Complex Systems Studies

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🎞 https://youtu.be/uvEUNSu63E4

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Complex Systems Studies

🔖 Statistical physics of balance theory

Andres M. Belaza, Kevin Hoefman, Jan Ryckebusch,Aaron Bramson, Milan van den Heuvel, Koen Schoors

🔗 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183696

📌 ABSTRACT
Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data.

journals.plos.org

Statistical physics of balance theory

Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively…

316 views21:48

Complex Systems Studies

🔖 General Framework of Studying Eigenvector Multicentrality in Multilayer Networks

Mincheng Wu, Yongtao Zhang, Shibo He, Jiming Chen, Youxian Sun, Yang-Yu Liu

🔗
https://arxiv.org/pdf/1708.07763

📌 ABSTRACT
Multilayer networks have drawn much attention in the community of network science recently. Tremendous effort has been invested to understand their structure and functions, among which centrality is one of the most effective approaches. While various metrics of centrality have been proposed for single-layer networks, a general framework of studying centrality in multiplayer networks is lacking. Here we introduce a mathematical framework to study eigenvector multicentrality, which enables us to quantify the relationship between interlayer influences and eigenvector multicentrality, providing an analytical tool to describe how eigenvector multicentralities of nodes propagate among different layers. Further, the framework is flexible for integrating prior knowledge of the interplay among layers so as to attain a tailored eigenvector multicentrality for varying scenarios. We show how to model the multilayer influences by choosing appropriate influence weight functions and design algorithms to calculate eigenvector multicentrality in various typical scenarios. We apply this framework to analyze several empirical multilayer networks, finding that it can quantify the influences among layers and describe the structure-function relationship of multilayer networks very well.