scholarly journals Roles of Clustering Coefficient for the Network Reconstruction

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Jingti Han ◽  
Changmei Mao
Keyword(s):  
Matching Pursuit ◽  
Small World ◽  
Network Reconstruction ◽  
Network Size ◽  
Clustering Coefficient ◽  
Dynamical Structure ◽  
Accuracy Rate ◽  
Minimization Method ◽  
Norm Minimization ◽  
Kim Model

It is important to establish relations between the network reconstruction and the topological dynamical structure of networks. In this article, we quantify the effect for two types of network topologies on the performance of network reconstruction. First, we generate two network modes with variable clustering coefficient based on Holme-Kim model and Newman-Watts small-world model, then we reconstruct the artificial networks by using a novel framework called L1-norm minimization algorithm based on a theory called compressive sensing (CS), a framework for recovering sparse signals. The results of the simulation experiment show that the accuracy rate for the network reconstruction is a monotonically increasing function of the clustering coefficient in Holme-Kim model, whereas the opposite occurs in Newman-Watts small-world network. And this yet demonstrates that the larger the network size, the higher the accuracy rate. Morever, we compare the results of CS with orthogonal matching pursuit (OMP), a greedy algorithm. The results show that the accuracy rate of L1-norm minimization method is 10% higher than that of OMP, and OMP yields 1.2 times the computation speed of L1-norm minimization. Our work demonstrates that the topological structure of network has influence on the accurate reconstruction and it is helpful for offering proper method for the network reconstruction.

STOCHASTIC EVOLVING MODEL FOR COMPLEX NETWORKS

2004 ◽  
Vol 18 (23) ◽  
pp. 1157-1164 ◽  
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI ◽  
JIN MIN KIM
Keyword(s):  
Control Parameter ◽  
Small World ◽  
Network Size ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Hierarchical Topology ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
High Degree

We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We obtain the various values of degree exponent γ in the range 2<γ≤3 by adjusting the parameter p and find that the degree exponent decreases logarithmically with p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln ( ln N) with nonzero p, where N is the network size.

CELLULAR NEURAL NETWORKS CAN MIMIC SMALL-WORLD NETWORKS

1999 ◽  
Vol 09 (10) ◽  
pp. 2105-2126 ◽  
Author(s):  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Neural Networks ◽  
Coupling Strength ◽  
Initial Conditions ◽  
Computing Time ◽  
Small World ◽  
Cellular Neural Networks ◽  
Clustering Coefficient ◽  
High Survival ◽  
Game Of Life ◽  
Hole Detection

Small-world phenomenon can occur in coupled dynamical systems which are highly clustered at a local level and yet strongly coupled at the global level. We show that cellular neural networks (CNN's) can exhibit "small-world phenomenon". We generalize the "characteristic path length" from previous works on "small-world phenomenon" into a "characteristic coupling strength" for measuring the average coupling strength of the outputs of CNN's. We also provide a simplified algorithm for calculating the "characteristic coupling strength" with a reasonable amount of computing time. We define a "clustering coefficient" and show how it can be calculated by a horizontal "hole detection" CNN, followed by a vertical "hole detection" CNN. Evolutions of the game-of-life CNN with different initial conditions are used to illustrate the emergence of a "small-world phenomenon". Our results show that the well-known game-of-life CNN is not a small-world network. However, generalized CNN life games whose individuals have strong mobility and high survival rate can exhibit small-world phenomenon in a robust way. Our simulations confirm the conjecture that a population with a strong mobility is more likely to qualify as a small world. CNN games whose individuals have weak mobility can also exhibit a small-world phenomenon under a proper choice of initial conditions. However, the resulting small worlds depend strongly on the initial conditions, and are therefore not robust.

scholarly journals A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4260 ◽  
Author(s):  
Linyu Wang ◽  
Xiangjun Yin ◽  
Huihui Yue ◽  
Jianhong Xiang
Keyword(s):  
Blind Source Separation ◽  
Signal Reconstruction ◽  
Source Separation ◽  
Minimization Method ◽  
Underdetermined Blind Source Separation ◽  
Weighted Function ◽  
Performance Simulation ◽  
Linear System Of Equations ◽  
Norm Minimization ◽  
Magnetic Resonance Imaging Mri

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

scholarly journals A study on small-world characteristics of Chinaäó»s high-speed railway networks

