Related papers: Exact results for the Ising model on a small-world…
It has been recently proposed that the natural connectivity can be used to characterize efficiently the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating…
Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now…
Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Guassian model built on two typical Small-world Networks (SWNs) is studied. The results show much difference from the classical case,…
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering…
While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
A regular lattice in which the sites can have long range connections at a distance l with a probabilty $P(l) \sim l^{-\delta}$, in addition to the short range nearest neighbour connections, shows small-world behaviour for $0 \le \delta <…
In complex networks a common task is to identify the most important or "central" nodes. There are several definitions, often called centrality measures, which often lead to different results. Here we study extensively correlations between…
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The small-world property in the context of complex networks implies structural benefits to the processes taking place within a network, such as optimal information transmission and robustness. In this paper, we study a model network of…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link…
We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
Small-world networks (SWN) are found to be closer to the real social systems than both regular and random lattices. Then, a model for the evolution of economic systems is generalized to SWN. The Sznajd model for the two-state opinion…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…