scholarly journals SURVIVING OPINIONS IN SZNAJD MODELS ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (11) ◽  
pp. 1785-1792 ◽  
Author(s):  
F. A. RODRIGUES ◽  
L. DA F. COSTA
Keyword(s):  
Complex Networks ◽  
Scaling Law ◽  
Network Size ◽  
Random Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Network Topologies

The Sznajd model has been largely applied to simulate many sociophysical phenomena. In this paper, we applied the Sznajd model with more than two opinions on three different network topologies and observed the evolution of surviving opinions after many interactions among the nodes. As result, we obtained a scaling law which depends of the network size and the number of possible opinions. We also observed that this scaling law is not the same for all network topologies, being quite similar between scale-free networks and Sznajd networks but different for random networks.

scholarly journals Network topology optimization by turning non-scale-free networks into scale-free networks using nonlinear preferential rewiring method

2018 ◽  
Vol 14 (11) ◽  
pp. 155014771878447 ◽  
Author(s):  
Feng Su ◽  
Peijiang Yuan ◽  
Yuanwei Liu ◽  
Shuangqian Cao
Keyword(s):  
Topology Optimization ◽  
Network Topology ◽  
Random Networks ◽  
Practical Application ◽  
Performance Simulation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Network Topologies ◽  
Network Topology Optimization ◽  
Rigorous Mathematical Model

In practical application, the generation and evolution of many real networks always do not follow rigorous mathematical model, making network topology optimization a great challenge in the field of complex networks. In this research, we optimize the topology of non-scale-free networks by turning it into scale-free networks using a nonlinear preferential rewiring method. For different kinds of original networks generated by Watts and Strogatz model, we systematically demonstrate the optimization process and the modified networks to verify the performance of nonlinear preferential rewiring. We conduct further researches to explore the effect of nonlinear preferential rewiring’s parameters on performance. Simulation results show that various non-scale-free networks with different network topologies generated by WS model, including random networks and various networks between regular and random, are turned into scale-free networks perfectly by nonlinear preferential rewiring method.

NETWORK TRAFFIC ASSIGNMENTS AND TRANSPORTATION DYNAMICS OVER DIFFERENT TOPOLOGIES

2008 ◽  
Vol 19 (09) ◽  
pp. 1337-1347 ◽  
Author(s):  
YI-FAN ZHAO ◽  
JIAN-FENG ZHENG
Keyword(s):  
Complex Networks ◽  
Load Distribution ◽  
System Optimization ◽  
User Equilibrium ◽  
Total Cost ◽  
Scale Free ◽  
System Equilibrium ◽  
Scale Free Networks ◽  
Network Topologies ◽  
The Relationship

Many real systems can be regarded as complex networks. In this paper, we investigate the influence of traffic assignments on transportation dynamics in complex networks with different topologies. The sequential problem is motivated by the fact that some previous works are only on traffic assignment of user equilibrium (UE). We introduce traffic assignments of system equilibrium (SE) and system optimization (SO) to analyze the relationship between traffic assignments and network topologies. In terms of these traffic assignments, some interesting results concerning system total cost are obtained. Simulation results demonstrate that load distribution also exhibits a power-law behavior for SE and SO assignments in scale-free networks. Furthermore, the exponents for SE and SO assignments are much larger than that for UE assignment. It indicates that traffic assignments play an important role in determining the transportation dynamics in scale-free networks. Finally, cascading failures of link removal in different topologies are discussed.

SEARCHING EFFICIENCY ON COMPLEX NETWORKS UNDER VISUAL RANGE OF NODES

2012 ◽  
Vol 23 (01) ◽  
pp. 1250005
Author(s):  
BIN LIU ◽  
HONGZHONG DENG ◽  
XIAOYUE WU
Keyword(s):  
Numerical Simulation ◽  
Theoretical Prediction ◽  
Complex Networks ◽  
Generating Function ◽  
Function Method ◽  
Random Networks ◽  
Scale Free ◽  
Random Walkers ◽  
Scale Free Networks ◽  
Visual Range

We study the searching efficiency of complex networks considering node's visual range within which a node can see its neighbors and knows the topology. We firstly introduce the network generating models and searching strategies. Using the generating function method, in both random networks and scale-free networks we derive the most-effective-visual-range (MEVR) which means every step of random walkers can find most of new nodes and we also obtain the searching-cost (SC) under visual range. To validate the generating function method, we perform simulations in random networks and scale-free networks. We also explain why the deviation between numerical simulation and theoretical prediction in scale-free networks is much larger than that in random networks. By studying the visual range of nodes in the networks, the results open the possibility to learn about the searching on networks with unknown topologies.

scholarly journals Complex networks of earthquakes and aftershocks

2005 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
M. Baiesi ◽  
M. Paczuski
Keyword(s):  
Complex Networks ◽  
Time Windows ◽  
Scaling Law ◽  
Relative Strength ◽  
Modern Theory ◽  
Significant Information ◽  
Data Set ◽  
Scale Free ◽  
Main Shocks ◽  
Aftershock Sequences