2016 ◽  
Author(s):  
Xin Yuan ◽  
Guo Liu ◽  
Kun Hui Ye
Keyword(s):  
High Speed ◽  
Small World ◽  
Clustering Coefficient ◽  
High Speed Rail ◽  
Attribute Data ◽  
The Social ◽  
The Difference ◽  
Global And Local ◽  
The Relationship ◽  
Space Method

The small-world model provides a useful perspective and method to study the topological structure and intrinsic characteristics of high-speed rail networks (HRNs). In this paper, the P-space method is used to examine global and local HRNs in China, meanwhile the adjacency matrix is developed, then the social network analysis and visualization tool UCINET is used to calculate the spatial and attribute data of HRNs at national and local levels in China. The small-world characteristics of whole HRNs are discussed, three networks which have different properties are determined, and a comparative analysis of the small-world effect is detected. Then, the relationship between the construction of high-speed rail and regional development of China is analysed. The results show that: 1) China's HRNs have small average path length ( L ) and large clustering coefficient (C ), representing a typical small-world network; 2) Local HRNs have a certain correlation with economic development. The reasons for the difference of HRNs with respect to characteristics among regions are eventually discussed.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

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.

Dynamic Particle Swarm Optimization with Any Irregular Initial Small-World Topology

2017 ◽  
pp. 1185-1208
Author(s):  
Shuangxin Wang ◽  
Guibin Tian ◽  
Dingli Yu ◽  
Yijiang Lin
Keyword(s):  
Particle Swarm Optimization ◽  
Great Influence ◽  
Particle Swarm ◽  
Wind Farms ◽  
Small World ◽  
Laplacian Matrix ◽  
Pso Algorithm ◽  
Clustering Coefficient ◽  
Swarm Optimization ◽  
Benchmark Test Functions

It is realized that the topological structure of the particle swarm optimization (PSO) algorithm has a great influence on its optimization ability. This paper presents a new dynamic small-world neighborhood PSO (D-SWPSO) algorithm whose neighbourhood structure can be constructed with any irregular initial networks. The choice of the learning exemplar is not only based upon the big clustering coefficient and the average shortest distance for a regular network, but also based upon the eigenvalues of Laplacian matrix for irregular networks. Therefore, the D-SWPSO is a PSO algorithm based on small-world topological neighbourhood with universal significance. The proposed algorithm is tested by some typical benchmark test functions, and the results confirm that there is a significant improvement over the basic PSO algorithm. Finally, the algorithm is applied to a real-world optimization problem, the economic dispatch on the IEEE30 system with wind farms. The results demonstrate that the proposed D-SWPSO is a practically feasible and effective algorithm.

scholarly journals Monitoring Effective Connectivity in the Preterm Brain: A Graph Approach to Study Maturation

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
M. Lavanga ◽  
O. De Wel ◽  
A. Caicedo ◽  
K. Jansen ◽  
A. Dereymaeker ◽  
...  
Keyword(s):  
Graph Theory ◽  
Prediction Models ◽  
Mean Squared Error ◽  
Effective Connectivity ◽  
Small World ◽  
Clustering Coefficient ◽  
Postmenstrual Age ◽  
Eeg Connectivity ◽  
Preterm Babies ◽  
Age Prediction

In recent years, functional connectivity in the developmental science received increasing attention. Although it has been reported that the anatomical connectivity in the preterm brain develops dramatically during the last months of pregnancy, little is known about how functional and effective connectivity change with maturation. The present study investigated how effective connectivity in premature infants evolves. To assess it, we use EEG measurements and graph-theory methodologies. We recorded data from 25 preterm babies, who underwent long-EEG monitoring at least twice during their stay in the NICU. The recordings took place from 27 weeks postmenstrual age (PMA) until 42 weeks PMA. Results showed that the EEG-connectivity, assessed using graph-theory indices, moved from a small-world network to a random one, since the clustering coefficient increases and the path length decreases. This shift can be due to the development of the thalamocortical connections and long-range cortical connections. Based on the network indices, we developed different age-prediction models. The best result showed that it is possible to predict the age of the infant with a root mean-squared error (MSE) equal to 2.11 weeks. These results are similar to the ones reported in the literature for age prediction in preterm babies.

scholarly journals Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

Sign in / Sign up

Export Citation Format

Share Document