Related papers: Input graph: the hidden geometry in controlling co…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…
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…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
Human learners are adept at grasping the complex relationships underlying incoming sequential input. In the present work, we formalize complex relationships as graph structures derived from temporal associations in motor sequences. Next, we…
Topology inference is a powerful tool to better understand the behaviours of network systems (NSs). Different from most of prior works, this paper is dedicated to inferring the directed topology of NSs from noisy observations, where the…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear…