Related papers: The Hypergraphite: A possible extension of graphit…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…
Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…
Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here we study moir\'e superlattice minibands in…
Bernal stacked bilayer graphene subject to a superlattice potential can realize topological and stacked flat bands [1]. In the present work, we extend the study of a superlattice potential on graphene heterostructures to trilayer and…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
Undoped graphene is semi-metallic and thus not suitable for many electronic and optoelectronic applications requiring gapped semiconductor materials. However, a periodic array of holes (antidot lattice) renders graphene semiconducting with…
Graphene's original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in…
We view $MgB_2$ as electronically equivalent to (non-staggered) graphite ($B^-$ layer) that has undergone a zero gap semiconductor to a superconductor phase transition by a large c-axis (chemical) pressure due to $Mg^{++}$ layers. Further,…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
The electronic transport properties of graphene-based superlattice structures are investigated. A graphene-based modulation-doped superlattice structure geometry is proposed and consist of periodically arranged alternate layers:…
We demonstrate, by explicit construction, that a single band tight binding Hamiltonian defined on a class of deterministic fractals of the b = 3N Sierpinski type can give rise to an infinity of dispersionless, flat-band like states which…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
Networked structure emerged from a wide range of fields such as biological systems, World Wide Web and technological infrastructure. A deeply insight into the topological complexity of these networks has been gained. Some works start to pay…
In this document we explore graphene, a two-dimensional material with remarkable properties. We center our discussion around its electronic characteristics and their applications. We begin by giving a simple electronic model which will then…
Semiconductor glasses exhibit many unique optical and electronic anomalies. We have put forth a semi-phenomenological scenario (J. Chem. Phys. 132, 044508 (2010)) in which several of these anomalies arise from deep midgap electronic states…
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
Bilayer graphene nanoribbon with zigzag edge is investigated with the tight binding model. Two stacking structures, alpha and beta, are considered. The band splitting is seen in the alpha structure, while the splitting in the wave number…
We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental results for this notion. First, we show that affine rigidity can be determined by the rank of a specific matrix which implies that affine rigidity is…