Related papers: Topological Reduction of Tight-Binding Models on C…

Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph theoretical methods. We show that the group structure of real…

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these…

One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…

In typical flat-band models, defined as nearest-neighbor tight-binding models, flat bands are usually pinned to the special energies, such as top or bottom of dispersive bands, or band-crossing points. In this paper, we propose a simple…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…

Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…

Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular…

We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…

This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…

Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…

Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…

The models of the Internet reported in the literature are mainly aimed at reproducing the scale-free structure, the high clustering coefficient and the small world effects found in the real Internet, while other important properties (e.g.…