Related papers: Scaling in Small-World Resistor Networks
Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a…
We study excitation waves on a Newman-Watts small-world network model of coupled excitable elements. Depending on the global coupling strength, we find differing resilience to the added long-range links and different mechanisms of…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…
Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating…
Resilience of the most important properties of stochastic and regular (deterministic) small-world interconnection networks is studied. It is shown that in the broad range of values of the fraction of faulty nodes the networks under…
We investigate the behavior of two dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct the network by having a network-element repeat itself $L_x$…
We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and biased processes of breaking and recovery…
It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
We investigate the steady state of a two-dimensional random resistor network subjected to two competing biased percolations as a function of the bias strength. The properties of the linear and nonlinear regimes are studied by means of Monte…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the…
We study electric properties of random resistor networks consisting of resistors of two kinds numerically, focusing on the power loss across each bond. Tuning the ratio of the resistances $r$ and their respective fraction $\alpha$ we find…
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 study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…
We study vibrational thermodynamic stability of small-world oscillator networks, by relating the average mean-square displacement $S$ of oscillators to the eigenvalue spectrum of the Laplacian matrix of networks. We show that the…
The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge…
The state of a 2-D random resistor network, resulting from the simultaneous evolutions of two competing biased percolations, is studied in a wide range of bias values. Monte Carlo simulations show that when the external current $I$ is below…