A NOVEL SMALL-WORLD NETWORK MODEL: KEEPING CONNECTIVITY WITHOUT ADDING EDGES

2008 ◽  
Vol 22 (29) ◽  
pp. 5229-5234 ◽  
Author(s):  
XUHUA YANG ◽  
BO WANG ◽  
WANLIANG WANG ◽  
YOUXIAN SUN
Keyword(s):  
Network Model ◽  
Regular Ring ◽  
Nearest Neighbor ◽  
Small World ◽  
Clustering Coefficient ◽  
The Novel ◽  
Small World Network ◽  
Characteristic Path Length ◽  
Large N ◽  
Novel Model

Considering the problems of potentially generating a disconnected network in the WS small-world network model [Watts and Strogatz, Nature393, 440 (1998)] and of adding edges in the NW small-world network model [Newman and Watts, Phys. Lett. A263, 341 (1999)], we propose a novel small-world network model. First, generate a regular ring lattice of N vertices. Second, randomly rewire each edge of the lattice with probability p. During the random rewiring procedure, keep the edges between the two nearest neighbor vertices, namely, always keep a connected ring. This model need not add edges and can maintain connectivity of the network at all times in the random rewiring procedure. Simulation results show that the novel model has the typical small-world properties which are small characteristic path length and high clustering coefficient. For large N, the model is approximately equal to the WS model. For large N and small p, the model is approximately equal to the WS model or the NW model.

SMALL-WORLD EFFECT IN GEOGRAPHICAL ATTACHMENT NETWORKS

2019 ◽  
pp. 1-21
Author(s):  
Qunqiang Feng ◽  
Yongkang Wang ◽  
Zhishui Hu
Keyword(s):  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Clustering Coefficient ◽  
Probabilistic Methods ◽  
Small World Network ◽  
Computational Simulations ◽  
Physical Literature

AbstractIn this work, we use rigorous probabilistic methods to study the asymptotic degree distribution, clustering coefficient, and diameter of geographical attachment networks. As a type of small-world network model, these networks were first proposed in the physical literature, where they were analyzed only with heuristic arguments and computational simulations.

A deterministic pseudo-fractal networks with time-delay

2015 ◽  
Vol 29 (22) ◽  
pp. 1550155 ◽  
Author(s):  
Changming Xing ◽  
Lin Yang ◽  
Jun Ma
Keyword(s):  
Time Delay ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
The Novel ◽  
Delay Effect ◽  
Scale Free ◽  
Topological Parameters ◽  
Novel Model

In this paper, inspired by the pseudo-fractal networks (PFN) and the delayed pseudo-fractal networks (DPFN), we present a novel delayed pseudo-fractal networks model, denoted by NDPFN. Different from the generation algorithm of those two networks, every edge of the novel model has a time-delay to generate new nodes after producing one node. We derive exactly the main structural properties of the novel networks: degree distribution, clustering coefficient, diameter and average path length. Analytical results show that the novel networks have small-world effect and scale-free topology. Comparing topological parameters of these three networks, we find that the degree exponent of the novel networks is the largest while the clustering coefficient and the average path length are the smallest. It means that this kind of delay could weaken the heterogeneity and the small-world features of the network. Particularly, the delay effect in the NDPFN is contrary to that in the DPFN, which illustrates the variety of delay method could produce different effects on the network structure. These present findings may be helpful for a deeper understanding of the time-delay influence on the network topology.

scholarly journals Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Yang Lou ◽  
Lin Wang ◽  
Guanrong Chen
Keyword(s):  
Numerical Simulations ◽  
Network Model ◽  
Nearest Neighbor ◽  
Small World ◽  
Small World Network ◽  
Edge Removal ◽  
Regular Network ◽  
Node Removal ◽  
Network Controllability

The well-known small-world network model was established by randomly rewiring edges, aiming to enhance the synchronizability of an undirected nearest-neighbor regular network. This paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

scholarly journals Smallest-Small-World Cellular Harmony Search for Optimization of Unconstrained Benchmark Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Sung Soo Im ◽  
Do Guen Yoo ◽  
Joong Hoon Kim
Keyword(s):  
Topological Structure ◽  
Optimization Problems ◽  
Harmony Search ◽  
Small World ◽  
Clustering Coefficient ◽  
Benchmark Problems ◽  
Small World Network ◽  
Exploration And Exploitation ◽  
Characteristic Path Length ◽  
Population Structures

We presented a new hybrid method that combines cellular harmony search algorithms with the Smallest-Small-World theory. A harmony search (HS) algorithm is based on musical performance processes that occur when a musician searches for a better state of harmony. Harmony search has successfully been applied to a wide variety of practical optimization problems. Most of the previous researches have sought to improve the performance of the HS algorithm by changing the pitch adjusting rate and harmony memory considering rate. However, there has been a lack of studies to improve the performance of the algorithm by the formation of population structures. Therefore, we proposed an improved HS algorithm that uses the cellular automata formation and the topological structure of Smallest-Small-World network. The improved HS algorithm has a high clustering coefficient and a short characteristic path length, having good exploration and exploitation efficiencies. Nine benchmark functions were applied to evaluate the performance of the proposed algorithm. Unlike the existing improved HS algorithm, the proposed algorithm is expected to have improved algorithmic efficiency from the formation of the population structure.

