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![(Colour online) European gas pipeline network. We show the transmission network [blue (dark gray) pipelines] overlaid with the distribution network [brown (light gray) pipelines]. Link thickness is proportional to the pipeline diameter. We projected the data with the Lambert azimuthal equal area projection [16]. Background colours identify EU member states.](/web/20220408004546im_/https://www.researchgate.net/profile/Rui-Carvalho-22/publication/26720900/figure/fig1/AS:310077216051203@1450939577958/Colour-online-European-gas-pipeline-network-We-show-the-transmission-network-blue.png)
(Colour online) European gas pipeline network. We show the transmission network [blue (dark gray) pipelines] overlaid with the distribution network [brown (light gray) pipelines]. Link thickness is proportional to the pipeline diameter. We projected the data with the Lambert azimuthal equal area projection [16]. Background colours identify EU member states.
Source publication
Here, we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on intercountry 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 flo...
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Context 1
... σ s,t is the number of shortest paths from node s to node t and σ s,t ( e ij ) is the number of these paths passing through link e ij . The concept of betweenness centrality was originally developed to characterise the influence of nodes in social networks [27, 28] and, to our knowledge, was used for the first time in the physics literature in the context of social networks by Newman [29] and in the context of communication networks by Goh et al. [30][45]. Betweenness centrality is relevant in man-made networks which deliver products, substances or materials as cost constraints on these networks condition transportation to occur along shortest paths. However, nodes and links with high betweenness in spatial networks are often near the network barycentre [31], whose location is given by x G = i x i /N , whereas the most important infrastructure elements are frequently along the periphery, close to either the sources or the sinks. Although flows are conditioned by a specific set of sources and sinks, the traffic between these nodes may be highly heteroge- neous and one may have only access to aggregate transport data, but not to the detailed flows between individual sources and sinks (e.g. competition between operators may prevent the release of detailed data). Here we propose a generalization of betweenness centrality in the context of flows taking place on a substrate network, but where flow data are available only at an aggregate level. We then show in the next section how the generalized betweenness centrality can help us to gain insights into the structure of trans-European gas pipeline networks. The substrate network is often composed of sets of nodes which act like aggregate sources and sinks. The aggregation can be geographical (e.g., countries, regions or cities), or organizational (e.g., companies or institu- tions). If the flow information is only available at aggregate level then a possible extension of the betweenness centrality for these networks is to weight the number of shortest paths between pairs of source and sink nodes by the amount of flow which is known to go through the network between aggregated pairs of sources and sinks. To do this, we must first create a flow network by parti- tioning the substrate network, G S = ( V S , E S ), into a set of disjoint subgraphs V F = { ( V S 1 , E S 1 ) , · · · , ( V S M , E M ) } . The flow network G F = ( V F , E F ) is then defined as the directed network of flows among the subgraphs in V F , where the links E F are weighted by the value of aggregate flow among the V F . For our purposes, the substrate network is the trans-European gas pipeline network rep- resented in Fig. 1 and the flow network is the network of international gas trade movements by pipeline in Fig. 2. The generalized betweenness centrality (generalized betweenness) of link e ij ∈ E S is defined as follows. Let T K,L be the flow from source subgraph K = ( V K , E K ) ∈ V F to sink subgraph L = ( V , E ) ∈ V . Take each ...
Context 2
... such as Norway and Switzerland), North Africa (main pipelines from Morocco and Tunisia), Eastern Europe (Belarus, Ukraine, Lithuania, Latvia, Estonia, and Turkey) and Western Russia (see Fig. 1). Similarly to electrical power grids, gas pipeline networks have two main layers: transmission and distribution. The transmission network transports natural gas over long distances (typically across different countries), whereas pipelines at the distribution level cover urban areas and deliver gas directly to end consumers. We extracted the gas pipeline transmission network from the complete natural gas network, as the connected component composed of all the important pipelines with diameter d ≥ 15 inches. To finalize the network, we added all other pipelines interconnecting major branches [19]. We treated the resulting network as undirected due to the lack of information on the direction of flows. However, network links are weighted according to pipeline diameter and length. The European gas pipeline infrastructure is a continent-wide sparse network which crosses 38 countries, has about 2 . 4 × 10 4 nodes [compressor stations, city gate stations, liquefied natural gas (LNG) termi- nals, storage facilities, etc.] connected by approximately 2 . 5 × 10 4 pipelines (including urban pipelines), spanning more than 4 . 3 × 10 5 km (see Table I). The trans- European gas pipeline network is, in fact, a union of national infrastructure networks for the transport and delivery of natural gas over Europe. These ...
