scholarly journals Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Small World Network ◽  
Two Dimensional ◽  
Small World Networks

This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.

DISTANCE PREFERENCES SMALL-WORLD COMMUNICATION TOPOLOGY FOR AGENT NETWORK

2010 ◽  
Vol 24 (11) ◽  
pp. 1489-1499
Author(s):  
ZHENGPING WU ◽  
RENMING WANG
Keyword(s):  
Communication Networks ◽  
Path Length ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Average Path Length ◽  
Small World Networks ◽  
Network Parameter ◽  
Communication Topology ◽  
Multi Agent

In multi-agent system (MAS), the communication topology of agent network plays a very important role in its collaboration. Small-world networks are the networks with high local clustering and small average path length, and the communication networks of MAS can be analyzed within the frame of small-world topology. Yet the real multiagent communication networks are abundant and the classical WS small-world model is not suitable for all cases. In this paper, two new small-world network models are presented. One is based on random graph substrate and local nodes preference reconnection and the other is based on regular graph substrate and long-range nodes preference reconnection. The characteristic of the network parameter such as the clustering coefficients, average path length, and eigenvalue λ2 and λn of the Laplacian matrix for these two models and WS model is studied. The consensus problem that based on these three models is also studied. An example is given and the conclusions are made in the end.

A Kind of Deterministic Small-World Network Derived from Polygonal Nesting

2014 ◽  
Vol 614 ◽  
pp. 543-549
Author(s):  
Hui Li ◽  
Liang Yuan
Keyword(s):  
Long Range ◽  
Outer Layer ◽  
Degree Distribution ◽  
Path Length ◽  
Small Diameter ◽  
Small World ◽  
Average Path Length ◽  
Node Degree ◽  
Small World Network ◽  
Central Node

A kind of deterministic small-world network is constructed based on polygonal nesting with discrete degree distribution. By adding contrapuntal edges and alternate-position edges between adjacent nests, the intra-nest edges and the long-range edges from the central node to certain outer layer nodes, the proposed polygonal nesting small-world (PNSW) networks have the property of large clustering coefficients. Also these kinds of PNSW networks have small diameter, average node degree and average path length, whose moments ofkorder are given.

scholarly journals On the Influence of Topological Characteristics on Robustness of Complex Networks

2013 ◽  
Vol 3 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Dharshana Kasthurirathna ◽  
Mahendra Piraveenan ◽  
Gnanakumar Thedchanamoorthy
Keyword(s):  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Scale Free ◽  
Rich Club ◽  
Targeted Attacks ◽  
Topological Characteristics ◽  
Topological Robustness

Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.

The Study on Wireless Sensor Network Topological Structure for Improving Network Energy Utilization

2013 ◽  
Vol 443 ◽  
pp. 509-512
Author(s):  
Yan Zhu ◽  
Yun Yu
Keyword(s):  
Energy Consumption ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Complex Network ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Wireless Sensor ◽  
Small World Network

Based on the complex network property of wireless sensor networks, this study focus on the topology of wireless sensor network and carry out series simulation according to complex network research methods. The characteristic of topology for the wireless sensor network is probed in the experiment. The degree distribution, clustering coefficient and average path length are analyzed during the experimental process. Our results verify that the topology of wireless sensor network is neither regular nor random. It is between random network and small-world network which has comparatively smaller average path length and bigger cluster coefficient. In order to form a network that is similar to the property of small-world network, which can reduce network energy consumption by decrease the average hops, our experiment constructs a network model which has significant small-world network characteristic. The results indicate that the added small sum of long range edges in the network will not increase the network load while it can reduce the energy consumption of the network effectively.

INFLUENCE OF THE INITIAL SOURCE OF EPIDEMIC AND PREVENTIVE VACCINATION ON THE SPREADING PHENOMENA IN A TWO-DIMENSIONAL LATTICE

2004 ◽  
Vol 15 (06) ◽  
pp. 755-765 ◽  
Author(s):  
R. A. KOSIŃSKI ◽  
Ł. ADAMOWSKI
Keyword(s):  
Long Range ◽  
Probabilistic Model ◽  
Small World ◽  
Two Dimensional ◽  
Small World Networks ◽  
Spreading Process ◽  
Dimensional Lattice ◽  
Epidemic Curve ◽  
Preventive Vaccination ◽  
Initial Source

The probabilistic model of epidemic in a two-dimensional lattice with an additional random, long range connections characteristic for the small world networks is presented. Relations describing the spreading process of epidemics, like epidemic curve or range of epidemic in time, were found. The influence of the borders of the lattice and the localization of the initial source of epidemic on the epidemic curve is found analytically. The application of the preventive vaccination in the population is discussed.

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.

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.

Complex Systems in a Nutshell

2020 ◽  
pp. 19-32
Author(s):  
Megan S. Patterson ◽  
Michael K. Lemke ◽  
Jordan Nelon
Keyword(s):  
Complex Systems ◽  
Path Length ◽  
Path Dependence ◽  
Small World ◽  
Cardiometabolic Disease ◽  
Small World Networks ◽  
Stable States ◽  
Scale Free ◽  
Critical Transitions ◽  
Random Scale

This chapter provides an overview of the key foundational concepts and principles of the study of complex systems. First, a definition for system is provided, and the distinctions between complicated and complex systems are demarcated, as are detail, disorganized, organized, and dynamic types of complexity. Common properties across complex systems are defined and described, including stable states and steady states, path dependence, resilience, critical transitions and tipping points, early warning signals, feedback loops, and nonlinearity. This chapter also delves into how complex issues often consist of networks, with random, scale-free, and small world networks defined and network concepts such as degrees, path length, and heterogeneity defined. The concept of emergence is also emphasized, as well as related principles such as adaptation and self-organization. Cardiometabolic disease (and associated comorbidities) is used in this chapter as a thematic population health example.

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