Balance In Social Networks Research Articles

Testing for Balance in Social Networks

Friendship and antipathy exist in concert with one another in real social networks. Despite the role they play in social interactions, antagonistic ties are poorly understood and infrequently measured. One important theory of negative ties that has received relatively little empirical evaluation is balance theory, the codification of the adage “the enemy of my enemy is my friend” and similar sayings. Unbalanced triangles are those with an odd number of negative ties, and the theory posits that such triangles are rare. To test for balance, previous works have used a permutation test on the edge signs. The flaw in this method, however, is that it assumes that negative and positive edges are interchangeable. In reality, they could not be more different. Here, we propose a novel test of balance that accounts for this discrepancy and show that our test is more accurate at detecting balance. Along the way, we prove asymptotic normality of the test statistic under our null model, which is of independent interest. Our case study is a novel dataset of signed networks we collected from 32 isolated, rural villages in Honduras. Contrary to previous results, we find that there is only marginal evidence for balance in social tie formation in this setting.

Partial balance in social networks with stubborn links

Structural balance theory affirms that in signed social networks with simultaneous friendly/hostile interactions, there is a general tendency of evolving to reduce the tensions. From this perspective, individuals iteratively invert their sentiments to reduce the felt tensions induced by imbalance. Each agent in a signed network has a mixture of positive and negative links representing friendly or antagonistic interactions and his stubbornness about interactions. We define stubbornness as an extreme antagonistic interaction that is resistant to change. In the current paper, we investigate if the presence of stubborn links renders an impact on the balanced state of the network and whether or not the degree of balance in a signed network depends on the location of stubborn links. Our results show that a poorly balanced configuration consists of multiple antagonistic groups. Both analytical and simulation results demonstrate that the global level of balance of the network is more influenced by the locations of stubborn links in the resulting network topology than by the fraction of stubborn links. This means that even with a large fraction of stubborn links the network would evolve towards a balanced state. On the other hand, if a small fraction of stubborn links are clustered in five stubborn communities, the network evolves into an unbalanced state.

On the Logic of Balance in Social Networks

Modal logics for reasoning about social networks is currently an active field of research. There is still a gap, however, between the state of the art in logical formalisations of concepts related to social networks and the much more mature field of social network analysis. In this paper we take a step to bridge that gap. One of the key foundations of social network analysis is balance theory, which is used to analyse signed social networks where agents can have positive (“friends”) or negative (“enemies”) relationships. Certain combinations of positive and negative relationships are considered to be unbalanced, or unstable—in particular the occurrence of cycles with an odd number of negative relationships. Especially relatively short cycles with an odd number of negative relationships are thought to put pressure on the agents to change one or more of the involved relationships from negative to positive or the other way around. Most existing logics for reasoning about social networks are defined for unsigned networks. In this paper we develop a modal logic for reasoning about structural properties of signed social networks, and give a sound and complete Hilbert-style axiomatic system. Furthermore, we completely axiomatise classes of signed social networks that are balanced to a certain degree n, in the sense that there are no cycles of length up to n with an odd number of negative relationships. Finally, we completely axiomatise the class of all fully balanced complete signed social networks, i.e., networks where everyone is connected with everyone else. Axiomatic completeness is non-trivial because neither the balance properties, nor the dichotomy between positive and negative relations, are modally definable. The paper thus provides a logical basis for reasoning about signed social networks in general and balanced networks in particular.

