Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

A MDP-Based Vulnerability Analysis of Power Networks Considering Network Topology and Transmission Capacity

Abstract: This paper aims to study the vulnerability of the network to sequential cascading failures attacks where the attack strategy integrates network theory and discounted reward with Markov decision process (MDP) in the target selection process. A control strategy is designed to maximize the attack's long-term expected reward while reducing the attack sequence duration. The attack model identifies the most suitable targets by prediction through a Markov process for predicting the propagation and consequences of the failure. The state transition probabilities through a hidden failure model embedded in an independent edge-dependent network evolution model is estimated. Value iteration algorithms are used to identify targets at every attack stage. Target selection is updated depending on network changes. The results provide an optimal attack strategy based on network congestion with maximum damage, considering congestion as a cascade propagation mechanism. Reward functions based on increasing congestion and immediate power loss are compared. Strategies designed with network congestion as the attack reward function produce more vulnerability of the network to sequential attacks.

Ecological Multilayer Networks: A New Frontier for Network Ecology

Abstract: Networks provide a powerful approach to address myriad phenomena across ecology. Ecological systems are inherently 'multilayered'. For instance, species interact with one another in different ways and those interactions vary spatiotemporally. However, ecological networks are typically studied as ordinary (i.e., monolayer) networks. 'Multilayer networks' are currently at the forefront of network science, but ecological multilayer network studies have been sporadic and have not taken advantage of rapidly developing theory. Here we present the latest concepts and tools of multilayer network theory and discuss their application to ecology. This novel framework for the study of ecological multilayer networks encourages ecologists to move beyond monolayer network studies and facilitates ways for doing so. It thereby paves the way for novel, exciting research directions in network ecology.

Systems Ecology: Ecological Network Analysis ☆

Abstract: Ecological Network Analysis (ENA), based on network theory, is a methodology to quantify how objects interact with and depend on other objects in a system. Primary results from the method provide structural and functional properties of networks. A subset of ENA, Network Environ Analysis, divides the network into input and output “environs.” Application on empirical datasets and ecosystem models has revealed several important and unexpected results that have been identified and summarized in the literature. Data requirements for the analysis include the intercompartmental flows, compartmental storages, and boundary input and output flows. This article reviews the theoretical underpinning of several types of analyses of networks and briefly introduces some the main properties such as indirect effects ratio, network homogenization, network mutualism, ascendency and robustness. References for further reading are provided.

Predicting Heuristic Search Performance with PageRank Centrality in Local Optima Networks

Abstract: Previous studies have used statistical analysis of fitness landscapes such as ruggedness and deceptiveness in order to predict the expected quality of heuristic search methods. Novel approaches for predicting the performance of heuristic search are based on the analysis of local optima networks (LONs). A LON is a compressed stochastic model of a fitness landscape's basin transitions. Recent literature has suggested using various LON network measurements as predictors for local search performance.In this study, we suggest PageRank centrality as a new measure for predicting the performance of heuristic search methods using local search. PageRank centrality is a variant of Eigenvector centrality and reflects the probability that a node in a network is visited by a random walk. Since the centrality of high-quality solutions in LONs determines the search difficulty of the underlying fitness landscape and since the big valley property suggests that local optima are not randomly distributed in the search space but rather clustered and close to one another, PageRank centrality can serve as a good predictor for local search performance. In our experiments for NK-models and the traveling salesman problem, we found that the PageRank centrality is a very good predictor for the performance of first-improvement local search as well as simulated annealing, since it explains more than 90% of the variance of search performance. Furthermore, we found that PageRank centrality is a better predictor of search performance than traditional approaches such as ruggedness, deceptiveness, and the length of the shortest path to the optimum.

Lightweight Centrality Measures in Networks under Attack

Abstract: In this paper we study deliberate attacks on the infrastructure of large scale-free networks. These attacks are based on the importance of individual vertices in the network in order to be successful, and the concept of centrality (originating from social science) has already been utilized in their study with success. Some measures of centrality however, as betweenness, have disadvantages that do not facilitate the research in this area. We show that with the aid of scale-free network characteristics such as the clustering coeffi cient we can get results that balance the current centrality measures, but also gain insight into the workings of these networks.