy landscape of social relationships has been conceptualized using interacting spin models, based on the contrast between balanced and imbalanced relationships in social networks.^[6] This framework has also been applied to the study of brain network dynamics, providing insights into the mechanisms underlying cognitive and brain systems and contributing to the development of improved neurobiomarkers.^[7]

Features of the theory

3 Relationship Types

Structural balance theory, proposed by the psychologist Fritz Heider in the 1940s, is a framework used to understand the dynamics of relationships within social networks. The theory focuses on the notion that individuals strive for consistency and harmony in their interpersonal relationships.

According to structural balance theory, relationships between individuals can be categorized into three types:

Positive (or balanced) relationships: These are relationships where all parties involved have mutual positive sentiments toward each other. For example, if A likes B and B likes C, then A should also like C to maintain balance.
Negative (or imbalanced) relationships: These are relationships where there is conflict or antagonism between individuals. For example, if A dislikes B and B dislikes C, then A should like C to restore balance.
Mixed relationships: These are relationships that are neither entirely positive nor entirely negative. They can create tension or discomfort within the social network until balance is achieved.

Structural balance theory suggests that individuals tend to seek and maintain balanced relationships within their social networks. When imbalances occur, individuals may adjust their relationships or perceptions to restore balance. This theory has been applied in various fields such as sociology, psychology, and computer science to study phenomena like group dynamics, social influence, and network stability.

4 Rules

Structural balance theory posits that some types of triads are forbidden and others are permitted on the basis of four rules.^[8]

Using the term “friend” to designate a positive sentiment and the term “enemy” to designate a negative sentiment, the classic balance model defines a sentiment network as balanced if it contains no violations of four assumptions:

(A1) A friend of a friend is a friend,

(A2) A friend of an enemy is an enemy,

(A3) An enemy of a friend is an enemy,

(A4) An enemy of an enemy is a friend.

16 Triad Types

The configuration of sentiments in each triad can be classified as one of 16 possible types.^[8]

The 16 types of triads that are possible in any group of three or more individuals are characterized by three numbers indicating the number of mutual (M), asymmetric (A), and null (N) ties, and symbols that discriminate triads with identical MAN numbers. These symbols include transitive (T), up (U), down (D), and cyclic (C) when required. Only two triads (300 and 102) do not violate any of the four rules, leading to the classic model's implication of united or bifurcated macrostructures (page 6).

Sources: p.6, p.9, p.15

Related Research Articles

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Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes and the ties, edges, or links that connect them. Examples of social structures commonly visualized through social network analysis include social media networks, meme proliferation, information circulation, friendship and acquaintance networks, business networks, knowledge networks, difficult working relationships, collaboration graphs, kinship, disease transmission, and sexual relationships. These networks are often visualized through sociograms in which nodes are represented as points and ties are represented as lines. These visualizations provide a means of qualitatively assessing networks by varying the visual representation of their nodes and edges to reflect attributes of interest.

<span class="mw-page-title-main">Network theory</span> Study of graphs as a representation of relations between discrete objects

In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.

Fritz Heider was an Austrian psychologist whose work was related to the Gestalt school. In 1958 he published The Psychology of Interpersonal Relations, which expanded upon his creations of balance theory and attribution theory. This book presents a wide-range analysis of the conceptual framework and the psychological processes that influence human social perception. It had taken 15 years to complete; before it was completed it had already circulated through a small group of social psychologists.

In the psychology of motivation, balance theory is a theory of attitude change, proposed by Fritz Heider. It conceptualizes the cognitive consistency motive as a drive toward psychological balance. The consistency motive is the urge to maintain one's values and beliefs over time. Heider proposed that "sentiment" or liking relationships are balanced if the affect valence in a system multiplies out to a positive result.

In graph theory, the degree of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex $is denoted or . The maximum degree of a graph is denoted by, and is the maximum of's vertices' degrees. The minimum degree of a graph is denoted by, and is the minimum of's vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0.$

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.

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<span class="mw-page-title-main">Signed graph</span> Graph with sign-labeled edges

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign.

