CONSTRUCTING SCALE-FREE NETWORKS WITH A GIVEN CLUSTER COEFFICIENT

2013 ◽  
Vol 24 (02) ◽  
pp. 1350003 ◽  
Author(s):  
MOHAMMAD ARIAPOUR ◽  
EHSAN NEDAAEE OSKOEE
Keyword(s):  
Hierarchical Structure ◽  
Real World ◽  
Cluster Coefficient ◽  
Scaling Exponent ◽  
Scale Free ◽  
Local Thresholding ◽  
Wide Range ◽  
Scale Free Networks ◽  
New Generation ◽  
Generation Rule

We introduce a new generation rule for local thresholding in scale-free networks based on the nodes' degree. The resulting networks are disassortative with a hierarchical structure. There is, however, a subnet of the nodes, which we call the active nodes, which is neither disassortative nor has such a structure. It is shown that networks with a wide range of cluster coefficients, ranging from very small to close to unity and with scaling exponent from 2.5 to 4 are generated by the new method, which mimic some important real-world networks.

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.

EVOLVING MODEL OF SCALE-FREE NETWORKS WITH INTRINSIC LINKS

2008 ◽  
Vol 19 (07) ◽  
pp. 1129-1144 ◽  
Author(s):  
XIANMIN GENG ◽  
GUANGHUI WEN ◽  
YING WANG ◽  
JINXIA LI
Keyword(s):  
Numerical Simulation ◽  
Preferential Attachment ◽  
Scaling Exponent ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Behavior ◽  
Simulation Results ◽  
Evolving Model ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, we introduce the concept of intrinsic link, which is used to describe the intrinsic interactions between the individuals in complex systems. Furthermore, we present a model for the evolution of complex networks, in which the system dynamics motivated by four mechanisms: the addition of new nodes with preferential attachment, the addition of new nodes with intrinsic attachment, the addition of new links with preferential attachment and the addition of new intrinsic links. The model yields scale-free behavior for the degree distributions as confirmed in many real networks. With continumm theory, we get the analytical expressions of the degree distribution and the scaling exponent γ. The analytical expressions are in good agreement with the numerical simulation results.

EFFECT OF CLIENT DEMANDS ON DESTRUCTIVENESS OF TARGETED ATTACKS IN DIRECTED WEIGHTED SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (19) ◽  
pp. 1603-1617 ◽  
Author(s):  
LI-LI MA ◽  
XIN JIANG ◽  
ZHAN-LI ZHANG ◽  
ZHI-MING ZHENG
Keyword(s):  
Real World ◽  
Weight Distribution ◽  
Network Robustness ◽  
Network Nodes ◽  
Scale Free ◽  
Node Importance ◽  
Targeted Attacks ◽  
Link Weight ◽  
Scale Free Networks ◽  
Unique Mechanism

Network resilience is vital for the survival of networks, and scale-free networks are fragile when confronted with targeted attacks. We survey network robustness to targeted attacks from the viewpoint of network clients by designing a unique mechanism based on the undeniable roles of network clients in real-world networks. Especially, the mechanism here is designed on the actual phenomenon that the vital nodes in a network may be totally different for clients with different demands. Concretely, node client-demand centrality is proposed to quantify the contributions of nodes to network clients and we show that it is a proper index to assign an order to network nodes according to node importance for network clients. Great discrepancy of node importance order for clients with different demands is found in scale-free networks with four different kinds of link weight distribution, which suggests that the destructiveness of fatal attacks on networks can be greatly reduced by adjusting the demands of network clients.

Synchronization of Chaotic Circuits with Stochastically-Coupled Network Topology

2021 ◽  
Vol 31 (01) ◽  
pp. 2150015
Author(s):  
Yoko Uwate ◽  
Yoshifumi Nishio ◽  
Thomas Ott
Keyword(s):  
Secure Communication ◽  
Communication Systems ◽  
Small World ◽  
Chaotic Circuit ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
Dynamic Topology ◽  
Chaotic Circuits ◽  
Fully Coupled

In recent years, research on synchronization between coupled chaotic circuits has attracted interest in a wide range of fields. This is because the synchronization of coupled chaotic circuits is a multidisciplinary phenomenon that occurs in various applications, such as broadband communication systems or secure communication. In this study, we propose a coupled chaotic circuit network model with stochastic couplings. We investigate the synchronization phenomena observed for the proposed network using different network structures such as fully-coupled, random, small world and scale-free networks. We find that the same synchronization characteristics can be obtained for these networks with a dynamic topology as when the coupling strength is changed in static networks.

scholarly journals Node diversification in complex networks by decentralized colouring

2018 ◽  
Vol 7 (4) ◽  
pp. 554-563 ◽  
Author(s):  
Richard Garcia-Lebron ◽  
David J Myers ◽  
Shouhuai Xu ◽  
Jie Sun
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Local Information ◽  
Connected Component ◽  
Scale Free ◽  
Scale Free Networks

Abstract We develop a decentralized colouring approach to diversify the nodes in a complex network. The key is the introduction of a local conflict index (LCI) that measures the colour conflicts arising at each node which can be efficiently computed using only local information. We demonstrate via both synthetic and real-world networks that the proposed approach significantly outperforms random colouring as measured by the size of the largest colour-induced connected component. Interestingly, for scale-free networks further improvement of diversity can be achieved by tuning a degree-biasing weighting parameter in the LCI.

