Applications of Temporal Graph Metrics to Real-World Networks

Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network of human contacts throughout the day. Recent studies have demonstrated that static network analysis is perhaps unsuitable in the study of real world network since static paths ignore time order, which, in turn, results in static shortest paths overestimating available links and underestimating their true corresponding lengths. Temporal extensions to centrality and efficiency metrics based on temporal shortest paths have also been proposed. Firstly, we analyse the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal; secondly, we present how such temporal metrics can be used to study the robustness of temporal networks in presence of random errors and intelligent attacks; thirdly, we study containment schemes for mobile phone malware which can spread via short range radio, similar to biological viruses; finally, we study how the temporal network structure of human interactions can be exploited to effectively immunise human populations. Through these applications we demonstrate that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.Comment: 25 page

A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids

Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimize a power grid topology for an enhanced phase transition behavior of the system

Robustness surfaces of complex networks

Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the $R^*$-value and introducing the concept of \emph{robustness surface} ($\Omega$). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.Comment: submitted to Scientific Report

Some Remarks about the Complexity of Epidemics Management

Recent outbreaks of Ebola, H1N1 and other infectious diseases have shown that the assumptions underlying the established theory of epidemics management are too idealistic. For an improvement of procedures and organizations involved in fighting epidemics, extended models of epidemics management are required. The necessary extensions consist in a representation of the management loop and the potential frictions influencing the loop. The effects of the non-deterministic frictions can be taken into account by including the measures of robustness and risk in the assessment of management options. Thus, besides of the increased structural complexity resulting from the model extensions, the computational complexity of the task of epidemics management - interpreted as an optimization problem - is increased as well. This is a serious obstacle for analyzing the model and may require an additional pre-processing enabling a simplification of the analysis process. The paper closes with an outlook discussing some forthcoming problems