相关论文: The Hypergraphite: A possible extension of graphit…

Systems that can be described with the same mathematical models that account for the properties of electrons in graphene are known as graphene-like systems. These include magnons, photons, polaritons, acoustic waves, and electrons in…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…

It has been found that periodically closely spaced vacancies on a graphite sheet cause a significant rearrange-ment of its electronic spectrum: metallic waveguides with a high density of states near the Fermi level are formed along the…

Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken, by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion.…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Electronic band structures in hydrogenated graphene are theoretically investigated by means of first-principle calculations and an effective tight-binding model. It is shown that regularly designed hydrogenation to graphene gives rise to a…

The electronic properties of a material depend on the spatial freedom of the electron wavefunction. A well-known example is graphite, which is a conventional gapless semiconductor, while a single layer of it, graphene, exhibits extremely…

Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…

We study characteristic electronic structures in an extended martini lattice model and propose its materialization in $\pi$-electron networks constructed by designated chemisorption on graphene and silicene. By investigating the minimal…

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…

The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…