Hybrid routing for interconnected BA scale-free networks

2015 ◽  
Vol 29 (33) ◽  
pp. 1550212
Author(s):  
Xue-Jun Zhang ◽  
Yan-Bo Zhu ◽  
Xiang-Min Guan
Keyword(s):  
Real World ◽  
Traffic Condition ◽  
Scale Free ◽  
Hybrid Routing ◽  
Multiple Networks ◽  
Routing Strategy ◽  
Traffic Performance ◽  
Scale Free Networks ◽  
Interconnected Networks ◽  
Simulation Results

Interconnections between networks make the traffic condition in interconnected networks more complicated than that in an isolated network. They make the load and capacity of nodes mismatch and restrict the traffic performance accordingly. To improve the performance, in this paper, we propose a hybrid routing strategy, which distinguishes the traffic within each individual network and the traffic across multiple networks and uses different routing rules for these two types of traffic. Simulation results show that this routing strategy can achieve better traffic performance than traditional strategies when networks are coupled by a small number of interconnected links, which is the case in most of real-world interconnected networks. Therefore, the proposed hybrid routing strategy can find applications in the planning and optimization of practical interconnected networks.

The structure of real-world networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Power Law ◽  
Real World ◽  
Small World ◽  
Component Structure ◽  
Scale Free ◽  
Scale Free Networks ◽  
Path Lengths ◽  
Power Law Distributions

This chapter brings together the ideas and techniques developed in previous chapters, applying them to a range of real-world networks to describe and understand the structure of those networks. Topics discussed include the observed component structure of networks, average path lengths between nodes and the small-world effect, degree distributions including power-law distributions and scale-free networks, clustering and transitivity, and assortative mixing.

SYNCHRONIZABILITY OF COMPLEX NETWORKS WITH COMMUNITY STRUCTURE

2012 ◽  
Vol 23 (04) ◽  
pp. 1250029 ◽  
Author(s):  
MAHDI JALILI
Keyword(s):  
Community Structure ◽  
Real World ◽  
Order Parameter ◽  
Small World ◽  
Laplacian Matrix ◽  
Small World Networks ◽  
Scale Free ◽  
Community Connections ◽  
Scale Free Networks ◽  
Kuramoto Oscillators

Many real-world networks show community structure characterized by dense intra-community connections and sparse inter-community links. In this paper we investigated the synchronization properties of such networks. In this work we constructed such networks in a way that they consist of a number of communities with scale-free or small-world structure. Furthermore, with a probability, the intra-community connections are rewired to inter-community links. Two synchronizability measures were considered as the eigenratio of the Laplacian matrix and the phase order parameter obtained for coupled nonidentical Kuramoto oscillators. We found a power-law relation between the eigenratio and the inter-community rewiring probability in which as the rewiring probability increased, the eigenratio decreased, and hence, the synchronizability enhanced. The phase order parameter also increased by increasing the rewiring probability. Also, small-world networks with community structure showed better synchronization properties as compared to scale-free networks with community structure.

The trapping problem and the average shortest weighted path of the weighted pseudofractal scale-free networks

2019 ◽  
Vol 30 (01) ◽  
pp. 1950010 ◽  
Author(s):  
Meifeng Dai ◽  
Changxi Dai ◽  
Huiling Wu ◽  
Xianbin Wu ◽  
Wenjing Feng ◽  
...  
Keyword(s):  
Network Size ◽  
Exceptional Case ◽  
Weight Factor ◽  
Rigorous Solution ◽  
Network Nodes ◽  
Trapping Time ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
Power Law Function

In this paper, we study the trapping time in the weighted pseudofractal scale-free networks (WPSFNs) and the average shortest weighted path in the modified weighted pseudofractal scale-free networks (MWPSFNs) with the weight factor [Formula: see text]. At first, for exceptional case with the trap fixed at a hub node for weight-dependent walk, we derive the exact analytic formulas of the trapping time through the structure of WPSFNs. The obtained rigorous solution shows that the trapping time approximately grows as a power-law function of the number of network nodes with the exponent represented by [Formula: see text]. Then, we deduce the scaling expression of the average shortest weighted path through the iterative process of the construction of MWPSFNs. The obtained rigorous solution shows that the scalings of average shortest weighted path with network size obey three laws along with the range of the weight factor. We provide a theoretical study of the trapping time for weight-dependent walk and the average shortest weighted path in a wide range of deterministic weighted networks.

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