Asymmetry of social interactions and its role in link predictability: the case of coauthorship networks

The paper provides important insights into understanding the factors that influence tie strength in social networks. Using local network measures that take into account asymmetry of social interactions we show that the observed tie strength is a kind of compromise, which depends on the relative strength of the tie as seen from its both ends. This statement is supported by the Granovetter-like, strongly positive weight-topology correlations, in the form of a power-law relationship between the asymmetric tie strength and asymmetric neighbourhood overlap, observed in three different real coauthorship networks and in a synthetic model of scientific collaboration. This observation is juxtaposed against the current misconception that coauthorship networks, being the proxy of scientific collaboration networks, contradict the Granovetter's strength of weak ties hypothesis, and the reasons for this misconception are explained. Finally, by testing various link similarity scores, it is shown that taking into account the asymmetry of social ties can remarkably increase the efficiency of link prediction methods. The perspective outlined also allows us to comment on the surprisingly high performance of the resource allocation index -- one of the most recognizable and effective local similarity scores -- which can be rationalized by the strong triadic closure property, assuming that the property takes into account the asymmetry of social ties

Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure

Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks

Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local information. We explain microscopic origins of the transition from the flow to the jammed phase and discuss how the node neighbourhood topology affects the transport capacity in uncorrelated and correlated networks.Comment: 6 pages, 5 figure

Phase transitions in social networks

We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential random graphs. We show by numerical simulations and analytical considerations how a very simple Hamiltonian can lead to surprisingly complicated and eventful phase diagram.Comment: 8 pages, 8 figure

A minimal model for congestion phenomena on complex networks

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase and a congested phase, critical points and different scaling behaviors in the system size. It consists of random walkers on a queueing network with one-range repulsion, where particles can be destroyed only if they can move. We focus on the dependence on the topology as well as on the level of traffic control. We are able to obtain transition curves and phase diagrams at analytical level for the ensemble of uncorrelated networks and numerically for single instances. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces non-linear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the cross-over in the scaling of traffic fluctuations empirically observed in the Internet, and moreover, a conserved version can reproduce qualitatively some stylized facts of traffic in transportation networks

Coexistence of bicuspid aortic valve, aberrant right subclavian artery and common origin of carotid arteries

Background: Prevalence of bicuspid aortic valve (BAV) and right aberrant sub-clavian artery (ASA) separately is relatively common in general population, and much higher in some disorders. Surprisingly, coexistence of both valve and vessel anomalies has only been reported in single cases. Materials and methods: From 2008 to 2016, in a single, high-volume tertiary cardiac centre, patients who underwent chest computed tomography (CT) for various reasons, were retrospectively screened for the presence of right ASA. Results: Seventy-two patients with either right or left ASA were identified by CT. Among them 7 cases of BAV and right ASA coexistence were identified. Additionally, 1 case with coexisting common origin of carotid arteries (COCA) was visualised in this subgroup. Conclusions: Although coexistence of ASA and BAV has not been reported in paediatric population, it has been diagnosed in very few adults as well as in our series. Additional presence of COCA in this group seems to be very rare. From practical point of view, heart cannulation via the radial artery and subsequent ASA may be challenging. Similarly, COCA presence may have surgical implications during corrective procedures

Self-organized network evolution coupled to extremal dynamics

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a fitness, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.Comment: Accepted version. Supplementary information at http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm

Evolutionary Events in a Mathematical Sciences Research Collaboration Network

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5 figures; published in Scientometric