Abstract. We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no correlated predecessors. A correlation threshold is set to drastically reduce the size of the data set without losing significant information. Events can be aftershocks of many previous events, and also generate many aftershocks. The probability distribution for the number of incoming and outgoing links are both scale free, and the networks are highly clustered. The Omori law holds for aftershock rates up to a decorrelation time that scales with the magnitude, m, of the initiating shock as tcutoff~10β m with β~-3/4. Another scaling law relates distances between earthquakes and their aftershocks to the magnitude of the initiating shock. Our results are inconsistent with the hypothesis of finite aftershock zones. We also find evidence that seismicity is dominantly triggered by small earthquakes. Our approach, using concepts from the modern theory of complex networks, together with a metric to estimate correlations, opens up new avenues of research, as well as new tools to understand seismicity.

scholarly journals A Novel Edge Rewire Mechanism Based on Multiobjective Optimization for Network Robustness Enhancement

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhaoxing Li ◽  
Qionghai Liu ◽  
Li Chen
Keyword(s):  
Multiobjective Optimization ◽  
Complex Networks ◽  
Optimization Algorithm ◽  
Real World ◽  
Network Robustness ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Scale Free ◽  
Scale Free Networks ◽  
The Given

A complex network can crash down due to disturbances which significantly reduce the network’s robustness. It is of great significance to study on how to improve the robustness of complex networks. In the literature, the network rewire mechanism is one of the most widely adopted methods to improve the robustness of a given network. Existing network rewire mechanism improves the robustness of a given network by re-connecting its nodes but keeping the total number of edges or by adding more edges to the given network. In this work we propose a novel yet efficient network rewire mechanism which is based on multiobjective optimization. The proposed rewire mechanism simultaneously optimizes two objective functions, i.e., maximizing network robustness and minimizing edge rewire operations. We further develop a multiobjective discrete partite swarm optimization algorithm to solve the proposed mechanism. Compared to existing network rewire mechanisms, the developed mechanism has two advantages. First, the proposed mechanism does not require specific constraints on the rewire mechanism to the studied network, which makes it more feasible for applications. Second, the proposed mechanism can suggest a set of network rewire choices each of which can improve the robustness of a given network, which makes it be more helpful for decision makings. To validate the effectiveness of the proposed mechanism, we carry out experiments on computer-generated Erdős–Rényi and scale-free networks, as well as real-world complex networks. The results demonstrate that for each tested network, the proposed multiobjective optimization based edge rewire mechanism can recommend a set of edge rewire solutions to improve its robustness.

scholarly journals Optimal shattering of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Nicole Balashov ◽  
Reuven Cohen ◽  
Avieli Haber ◽  
Michael Krivelevich ◽  
Simi Haber
Keyword(s):  
Complex Networks ◽  
Random Graphs ◽  
Polynomial Time ◽  
Optimal Performance ◽  
Regular Graphs ◽  
Scale Free ◽  
Scale Free Networks ◽  
Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

scholarly journals EPIDEMIC DYNAMICS ON RANDOM AND SCALE-FREE NETWORKS

2012 ◽  
Vol 54 (1-2) ◽  
pp. 3-22 ◽  
Author(s):  
J. BARTLETT ◽  
M. J. PLANK
Keyword(s):  
Random Network ◽  
Infectious Agent ◽  
Mixed Population ◽  
Random Networks ◽  
Scale Free Network ◽  
Final Size ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Scale Free Networks ◽  
Free Network

AbstractRandom networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number ${R}_{0} $ of an infectious agent on a network. We investigate how final epidemic size depends on ${R}_{0} $ and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of ${R}_{0} $; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if ${R}_{0} \lt 1$, and a smaller average final size than in a well-mixed population if ${R}_{0} \gt 1$; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.

scholarly journals The use of the power law for designing wireless networks

2018 ◽  
Vol 21 ◽  
pp. 00012
Author(s):  
Andrzej Paszkiewicz
Keyword(s):  
Wireless Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Limited Resources ◽  
Random Networks ◽  
New Approach ◽  
Available Bandwidth ◽  
Scale Free ◽  
Scale Free Networks ◽  
Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

Asymptotic Behavior and Synchronizability Characteristics of a Class of Recurrent Neural Networks

2007 ◽  
Vol 19 (9) ◽  
pp. 2492-2514 ◽  
Author(s):  
Christof Cebulla
Keyword(s):  
Neural Network ◽  
Asymptotic Behavior ◽  
Recurrent Neural Networks ◽  
Random Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Zhang Model ◽  
Random Scale ◽  
Connectivity Distribution ◽  
Time Asymptotic Behavior

We propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model. The model we introduce is a variation of the Zhang model. We investigate the time-asymptotic behavior of the corresponding dynamical system (in particular, the conditions for the existence of an invariant compact asymptotic set) and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with Poisson connectivity distribution.

The Scale-Free Characteristics of the Micro-Blog Community

2013 ◽  
Vol 278-280 ◽  
pp. 2118-2122
Author(s):  
Bo Wang ◽  
Meng Jia Zhao ◽  
Sheng Li
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Government Policies ◽  
Scale Free ◽  
Scale Free Networks

The micro-blog community is the complex composed of many nodes. Based on interrelated theory of complex networks, this paper constructs the micro-blog community complex network by taking users as nodes, relationship between users as edges, then analyzes the scale-free features and shows that micro-blog community fits the two main characteristics of scale-free networks. Finally from the aspects of government policies、operators and users, putting forward some suggestions about micro-blog community according to its scale-free characteristics in order to let micro-blog play a better role in society.

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