Mathematical sociology is an interdisciplinary field of research concerned with the use of mathematics within sociological research.

<span class="mw-page-title-main">Interpersonal ties</span>

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"The enemy of my enemy is my friend" is an ancient proverb which suggests that two parties can or should work together against a common enemy. The exact meaning of the modern phrase was first expressed in the Latin phrase "Amicus meus, inimicus inimici mei", which had become common throughout Europe by the early 18th century, while the first recorded use of the current English version came in 1884.

Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel in his 1908 book Soziologie [Sociology: Investigations on the Forms of Sociation]. Triadic closure is the property among three nodes A, B, and C, that if the connections A-B and A-C exist, there is a tendency for the new connection B-C to be formed. Triadic closure can be used to understand and predict the growth of networks, although it is only one of many mechanisms by which new connections are formed in complex networks.

Triad refers to a group of three people in sociology. It is one of the simplest human groups that can be studied and is mostly looked at by microsociology. The study of triads and dyads was pioneered by German sociologist Georg Simmel at the end of the nineteenth century.

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In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks. The uprise of hubs in scale-free networks is associated with power-law distribution. Hubs have a significant impact on the network topology. Hubs can be found in many real networks, such as the brain or the Internet.

Attitude-behaviour consistency is a central concept in social psychology that examines the relationship between individual’s attitudes and their behaviour. Although, people often act in ways inconsistent with their attitudes, and the relationship has been highly debated among researchers. Many argue that attitudes are not the only factors influencing behaviour; some people behave more in line with their attitudes than do others, and people’s behaviour aligns with their attitudes is some circumstances more than in others.

Cognitive social structures (CSS) is the focus of research that investigates how individuals perceive their own social structure. It is part of social network research and uses social network analysis to understand how various factors affect one's cognitive representation of the network. Importantly, an individual's perception of the network may be different than reality. In fact, these differences between the perceived network and the actual network are the focus of many studies that seek insight into how we think about others and our relationships.

References

↑ Hokky Situngkir and Deni Khanafiah. 2004. Social balance theory: Revisiting heider’s balance theory for many agents. Technical Report.
↑ Saberi M, Khosrowabadi R, Khatibi A, Misic B, Jafari G (January 2021). "Topological impact of negative links on the stability of resting-state brain network". Scientific Reports. 11 (1): 2176. Bibcode:2021NatSR..11.2176S. doi:10.1038/s41598-021-81767-7. PMC 7838299 . PMID 33500525.
↑ Facchetti G, Iacono G, Altafini C (December 2011). "Computing global structural balance in large-scale signed social networks". Proceedings of the National Academy of Sciences. 108 (52): 20953–20958. doi:10.1073/pnas.1109521108. PMID 22167802.
↑ Antal T, Krapivsky PL, Redner S (2005). "Dynamics of social balance on networks". Physical Review E—Statistical, Nonlinear, and Soft Matter Physics. 72 (3): 036121. doi:10.1103/PhysRevE.72.036121.
↑ Manshour P, Montakhab A (2021). "Dynamics of social balance on networks: The emergence of multipolar societies". Physical Review E. 104 (3): 034303. doi:10.1103/PhysRevE.104.034303.
↑ Marvel SA, Strogatz SH, Kleinberg JM (2009). "Energy landscape of social balance". Physical Review Letters. 103 (19): 198701. doi:10.1103/PhysRevLett.103.198701.
↑ Saberi M, Rieck JR, Golafshan S, Grady CL, Misic B, Dunkley BT, Khatibi A (2024). "The brain selectively allocates energy to functional brain networks under cognitive control". Scientific Reports. 14 (1): 32032. doi:10.1038/s41598-024-83696-7.
1 2 Rawlings, Craig M.; Friedkin, Noah E. (2017-09-01). "The Structural Balance Theory of Sentiment Networks: Elaboration and Test". American Journal of Sociology. 123 (2): 510–548. doi:10.1086/692757. ISSN 0002-9602.