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Citations
... The authors in (Chai et al., 2016;Gao et al., 2015;Hu et al., 2011;Michael et al., 2016), use percolation theory to analyze the robustness of CIs and evaluate the importance of the different network nodes by means different centrality measures. The author in (Carvalho et al., 2009), using the percolation theory (Linkov et al., 2019;Goel et al., 2011;Huang et al., 2015), performs the robustness analysis of the trans-European gas pipeline network from a topological point of view. The author proposes an analysis model based on the maximum flow method to estimate the tolerance of the network to failures. ...
The vulnerability of gas pipeline networks to physical and cyber-attacks calls for a resilience analysis based on models, capable of quantifying the network robustness and recovery from failures.
This work proposes an original resilience analysis framework for a complex gas pipeline transmission network, considering the cybernetic interdependence of the physical gas pipeline network with the SCADA system. The maximum flow algorithm computes the gas network supply capacity and when a failure occurs, the pressure of the network nodes and the gas supply capacity change, leading to dissatisfaction of customer demands. The framework allows quantifing the value of resilience through specific performance metrics.
The SCADA communication network, implemented in Network Simulator®, provides the necessary information regarding the delay of data packets coming from the sensors located along the pipelines. The packet delay value allows to evaluate the actual time at which the SCADA system blocks the remote control valves, ready to keep the pipelines under pressure when a failure occurs.
Important insights on the resilience model are obtained through a systematic sensitivity analysis (SA) framework, customized for gas pipeline transmission networks. Specifically, we investigate the influence of model inputs to the network robustness and recovery uncertainty. The effects of individual parameters and groups formed by inputs with similar functionalities provide useful information, such as to what extent the supervisory SCADA system interconnection affects the degradation and the recovery process of the physical gas pipeline network.
The results of the case study confirm, as expected, that gas transmission networks are vulnerable to both cyber and physical failures, pointing at the need for systemic methods of analysis for managing the system resilience.
... Over the last decade, complex network approaches have demonstrated their great potential in the study of complex systems in multiple domains, from physical (e.g., Refs. [7,8]) to social areas (e.g., Refs. [9]). ...
The dispersion of airborne pollutants in the urban atmosphere is a complex, canopy-driven process. The intricate structure of the city, the high number of potential sources, and the large spatial domain make it difficult to predict dispersion patterns, to simulate a great number of scenarios, and to identify the high-impact emission areas. Here we show that these complex transport dynamics can be efficiently characterized by adopting a complex network approach. The urban canopy layer is represented as a complex network. Street canyons and their intersections shape the spatial structure of the network. The direction and the transport capacity of the flow in the streets define the direction and the weight of the links. Within this perspective, pollutant contamination from a source is modeled as a spreading process on a network, and the most dangerous areas in a city are identified as the best spreading nodes. To this aim, we derive a centrality metric tailored to mass transport in flow networks. By means of the proposed approach, vulnerability maps of cities are rapidly depicted, revealing the nontrivial relation between urban topology, transport capacity of the street canyons, and forcing of the external wind. The network formalism provides promising insight in the comprehensive analysis of the fragility of cities to air pollution.
... Graphical networks and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d M a n u s c r i p t network metrics provide a unified framework for both illustrating and quantifying interactions between multivariate time series. They have been applied to a range of problems including physical networks [2,3] and biological networks [4,5]. Their use in characterising the interactions within brain networks is becoming well established [6,7,8,9]. ...
Objective:
Graphical networks and network metrics are widely used to understand and characterise brain networks and brain function. These methods can be applied to a range of electrophysiological data including electroencephalography, local field potential and single unit recordings. Functional networks are often constructed using pair-wise correlation between variables. The objective of this study is to demonstrate that functional networks can be more accurately estimated using partial correlation than with pair-wise correlation.
Approach:
We compared network metrics derived from unconditional and conditional graphical networks, obtained using coherence and multivariate partial coherence (MVPC), respectively. Graphical networks were constructed using coherence and MVPC estimates, and binary and weighted network metrics derived from these: node degree, path length, clustering coefficients and small-world index.
Main results:
Network metrics were applied to simulated and experimental single unit spike train data. Simulated data used a 10x10 grid of simulated cortical neurons with centre-surround connectivity. Conditional network metrics gave a more accurate representation of the known connectivity: Numbers of excitatory connections had range 3-11, unconditional binary node degree had range 6-80, conditional node degree had range 2-13. Experimental data used multi-electrode array recording with 19 single-units from left and right hippocampal brain areas in a rat model for epilepsy. Conditional network analysis showed similar trends to simulated data, with lower binary node degree and longer binary path lengths compared to unconditional networks.
