Decelerated spreading in degree-correlated networks

While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show that the propagation becomes slow in positively (negatively) correlated networks if nodes with a high connectivity locally accelerate (decelerate) the propagation. Examining the efficient paths offers a coherent explanation for this result, while the $k$-core decomposition reveals the dependence of the nodal spreading efficiency on the correlation. Our findings should open new pathways to delicately control real-world spreading processes

Robustness of Trans-European Gas Networks

Here we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on inter-country flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual-purpose: on one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a non-operational pipeline causes only a minimal impact on network capacity, implying that the network is error-tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.Comment: 11 pages, 8 figures (minor changes

Congestion dependencies in the European gas pipeline network during crises.

Conflicts, geo-political crises, terrorist attacks, or natural disasters can turn large parts of energy distribution networks off-line, creating unexpected congestion in the remaining infrastructure. Given the importance of the security of natural gas supply, we need models that enable the management of network congestion, especially during crises. We develop a decentralized model of congestion control to explore the effects of removing supply or transit countries from the network. Recently, in R. Carvalho et. al. PLoS ONE, Vol. 9, no. 3, 2014, we evaluated how cooperation between countries helps to mitigate the effect of crises. Here, we extend our previous results by exploring the structure of downstream and upstream congestion dependencies between countries

Dynamic Effects Increasing Network Vulnerability to Cascading Failures

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robustness, and it is shown that {\it two} time scales $\tau$ and $\tau_0$, defined by the network dynamics, are important to consider prior to accurately addressing network robustness or vulnerability. The robustness of networks showing cascading failures is generally determined by a complex interplay between the network topology and flow dynamics, where the ratio $\chi=\tau/\tau_0$ determines the relative role of the two of them.Comment: 4 pages Latex, 4 figure

Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains

The Exact and Near Optimal Solution of the Competitive Uncapacitated Location Problem

This paper is dedicated to the recent unprecedented boom of new supermarkets and hypermarkets in middle Europe. The motivation is to provide for the newcomers the tool for decision support, and to help answer the questions: "Is still economically advantageous to build new shopping malls and where to locate them?" We introduce the four versions of data correcting algorithm and three heuristics: simple exchange heuristic, exchange heuristics enhanced by simulated annealing metaheuristic, and genetic algorithm. All these methods were examined at the benchmarks of practical nature. This research showed the data correcting method as useable for practical instances of this problem. There were also identified interesting dependencies between the computational time and the number of competitors