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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 ...

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over Aug 1998 -Oct 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to 1) whether we aggregate the data over a week, month, quarter or year; 2) whether we look at the "growth" versus "maturity" phases of interbank market development; and 3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.

Abstract.A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset (2015 Proc. 29th AAAI Conf. on Artificial Intelligence). We build on this methodology and extend it to also include the versatile stochastic block models (SBMs) as a parametric family for reconstructing the empirical networks. We use five dierent techniques for change point detection on prototypical temporal networks, including empirical and synthetic ones. We find that none of the considered methods can consistently outperform the others when it comes to detecting and locating the expected change points in empirical temporal networks. With respect to the precision and the recall of the results of the change points, we find that the method based on a degree-corrected SBM has better recall properties than other dedicated methods, especially for sparse networks and smaller sliding time window widths.

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