THE MODELLING OF WEIGHTED COMPLEX NETWORKS

In order to further explore the mechanism responsible for weighted complex networks, we introduce a new model that incorporates the network topology and the weights' dynamical evolutions. Our model can capture the details of weight dynamics caused not only by the addition of a new node with new links and new links between old nodes, but also the deletion of old links. We calculate analytically the distributions of both degree and strength and found that all these distributions show scale-free behavior, as confirmed in many real networks. Thus our model characterizes the real weighted complex networks more precisely.

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The Evolution of Price Competition Game on Complex Networks

Complexity ◽

10.1155/2018/9649863 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13

Author(s):

Feng Jie Xie ◽

Jing Shi

Keyword(s):

Complex Networks ◽

Real World ◽

Price Competition ◽

Small World ◽

Square Lattice ◽

Small World Network ◽

Scale Free Network ◽

The Real ◽

Scale Free ◽

Free Network

The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.

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Modeling Complex Networks Based on Deep Reinforcement Learning

Frontiers in Physics ◽

10.3389/fphy.2021.822581 ◽

2022 ◽

Vol 9 ◽

Author(s):

Wenbo Song ◽

Wei Sheng ◽

Dong Li ◽

Chong Wu ◽

Jun Ma

Keyword(s):

Reinforcement Learning ◽

Complex Networks ◽

Network Topology ◽

Network Structure ◽

Dynamic Change ◽

Intelligent Agent ◽

Small World ◽

Network Nodes ◽

Scale Free ◽

Internal Mechanism

The network topology of complex networks evolves dynamically with time. How to model the internal mechanism driving the dynamic change of network structure is the key problem in the field of complex networks. The models represented by WS, NW, BA usually assume that the evolution of network structure is driven by nodes’ passive behaviors based on some restrictive rules. However, in fact, network nodes are intelligent individuals, which actively update their relations based on experience and environment. To overcome this limitation, we attempt to construct a network model based on deep reinforcement learning, named as NMDRL. In the new model, each node in complex networks is regarded as an intelligent agent, which reacts with the agents around it for refreshing its relationships at every moment. Extensive experiments show that our model not only can generate networks owing the properties of scale-free and small-world, but also reveal how community structures emerge and evolve. The proposed NMDRL model is helpful to study propagation, game, and cooperation behaviors in networks.

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Detecting different topologies immanent in scale-free networks with the same degree distribution

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1816842116 ◽

2019 ◽

Vol 116 (14) ◽

pp. 6701-6706 ◽

Cited By ~ 12

Author(s):

Dimitrios Tsiotas

Keyword(s):

Complex Networks ◽

Power Law ◽

Network Topology ◽

Degree Distribution ◽

Growth Process ◽

Preferential Attachment ◽

Self Similarity ◽

Scale Free ◽

Scale Free Networks ◽

Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

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Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

Royal Society Open Science ◽

10.1098/rsos.160757 ◽

2017 ◽

Vol 4 (1) ◽

pp. 160757 ◽

Cited By ~ 19

Author(s):

Rinku Jacob ◽

K. P. Harikrishnan ◽

R. Misra ◽

G. Ambika

Keyword(s):

Time Series ◽

Network Analysis ◽

Complex Networks ◽

Network Topology ◽

Real World ◽

Degree Distribution ◽

Structural Complexity ◽

Chaotic Attractors ◽

Scale Free ◽

Low Dimensional

We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval [ 0 , 1 ] . To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N ) and for SF networks with γ and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.

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Dynamics analysis of an online gambling spreading model on scale-free networks

Advances in Difference Equations ◽

10.1186/s13662-020-03165-z ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Yu Kong ◽

Tao Li ◽

Yuanmei Wang ◽

Xinming Cheng ◽

He Wang ◽

...

Keyword(s):

Network Topology ◽

Negative Impact ◽

Online Gambling ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Scale Free ◽

Spreading Model ◽

Spreading Dynamics ◽

Scale Free Networks ◽

Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

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Network robustness improvement via long-range links

Computational Social Networks ◽

10.1186/s40649-019-0073-2 ◽

2019 ◽

Vol 6 (1) ◽

Cited By ~ 1

Author(s):

Vincenza Carchiolo ◽

Marco Grassia ◽

Alessandro Longheu ◽

Michele Malgeri ◽

Giuseppe Mangioni

Keyword(s):

Complex Networks ◽

Long Range ◽

Real World ◽

Network Robustness ◽

Scale Free ◽

Area Of Interest ◽

Before And After ◽

Significant Area ◽

Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

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