Randomized flow model and centrality measure for electrical power transmission network analysis

International audienceCommonly used centrality measures identify the most important elements in networks of components, based on the assumption that flow occurs in the network only along the shortest paths. This is not so in real networks, where different operational rules drive the flow. For this reason, a different model of flow in a network is considered here: rather than along shortest paths only, it is assumed that contributions come essentially from all paths between nodes, as simulated by random walks. Centrality measures can then be coherently defined. An example of application to an electrical power transmission system is presented

Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known it current betweenness and resistance closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks

A General Framework for Complex Network Applications

Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding of the real system and a correct mapping of complex network theory to practical problems in the system. Despite of certain limitations discussed in this paper, complex network theory provides a foundation on which to develop powerful tools in analyzing and optimizing large interconnected systems.Comment: 8 page

Temporal Networks

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Space Weather and Power Grids - A Vulnerability Assessment

Strong geomagnetic disturbances resulting from solar activity can have a major impact on ground-based infrastructures, such as power grids, pipelines and railway systems. The high voltage transmission network is particularly affected as currents induced by geomagnetic storms, so-called GICs, can severely damage network equipment possibly leading to system collapse. Therefore, increasing attention has been devoted to understanding the vulnerability of power grids to space weather conditions. In this study, we aim at analysing the vulnerability of power grids to extreme space weather. By means of complex network theory, we propose an analysis approach to understand how geomagnetically induced currents are driven through the power network based on its structural and physical characteristics. As a test network we used the Finnish power grid for which a study using network centrality measures was carried out to understand which components are the most critical for the system when exposed to an electric field of 1V/km. This information is helpful as the identification and ranking of critical components can help to identify where and how mitigation measures should be implemented to increase the system’s resilience to space weather impact. We have also subjected the grid to varying angles of the electric field. In addition, we have carried out a scoping study adding load flow to the GICs induced in the system. The preliminary results suggest that the benchmark system can resist GICs induced from high intensity electric fields. Moreover, the simplified network seems more prone to collapse if the electric field is oriented northward. Work is underway to further validate and expand our approach with the aim to eventually carry out a risk assessment of space weather impact on the power grid at EU level.JRC.G.5-Security technology assessmen

Structural Properties of the Caenorhabditis elegans Neuronal Network

Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are neither accurate nor complete and self-consistent. Using materials from White et al. and new electron micrographs we assemble whole, self-consistent gap junction and chemical synapse networks of hermaphrodite C. elegans. We propose a method to visualize the wiring diagram, which reflects network signal flow. We calculate statistical and topological properties of the network, such as degree distributions, synaptic multiplicities, and small-world properties, that help in understanding network signal propagation. We identify neurons that may play central roles in information processing and network motifs that could serve as functional modules of the network. We explore propagation of neuronal activity in response to sensory or artificial stimulation using linear systems theory and find several activity patterns that could serve as substrates of previously described behaviors. Finally, we analyze the interaction between the gap junction and the chemical synapse networks. Since several statistical properties of the C. elegans network, such as multiplicity and motif distributions are similar to those found in mammalian neocortex, they likely point to general principles of neuronal networks. The wiring diagram reported here can help in understanding the mechanistic basis of behavior by generating predictions about future experiments involving genetic perturbations, laser ablations, or monitoring propagation of neuronal activity in response to stimulation

Performance Review of Selected Topology-Aware Routing Strategies for Clustering Sensor Networks

In this paper, cluster-based routing (CBR) protocols for addressing issues pertinent to energy consumption, network lifespan, resource allocation and network coverage are reviewed. The paper presents an indepth  performance analysis and critical review of selected CBR algorithms. The study is domain-specific and simulation-based with emphasis on the tripartite trade-off between coverage, connectivity and lifespan. The rigorous statistical analysis of selected CBR schemes was also presented. Network simulation was conducted with Java-based Atarraya discrete-event simulation toolkit while statistical analysis was carried out using MATLAB. It was observed that the Periodic, Event-Driven and Query-Based Routing (PEQ) schemes performs better than Low-Energy Adaptive Clustering Hierarchy (LEACH), Threshold-Sensitive Energy-Efficient Sensor Network (TEEN) and Geographic Adaptive Fidelity (GAF) in terms of network lifespan, energy consumption and network throughput.Keywords: Wireless sensor network, Hierarchical topologies, Cluster-based routing, Statistical analysis, Network simulatio

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Connectivity Analysis of Directed Highway VANETs using Graph Theory

Graph theory is a promising approach in handling the problem of estimating the connectivity probability of vehicular ad-hoc networks (VANETs). With a communication network represented as graph, graph connectivity indicators become valid for connectivity analysis of communication networks as well. In this article, we discuss two different graph-based methods for VANETs connectivity analysis showing that they capture the same behavior as estimated using probabilistic models. The study is, then, extended to include the case of directed VANETs, resulting from the utilization of different communication ranges by different vehicles. Overall, the graph-based methods prove a robust performance, as they can be simply diversified into scenarios that are too complex to acquire a rigid probabilistic model for them.Comment: 21 pages, 6 figure