Related papers: Network susceptibilities: theory and applications

With the advance of efficient analytical methods for sensitivity analysis ofprobabilistic networks, the interest in the sensitivities revealed by real-life networks is rekindled. As the amount of data resulting from a sensitivity analysis…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…

A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…

The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how…

The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…

These notes introduce the theory of susceptibilities as developed in [arXiv:2504.18274, arXiv:2601.12703] for interpreting neural networks. The susceptibility of an observable $\phi$ to a data perturbation is defined as a derivative of a…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

In this paper, a methodology inspired on bond and site percolation methods is applied to the estimation of the resilience against failures in power grids. Our approach includes vulnerability measures with both dynamical and structural…

Power grids, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing…

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…

Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…

We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the…

The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…

Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…