Transitivity and structural balance in marmot social networks

Social relationships are composed of both positive (affiliative) and negative (agonistic) interactions, representing opposing effects. Social network theory predicts that positive relationships should be transitive; thus, the friend of a friend is more likely to be a friend. Further, when considering both positive and negative relationships jointly, structural balance theory predicts that certain configurations of positive and negative relationships in a triad are inherently less stable (unbalanced) and should tend to be eliminated. However, structural balance has been rarely examined in nonhuman social systems. We tested for transitivity and structural balance in social networks of socially flexible yellow-bellied marmots (Marmota flaviventer) and asked if group size, network density, or group composition affected the degree of structural balance. We found a consistent pattern of significant transitivity in positive interactions, some transitivity in negative interactions, and some evidence of structural balance. In particular, a “weak” definition of structural balance is probably more common than “strong” structural balance, which used a stricter definition of balance. Network size limited the ability to detect these social processes, and smaller networks were less likely to show significant transitivity or structural balance. The proportion of adult females in a group affected the level of transitivity but did not affect the degree of structural balance. Our study suggests that there are intriguing similarities in social processes across diverse animal societies and that studying triads and network motifs may help identify basic social mechanisms linking local to global structure. SIGNIFICANCE STATEMENT: Social network theory predicts that basic social mechanisms should lead to similar structural properties across different societies. For example, positive relationships should be transitive (a friend of a friend is a friend), and certain combinations of positive and negative relationships represent conflict and should be unstable over time (e.g., a friend of a friend being an enemy is an unstable state). This latter theory, called structural balance, has rarely been examined in nonhuman societies; hence, we tested for transitivity and structural balance in groups of free-living yellow-bellied marmots. Positive interactions were generally transitive, but evidence for structural balance was inconsistent. Furthermore, group composition could affect network transitivity, and small network size (associated with few interactions) limits ability to detect significant patterns. Our results suggest that transitivity is fundamental in structuring positive relationships, while some forms of structural balance are present but not widespread.

Erratum to: Evaluating balancing on social networks through the efficient solution of correlation clustering problems

One challenge for social network researchers is to evaluate balance in a social network. The degree of balance in a social group can be used as a tool to study whether and how this group evolves to a possible balanced state. The solution of clustering problems defined on signed graphs can be used as a criterion to measure the degree of balance in social networks and this measure can be obtained with the optimal solution of the correlation clustering problem, as well as a variation of it, the relaxed correlation clustering problem. However, solving these problems is no easy task, especially when large network instances need to be analyzed. In this work, we contribute to the efficient solution of both problems by developing sequential and parallel ILS metaheuristics. Then, by using our algorithms, we solve the problem of measuring the structural balance on large real-world social networks.

Evaluating balancing on social networks through the efficient solution of correlation clustering problems

One challenge for social network researchers is to evaluate balance in a social network. The degree of balance in a social group can be used as a tool to study whether and how this group evolves to a possible balanced state. The solution of clustering problems defined on signed graphs can be used as a criterion to measure the degree of balance in social networks and this measure can be obtained with the optimal solution of the correlation clustering problem, as well as a variation of it, the relaxed correlation clustering problem. However, solving these problems is no easy task, especially when large network instances need to be analyzed. In this work, we contribute to the efficient solution of both problems by developing sequential and parallel ILS metaheuristics. Then, by using our algorithms, we solve the problem of measuring the structural balance on large real-world social networks.

Walk-based measure of balance in signed networks: detecting lack of balance in social networks.

There is a longstanding belief that in social networks with simultaneous friendly and hostile interactions (signed networks) there is a general tendency to a global balance. Balance represents a state of the network with a lack of contentious situations. Here we introduce a method to quantify the degree of balance of any signed (social) network. It accounts for the contribution of all signed cycles in the network and gives, in agreement with empirical evidence, more weight to the shorter cycles than to the longer ones. We found that, contrary to what is generally believed, many signed social networks, in particular very large directed online social networks, are in general very poorly balanced. We also show that unbalanced states can be changed by tuning the weights of the social interactions among the agents in the network.

Active influence in dynamical models of structural balance in social networks

We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social psychology called structural balance, the negative links play a key role in both the structure and dynamics of the network. Recent research has shown that in a nonlinear dynamical system modeling the time evolution of “friendliness levels” in the network, two opposing factions emerge from almost any initial condition. Here we study active external influence in this dynamical model and show that any agent in the network can achieve any desired structurally balanced state from any initial condition by perturbing its own local friendliness levels. Based on this result, we also introduce a new network centrality measure for signed networks. The results are illustrated in an international-relations network using United Nations voting record data from 1946 to 2008 to estimate friendliness levels amongst various countries.

Cultures of the Central Highlands, New Guinea

Cultures of the Central Highlands, New Guinea