Related papers: Dimensions, Structures and Security of Networks

Network structures in a wide array of systems such as social networks, transportation, power and water distribution infrastructures, and biological and ecological systems can exhibit critical thresholds or tipping points beyond which there…

Modern urban resilience is threatened by cascading failures in multimodal transport networks, where localized shocks trigger widespread paralysis. Existing models, limited by their focus on pairwise interactions, often underestimate this…

Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…

Networks are a general language for representing relational information among objects. An effective way to model, reason about, and summarize networks, is to discover sets of nodes with common connectivity patterns. Such sets are commonly…

In this investigation we study a family of networks, called spiders, which covers a range of networks going from chains to complete graphs. These spiders are characterized by three parameters: the number of nodes in the core, the number of…

An important task in network analysis is the detection of anomalous events in a network time series. These events could merely be times of interest in the network timeline or they could be examples of malicious activity or network…

This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…

Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…

This paper deals with strong structural controllability of structured networks. A structured network is a family of structured systems (called node systems) that are interconnected by means of a structured interconnection law. The node…

The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast…

Power-law networks such as the Internet, terrorist cells, species relationships, and cellular metabolic interactions are susceptible to node failures, yet maintaining network connectivity is essential for network functionality.…

Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a…

An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control.…

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…

Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing.…

Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…

The power of networks manifests itself in a highly non-linear amplification of a number of effects, and their weakness - in propagation of cascading failures. The potential systemic risk effects can be either exacerbated or mitigated,…

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…

Real-world networks typically exhibit several aspects, or layers, of interactions among their nodes. By permuting the role of the nodes and the layers, we establish a new criterion to construct the dual of a network. This approach allows to…