Node influence identification via resource allocation dynamics

2014 ◽  
Vol 25 (11) ◽  
pp. 1450065 ◽  
Author(s):  
Shu-Jiao Ma ◽  
Zhuo-Ming Ren ◽  
Chun-Ming Ye ◽  
Qiang Guo ◽  
Jian-Guo Liu
Keyword(s):  
Resource Allocation ◽  
Complex Networks ◽  
Network Structure ◽  
Decomposition Method ◽  
Scale Free Network ◽  
Improved Method ◽  
Exponential Form ◽  
Ranking List ◽  
Scale Free ◽  
Free Network

Identifying the node influence in complex networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the resource allocation dynamics (RAD) and the k-shell decomposition method, we present an improved method namely RAD to generate the ranking list to evaluate the node influence. First, comparing with the epidemic process results for four real networks, the RAD method could identify the node influence more accurate than the ones generated by the topology-based measures including the degree, k-shell, closeness and the betweenness. Then, a growing scale-free network model with tunable assortative coefficient is introduced to analyze the effect of the assortative coefficient on the accuracy of the RAD method. Finally, the positive correlation is found between the RAD method and the k-shell values which display an exponential form. This work would be helpful for deeply understanding the node influence of a network.

EFFECTS OF CONFIDENCE SCALE AND NETWORK STRUCTURE ON MINORITY OPINION SPREADING

2010 ◽  
Vol 21 (08) ◽  
pp. 1001-1010 ◽  
Author(s):  
BO SHEN ◽  
YUN LIU
Keyword(s):  
Simple Model ◽  
Network Structure ◽  
Random Network ◽  
Random Networks ◽  
Scale Free Network ◽  
Opinion Formation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Confidence Scale

We study the dynamics of minority opinion spreading using a proposed simple model, in which the exchange of views between agents is determined by a quantity named confidence scale. To understand what will promote the success of minority, two types of networks, random network and scale-free network are considered in opinion formation. We demonstrate that the heterogeneity of networks is advantageous to the minority and exchanging views between more agents will reduce the opportunity of minority's success. Further, enlarging the degree that agents trust each other, i.e. confidence scale, can increase the probability that opinions of the minority could be accepted by the majority. We also show that the minority in scale-free networks are more sensitive to the change of confidence scale than that in random networks.

scholarly journals The Evolution of Price Competition Game on Complex Networks

Complexity ◽  
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.

A FAST ESTIMATION ALGORITHM OF COMMUNITY NUMBER IN LARGE SCALE-FREE COMPLEX NETWORKS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450039 ◽  
Author(s):  
PEIHUA FU ◽  
SHAN'AN ZHU ◽  
ANDING ZHU ◽  
XIAO DONG
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Optimal Parameter ◽  
Estimation Algorithm ◽  
Large Degree ◽  
Terminal Condition ◽  
Scale Free Network ◽  
Scale Free ◽  
Core Node ◽  
Free Network

In conventional community detecting algorithms, the community number is always a bypass product and cannot be estimated before partitioning. Since partitioning large scale and dynamic complex networks takes exhausting computation, the community number sometimes can be a terminal condition of iterations or a preset optimal parameter for speeding up partitioning algorithms. This paper assumes that communities are organized around the center of core nodes in a scale-free network. A separability function is built to dichotomize nodes into two classes and the class of large degree nodes is selected as the core node candidate set. An improved shortest path seeking algorithm is applied to remove the closest neighbors of a specific core node. The number of remaining core nodes is then the estimated number of communities. Experiments of real world scale-free networks and computer generated networks show that the results are very close to the well-proven results.

scholarly journals Quantitative Controllability Index of Complex Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lifu Wang ◽  
Yali Zhang ◽  
Jingxiao Han ◽  
Zhi Kong
Keyword(s):  
Complex Networks ◽  
Condition Number ◽  
Random Network ◽  
Small World ◽  
Scale Free Network ◽  
Scale Free ◽  
Network Topologies ◽  
Free Network ◽  
The Relationship ◽  
Controllability Index

In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

scholarly journals The evolution of trust and trustworthiness

2020 ◽  
Vol 17 (169) ◽  
pp. 20200491 ◽  
Author(s):  
Aanjaneya Kumar ◽  
Valerio Capraro ◽  
Matjaž Perc
Keyword(s):  
Network Structure ◽  
Trust Game ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Moral Behaviour ◽  
Mixed Populations ◽  
Parameter Values ◽  
Future Work

Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behaviour. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor’s investment and the trustee’s return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case, the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.

TIME-DELAY ROBUSTNESS OF CONSENSUS PROBLEMS IN REGULAR AND COMPLEX NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1339-1350 ◽  
Author(s):  
ZHENGPING WU ◽  
ZHI-HONG GUAN
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Nearest Neighbor ◽  
Small World ◽  
Node Degree ◽  
Small World Network ◽  
Scale Free Network ◽  
Star Network ◽  
Scale Free ◽  
Free Network

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

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