Measuring Propagation with Temporal Webs

Bramson, Aaron; Hoefman, Kevin; Heuvel, Milan van den; Vandermarliere, Benjamin; Schoors, Koen

doi:10.1007/978-981-10-5287-3_4

Cited by 8 publications

(18 citation statements)

References 60 publications

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“…This model labels all states of triads by balance or imbalance and predicts two final stable balanced states for signed networks: heaven and bipolar [2]. HBT has been applied to many branches of science such as studies of international networks [3][4][5], sociology [7][8][9][10] and ecology [11]. There exists disagreement between researchers on how much the networks based on real data are balanced [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Quartic balance theory: Global minimum with imbalanced triangles

et al. 2020

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Balance theory proposed by Heider for the first time modeled triplet interaction in a signed network, stating that relationships between two people, friendship or enmity, is dependent on a third person. The Hamiltonian of this model has an implicit assumption that all triads are independent, meaning that state of each triad, being balanced or imbalanced, is ineffective to others. This independence forces the network to have completely balanced final states. However, there exists evidence indicating that real networks are partially balanced raising the question of what is the mechanism preventing the system to be perfectly balanced. Our suggestion is to consider a quartic interaction which dissolves the triad's independence. We use mean field method to study thermal behavior of such systems where the temperature is a parameter that allows the stochastic behavior of agents. We show that under a certain temperature, the symmetry between balanced and imbalanced triads will spontaneously break and we have a discrete phase transition. As consequence stability arises where either similar balanced or imbalanced triads dominate, hence the system obtains two new imbalanced stable states. In this model, the critical temperature depends on the second power of the number of nodes, which was a linear dependence in thermal balance theory. Our simulations are in good agreement with the results obtained by the mean field method.

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Section: Introductionmentioning

confidence: 99%

Quartic balance theory: Global minimum with imbalanced triangles

et al. 2020

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“…The triad network is extremely dense, and a change in one edge to balance a frustrated triad can (and usually does) propagate across the triad network, inducing more triads to become frustrated (Bramson, Hoefman et al . 2017).…”

Section: Results: Structural Balance In Evementioning

confidence: 99%

“…Balance theory implies that not only should the frustrated triads constitute a small proportion of the total network, but also their prevalence in the system should exhibit a decreasing trend (unless some event injects new information into the system). Although the theory operates at the level of individual triads, because triads share edges, the change of a single edge can set in motion a series of subsequent edge changes, as the frustration cascades throughout the network (Bramson, Hoefman et al 2017).…”

Section: Methods: Structural Balance Theorymentioning

confidence: 99%

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Diplomatic Relations in a Virtual World

et al. 2021

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We apply variations and extensions of structural balance theory to analyze the dynamics of geopolitical relations using data from the virtual world Eve Online. The highly detailed data enable us to study the interplay of alliance size, power, and geographic proximity on the prevalence and conditional behavior of triads built from empirical political alliances. Through our analysis, we reveal the degree to which the behaviors of players conform to the predictions of structural balance theory and whether our augmentations of the theory improve these predictions. In addition to studying the time series of the proportions of triad types, we investigate the conditional changes in triad types and the formation of polarized political coalitions. We find that player behavior largely conforms to the predictions of a multipolar version of structural balance theory that separates strong and weak configurations of balanced and frustrated triads. The high degree of explanatory power of structural balance theory in this context provides strong support for both the theory and the use of virtual worlds in social science research.

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“…Unbalanced [+ + −] and [− − −] triads, however, are a key ingredient in real-life political networks. Balance theory has found applications in many branches of sciences including psychology [1], studies of international networks [3,4,5,6,7], sociology [8,9,10,11,12] and ecology [13].As balance theory introduces correlations between the edge attributes in triads, in a physics framework [14,15,16,17] it maps onto a system with predominant three-edge interactions. Associating the existence of unbalanced triads to the occurrence of a non-vanishing excitation energy, the principles of social balance can be mapped onto a model with variations in an energy landscape.…”

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confidence: 99%

Social stability and extended social balance—Quantifying the role of inactive links in social networks

Belaza¹,

Ryckebusch²,

Bramson³

et al. 2019

Physica A: Statistical Mechanics and its Applications

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Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states. arXiv:1807.09042v3 [physics.soc-ph] 17 Dec 2018Heider [1] and its extension to graphs by Cartwright [2] is based on active relationships that can be friendly ("+") or unfriendly ("−"). The four types of emerging triadic relationships are categorized in two stable (= balanced) and two unstable (= unbalanced) ones, whereby one anticipates an overall tendency to create more balanced triads. Balanced triads [+ + +] and [+ − −] have an even number of "−" edges. Unbalanced [+ + −] and [− − −] triads, however, are a key ingredient in real-life political networks. Balance theory has found applications in many branches of sciences including psychology [1], studies of international networks [3,4,5,6,7], sociology [8,9,10,11,12] and ecology [13].As balance theory introduces correlations between the edge attributes in triads, in a physics framework [14,15,16,17] it maps onto a system with predominant three-edge interactions. Associating the existence of unbalanced triads to the occurrence of a non-vanishing excitation energy, the principles of social balance can be mapped onto a model with variations in an energy landscape. Marvel et al. [14] investigated the energy landscape of a social-balance inspired system and stressed the occurrence ...

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Measuring Propagation with Temporal Webs

Cited by 8 publications

References 60 publications

Quartic balance theory: Global minimum with imbalanced triangles

Quartic balance theory: Global minimum with imbalanced triangles

Diplomatic Relations in a Virtual World

Social stability and extended social balance—Quantifying the role of inactive links in social networks

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