EFFECTS OF LONG-RANGE CONNECTIONS IN DISTRIBUTED CONTROL OF COLLECTIVE MOTION

2007 ◽  
Vol 17 (07) ◽  
pp. 2411-2417 ◽  
Author(s):  
ARTURO BUSCARINO ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
ALESSANDRO RIZZO
Keyword(s):  
Mobile Robots ◽  
Long Range ◽  
Distributed Control ◽  
Network Model ◽  
Path Length ◽  
Collective Motion ◽  
Small World ◽  
Clustering Coefficient ◽  
Characteristic Path Length ◽  
Original Topology

The introduction of long-range connections in locally connected networks leads to the so-called small-world effect: when few long-range connections are added to the original topology, the characteristic path length decreases, whereas a high clustering coefficient is preserved. In this paper, it is shown that long-range connections introduced in a network model describing the interactions of a group of mobile robots increase the tendency to form a coordinated group of robots which travel in the same direction. The leadership of informed individuals in the group is also increased.

Small World Network Model Validation. Case Study of Suartone Historical Fire in Corsica

2021 ◽  
pp. 1-16
Author(s):  
N. Hamamousse ◽  
A. Kaiss ◽  
F. Giroud ◽  
N. Bozabalian ◽  
J-P. Clerc ◽  
...  
Keyword(s):  
Model Validation ◽  
Network Model ◽  
Small World ◽  
Small World Network

scholarly journals Factor or Network Model? Predictions From Neural Networks

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Alexander P. Christensen ◽  
Keyword(s):  
Neural Networks ◽  
Network Model ◽  
Latent Variable ◽  
Random Network ◽  
Network Models ◽  
Small World ◽  
Small World Network ◽  
Monte Carlo Simulation Study ◽  
Psychological Phenomena ◽  
The Neural Networks

The nature of associations between variables is important for constructing theory about psychological phenomena. In the last decade, this topic has received renewed interest with the introduction of psychometric network models. In psychology, network models are often contrasted with latent variable (e.g., factor) models. Recent research has shown that differences between the two tend to be more substantive than statistical. One recently developed algorithm called the Loadings Comparison Test (LCT) was developed to predict whether data were generated from a factor or small-world network model. A significant limitation of the current LCT implementation is that it's based on heuristics that were derived from descriptive statistics. In the present study, we used artificial neural networks to replace these heuristics and develop a more robust and generalizable algorithm. We performed a Monte Carlo simulation study that compared neural networks to the original LCT algorithm as well as logistic regression models that were trained on the same data. We found that the neural networks performed as well as or better than both methods for predicting whether data were generated from a factor, small-world network, or random network model. Although the neural networks were trained on small-world networks, we show that they can reliably predict the data-generating model of random networks, demonstrating generalizability beyond the trained data. We echo the call for more formal theories about the relations between variables and discuss the role of the LCT in this process.

Abstract 17426: Pulmonary Vein Isolation ‘Rewires’ Electrical Communications to Enhance Small-world Network Topology During Atrial Fibrillation

Circulation ◽  
2015 ◽  
Vol 132 (suppl_3) ◽  
Author(s):  
Hiroshi Ashikaga ◽  
Jonathan Chrispin ◽  
Degang Wu ◽  
Joshua Garland
Keyword(s):  
Atrial Fibrillation ◽  
Communication Network ◽  
Mutual Information ◽  
Path Length ◽  
Random Network ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Network ◽  
Z Score ◽  
Network Properties

Recent evidence suggests that pulmonary vein isolation (PVI) may perturb the electrophysiological substrate for maintenance of atrial fibrillation (AF). Our previous work indicates that information theory metrics can quantify electrical communications during arrhythmia. We hypothesized that PVI ‘rewires’ the electrical communication network during AF such that the topology exhibits higher levels of small-world network properties, with higher clustering coefficient and lower path length, than would be expected by chance. Thirteen consecutive patients (n=6 with prior PVI and n=7 without) underwent AF ablation using a 64-electrode basket catheter in the left atrium. Multielectrode recording was performed during AF for 60 seconds, followed by PVI. Mutual information was calculated from the time series between each pair of electrodes using the Kraskov-Stögbauer-Grassberger estimator. The all-to-all mutual information matrix (64x64; Figure, upper panels) was thresholded by the median and standard deviations of mutual information to build a binary adjacency matrix for electrical communication networks. The properties of small-world network ( swn ; ‘small-world-ness’) were quantified by the ratio of the observed average clustering coefficient to that of a random network over the ratio of the observed average path length to that of a random network. swn was expressed in normal Z standard deviation units. As the binarizing threshold increased, the Z-score of swn decreased (Figure, lower panel). However, the Z-score at each threshold value was consistently higher with prior PVI than those without (p<0.05). In conclusion, electrical communication network during AF with prior PVI is associated with higher levels of small-world network properties than those without. This finding supports the concept that PVI perturbs the underlying substrate. In addition, swn of electrical communication network may be a promising metric to quantify substrate modification.

Sign in / Sign up

Export Citation Format

Share Document