Related papers: A Graph Theoretic Interpretation of Neural Complex…

Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…

Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…

Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the…

We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the…

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…

A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…

This paper aims to define, quantify, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method disentangles feature…

Curvature notions on graphs provide a theoretical description of graph topology, highlighting bottlenecks and denser connected regions. Artifacts of the message passing paradigm in Graph Neural Networks, such as oversmoothing and…

Graph theory has been extensively used to investigate brain network topology and its changes in disease cohorts. However, many graph theoretic analysis-based brain network studies focused on the shortest paths or, more generally,…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

The brain as an astonishingly remarkable device has been studied from various angles. It is now well known that neurons are the seat of all activities of the brain function. The dynamical properties pertaining to a single neuron and a…

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…

We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…

As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…

Noninvasive medical neuroimaging has yielded many discoveries about the brain connectivity. Several substantial techniques mapping morphological, structural and functional brain connectivities were developed to create a comprehensive road…