A quantum particle on a general discrete structure with a local external potential is described by a generalized tight-binding Hamiltonian on a graph. Here, we show that this model can be naturally mapped on a classical statistical model (the Gaussian model) on the same graph. This equivalence...

In this paper, the important issue of Laplacian eigenvalue distributions is investigated through theory-guided extensive numerical simulations, for four typical complex network models, namely, the ER random-graph networks, WS and NW small-world networks, and BA scale-free networks. It is found...

Transportation systems, being real-life examples of networks, are particularly interesting to analyze from the viewpoint of the new and rapidly emerging field of network science. Two particular concepts seem to be particularly relevant: scale-free patterns and small-worlds. By looking at 33...

The balance between the supply and demand of some kind of resource is critical for the functionality and security of many complex networks. Local contingencies that break this balance can cause a global collapse. These contingencies are usually dealt with by spare capacity, which is costly...

The objective of this work is to propose a new methodology to detect the imminence of abrupt changes in the stock market by combining a numerical indicator based on the wavelet decomposition technique with a measure of the interdependency of the markets using graph theory. While the indicator...

We sketch a subset of Professor F.Y. Wu's contributions in lattice statistical mechanics, solid state physics, graph theory, enumerative combinatorics and other domains of physics and mathematics. We will recall some of F.Y. Wu's most important and well-known classic results and we will also...

The neuronal network of the soil nematode Caenorhabditis elegans (C. elegans), which is a good prototype for biological studies, is investigated. Here, the neuronal network is simplified as a graph. We use three indicators to characterize the graph; vertex degree, generalized eccentricity (GE),...

Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show small-world network property. Various network...

In this paper, the stability problem for some coupled systems with time delay on networks (CSDNs) is investigated. We provide a systematic method for constructing a global Lyapunov functional for CSDNs by using graph theory. The stability, uniform stability and global uniform stability of the...

A method is presented for the calculation of all exact ground states of diluted Ising antiferromagnets and random field Ising systems in an arbitrary range of magnetic fields Bϵ [Bstart, Bend] resp. Δϵ [Δstart, Δend]. It works by calculating all jump-fields B, Δ where the system changes...