Significance:
We conclude that conditional networks, where common dependencies are removed through partial coherence analysis, give a more accurate representation of the interactions in a graphical network model. These results have important implications for graphical network analyses of brain networks and suggest that functional networks should be derived using partial correlation, based on MVPC estimates, as opposed to the common approach of pair-wise correlation.
... Energies 2019, 12, 4685 2 of 30 gas transmission networks rely on large scale models [6]. In the past, however, critical infrastructure networks were developed to minimize local rather than global failures. ...
... In the past, however, critical infrastructure networks were developed to minimize local rather than global failures. Consequently, the impact of local optimization on the European natural gas network's robustness and security of supply on a global scale was analyzed [6][7][8]. Although network flows were estimated [6], the focus was mainly on the network's topology rather than on the network's overall performance. ...
... Indeed, the performance of a network is, in most cases, more complex than the sum of the performance of its components [25,26]. Therefore, several studies proposed methodological frameworks that incorporate the highly complex thermal-hydraulic computation [6,[27][28][29][30] coupled with stochastic processes to estimate the component states of the network requiring very detailed information of the network's technical specifications and component conditions [29][30][31][32][33][34]. To take uncertainties of the demand and supply into account, simulations involving economic models [28,30,[34][35][36] and flow allocation strategies have been used [3,30]. ...
Natural gas covers more than 20% of Europe’s primary energy demand. A potential disruption could lead to supply shortages with severe consequences for the European economy and society. History shows that such a vast and complex network system is prone to exogenous and endogenous disruptions. A dedicated large-scale dataset of the European natural gas network from publicly available information sources is assembled first. The spatial coverage, completeness and resolution allows analyzing the behavior of this geospatial infrastructure network (including consumption) and its components under likely disruptive events, such as earthquakes, and/or technical failures. Using the developed system state simulation engine, the disruption impact is mapped. The results show that storage facilities cannot in all cases compensate for a pipeline disruption. Moreover, critical pipelines, such as the Transitgas pipeline crossing the Alps and the Trans-Mediterranean pipeline bringing natural gas from Northern Africa, are identified. To analyze the pipelines with high impact on the system performance, a detailed scenario analysis using a Monte Carlo simulation resulting in supply grade mapping is conducted and presented for the case of Italy. Overall, it can be concluded that locations with a dead-end, sole supply, and without storage facility nearby, are remarkably exposed to natural gas supply losses.
... The theoretical investigation of complex networks has proven to be a valuable tool for the study of many real-world systems [1][2][3][4][5][6]. One important aspect is how the topological properties of networks are linked to their function and robustness [7,8]. ...
We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale structures. We present results from numerical two-objective optimization simulations for networks with various fixed mean degree and number of blocks. The results provide strong evidence that three different blocks are sufficient to realize the best trade-off between the two measures of robustness, i.e.\ to obtain the complete front of Pareto-optimal networks. For all values of the mean degree, a characteristic three block structure emerges over large parts of the Pareto-optimal front. This structure can be often characterized as a core-periphery structure, composed of a group of core nodes with high degree connected among themselves and to a periphery of low-degree nodes, in addition to a third group of nodes which is disconnected from the periphery, and weakly connected to the core. Only at both extremes of the Pareto-optimal front, corresponding to maximal robustness against random and targeted node removal, a two-block core-periphery structure or a one-block fully random network are found, respectively.
... In the same way, scholars combine graph theory with risk assessment methodologies, stochastic models and optimization methods to assess structural vulnerability and analyze the impact of topology on the propagation of cascading failures [33][34][35][36][37]. Similarly, researchers incorporate load flow studies and Monte Carlo simulation techniques with the different graph measures described above [38]. These methods are useful for quantifying the degree of impact on infrastructure and for carrying out resilience studies against natural disasters and terrorist attacks [39]. ...
Gas and electricity transmission systems are increasingly interconnected, and an attack on certain assets can cause serious energy supply disruptions, as stated in recommendation (EU) 2019/553 on cybersecurity in the energy sector, recently approved by the European Commission. This study aims to assess the vulnerability of coupled natural gas and electricity infrastructures and proposes a method based on graph theory that incorporates the effects of interdependencies between networks. This study is built in a joint framework, where two different attack strategies are applied to the integrated systems: (1) disruptions to facilities with most links and (2) disruptions to the most important facilities in terms of flow. The vulnerability is measured after each network attack by quantifying the unmet load (UL) through a power flow analysis and calculating the topological damage of the systems with the geodesic vulnerability (v) index. The proposed simulation framework is applied to a case study that consists of the IEEE 118-bus test system and a 25-node high-pressure natural gas network, where both are coupled through seven gas-fired power plants (GFPPs) and three electric compressors (ECs). The methodology is useful for estimating vulnerability in both systems in a coupled manner, studying the propagation of interdependencies in the two networks and showing the applicability of the v index as a substitute for the UL index.
