Related papers: Forman curvature for directed networks

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…

This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…

We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of…

In many real-world networks the ability to synchronize is a key property for its performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive…

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network…

With improvements in data resolution and quality, researchers can now represent complex systems as signed, weighted, and directed networks. In this article, we introduce a framework for measuring net and indirect effects without simplifying…

The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a…

Graph neural networks (GNNs) have achieved great success in many graph-based tasks. Much work is dedicated to empowering GNNs with the adaptive locality ability, which enables measuring the importance of neighboring nodes to the target node…

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the…

We show that hypernetworks can be regarded as posets which, in their turn, have a natural interpretation as simplicial complexes and, as such, are endowed with an intrinsic notion of curvature, namely the Forman Ricci curvature, that…

First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…

A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world…

Discrete Forman-Ricci curvature (FRC) is an efficient tool that characterizes essential geometrical features and associated transitions of real-world networks, extending seamlessly to higher-dimensional computations in simplicial complexes.…

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…

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…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and…

Complex networks have been studied in recent years due to their relevance in biological, social and technical real systems, such as the world wide web, social networks and biochemical interactions. One of the most current features of…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…