Network theory

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

GNNGuard: Defending Graph Neural Networks against Adversarial Attacks

Abstract: Deep learning methods for graphs achieve remarkable performance on many tasks. However, despite the proliferation of such methods and their success, recent findings indicate that small, unnoticeable perturbations of graph structure can catastrophically reduce performance of even the strongest and most popular Graph Neural Networks (GNNs). Here, we develop GNNGuard, a general defense approach against a variety of training-time attacks that perturb the discrete graph structure. GNNGuard can be straightforwardly incorporated into any GNN. Its core principle is to detect and quantify the relationship between the graph structure and node features, if one exists, and then exploit that relationship to mitigate negative effects of the attack. GNNGuard uses network theory of homophily to learn how best assign higher weights to edges connecting similar nodes while pruning edges between unrelated nodes. The revised edges then allow the underlying GNN to robustly propagate neural messages in the graph. GNNGuard introduces two novel components, the neighbor importance estimation, and the layer-wise graph memory, and we show empirically that both components are necessary for a successful defense. Across five GNNs, three defense methods, and four datasets, including a challenging human disease graph, experiments show that GNNGuard outperforms existing defense approaches by 15.3% on average. Remarkably, GNNGuard can effectively restore the state-of-the-art performance of GNNs in the face of various adversarial attacks, including targeted and non-targeted attacks.

Scale-free trees: the skeletons of complex networks.

Abstract: We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing the total weight of the edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. Especially, in ubiquitous scale-free networks, it is found that the scale-free spanning tree shows very robust betweenness centrality distributions and the remaining shortcuts characterize the properties of the original network, such as the clustering coefficient and the classification of scale-free networks by the betweenness centrality distribution.

WANTED: A Good Network Theory of Organization

Abstract: Gerald R. Salancik Carnegie Mellon University Network analysis corrects a tendency in organizational theory to focus on the trees rather than the forest, on the actions of individual organizations rather than on the organization of their actions. Since it is fitting that organizational theory address organization, the reviews of Ronald Burt's book Structural Holes by David Krackhardt and Steven Andrews offer an opportunity for reflecting on the promise of social network analysis for organizational theory. Much of its promise has yet to be realized, in that social network analysis has been used mainly as a tool for analyzing data about organizations rather than for understanding organizations per se. Thus we know that personal interaction patterns in organizations are associated with power, turnover, information flows, attitudes, promotion opportunities, and social support. Beyond a single organization, we know that firms cluster because of their involvements on each other's boards and that such clusters relate to community influence, to corporate giving, to the adoption of defenses against corporate takeovers, or to the prices firms pay when acquiring other firms. We know also that network positions are related to power and that the structure of resource dependence relations shadows how firms conform to the demands of other firms or how they extract profits from one another.

Applying Network Theory to Quantify the Redundancy and Structural Robustness of Water Distribution Systems

Abstract: A water distribution system, represented as a spatially organized graph, is a complex network of multiple interconnected nodes and links. The overall robustness of such a system, in addition to the reliability of individual components, depends on the underlying network structure. This paper presents a deterministic network-based approach to study the relationship between the structure and function of water distribution systems and to critically review the application of structural measurements in the analysis of vulnerability and robustness of such systems. Benchmark water supply networks are studied, and their level of resistance to random failures and targeted attacks on their bridges and cut-sets are explored. Qualitative concepts such as redundancy, optimal connectivity, and structural robustness are quantified. Among other measurements, two metrics of meshedness coefficient and algebraic connectivity are found of great use toward quantifying redundancy and optimal connectivity, respectively. A brief ...