... The degree of a node has an important relationship with geographical population density (∼ 15 geographical population density) and it should be looked as indicator for functionality loss when a node is attacked [21]. 16 The dimensions of geographical population density is 1/Area 2 and it is combined with shortest path length (d ij ) between 17 affected nodes (j) and removed node (i) because Metro networks are generally planner graphs (most portions of it) and 18 metro rails travels on shortest paths between metro stations (in majority of the cases). The square of shortest path length 19 (d 2 ij ) is multiplied with degree of node (k j ) to get functionality of a node in its vicinity. ...
Recently, cities are expanding due to population growth and migration from rural areas. This phenomenon has caused baffling traffic congestions. Metro network is a viable solution to tackle this problem. With the expansion of cities, Metro infrastructure is required to be updated and expanded. Delhi city and Delhi Metro network is a typical example of this case. Delhi Metro network is undergoing expansion and it is scheduled to be completed by the year 2021. In this work, a complex network based comparative analysis of existing Delhi Metro (DMop) network and its extension (DMext) is performed. The results show that degree distribution and parameters related to degree are almost same in both networks. The local connectivity will improve marginally but global connectivity will fall significantly (15%) for DMext. The transport capacity of DMext will increase by 64% compared to DMop. To study the connectivity vulnerability and functionality vulnerability, five malicious attacks protocols are deployed. Two malicious hybrid attack protocols are proposed which are more efficient compared to other malicious attack protocols available in the literature. Pertaining to functionality, it is found that if same fraction of nodes (or edges) is attacked in both networks then DMext is slightly more vulnerable as compared to DMop. But, if same number of nodes (or edges) is attacked under any attack protocol then the DMext is more robust. In case of connectivity, DMext is slightly more vulnerable for same fraction of nodes attacked as well as for same number of nodes attacked.
... The most important variable in a gas network is pressure, which is the driving force for the transport of the NG through the pipe. When gas flows, the pressure decreases due to the frictional interaction between the gas and the pipe wall, exerting a shear force on the gas [2,[13][14][15][16][17]. ...
The continuous uninterrupted supply of Natural Gas (NG) is crucial to today's economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton-Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids.
... Another cause for uncertainty about the network graph might be malicious attacks and unintentional failures. This issue is encountered in transportation networks [18], sensor networks [19] and gas networks [20]. ...
This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work.
... Metro networks can be modeled as complex systems and complex network theory can be applied to study the effect of failure on performance and connectivity. Many Scholars have applied complex network theory to study a different kind of infrastructure networks such as power grids [10,11,12,13], air transport [14], pipeline [15,16], 20 bus network [17] and Metro networks [1,18,19,20,21]. Vulnerability analysis is a key area in the study of Metro networks from complex network perspective [1,21,22,23,24,25,26,27,28,29,30]. ...
Recently, cities are expanding due to population growth and migration from rural areas. This phenomenon has caused baffling traffic congestions. Metro network is a viable solution to tackle this problem. With the expansion of cities, Metro infrastructure is required to be updated and expanded. Delhi city and Delhi Metro network is a typical example of this case. Delhi Metro network is undergoing expansion and it is scheduled to be completed by the year 2021. In this work, a complex network based comparative analysis of existing Delhi Metro (DMop) network and its extension (DMext) is performed. The results show that degree distribution and parameters related to degree are almost same in both networks. The local connectivity will improve marginally but global connectivity will fall significantly (15%) for DMext. The transport capacity of DMext will increase by 64% compared to DMop. To study the connectivity vulnerability and functionality vulnerability, five malicious attacks protocols are deployed. Two malicious hybrid attack protocols are proposed which are more efficient compared to other malicious attack protocols available in the literature. Pertaining to functionality, it is found that if same fraction of nodes (or edges) is attacked in both networks then DMext is slightly more vulnerable as compared to DMop. But, if same number of nodes (or edges) is attacked under any attack protocol then the DMext is more robust. In case of connectivity, DMext is slightly more vulnerable for same fraction of nodes attacked as well as for same number of nodes attacked.
