Scale-free growing networks imply linear preferential attachment

2001 ◽  
Vol 65 (1) ◽  
Author(s):  
Kasper Astrup Eriksen ◽  
Michael Hörnquist
Keyword(s):  
Preferential Attachment ◽  
Scale Free ◽  
Growing Networks

scholarly journals The evolution of network topology by selective removal

2005 ◽  
Vol 2 (5) ◽  
pp. 533-536 ◽  
Author(s):  
Marcel Salathé ◽  
Robert M May ◽  
Sebastian Bonhoeffer
Keyword(s):  
Network Topology ◽  
Biological Networks ◽  
Preferential Attachment ◽  
Protein Interaction Networks ◽  
Interaction Networks ◽  
Network Growth ◽  
Scale Free ◽  
The Past ◽  
The World ◽  
Growing Networks

The topology of large social, technical and biological networks such as the World Wide Web or protein interaction networks has caught considerable attention in the past few years (reviewed in Newman 2003 ), and analysis of the structure of such networks revealed that many of them can be classified as broad-tailed, scale-free-like networks, since their vertex connectivities follow approximately a power-law. Preferential attachment of new vertices to highly connected vertices is commonly seen as the main mechanism that can generate scale-free connectivity in growing networks ( Watts 2004 ). Here, we propose a new model that can generate broad-tailed networks even in the absence of network growth, by not only adding vertices, but also selectively eliminating vertices with a probability that is inversely related to the sum of their first- and second order connectivity.

scholarly journals Scale free is not rare in international trade networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Linqing Liu ◽  
Mengyun Shen ◽  
Chang Tan
Keyword(s):  
International Trade ◽  
Preferential Attachment ◽  
Developed Countries ◽  
Total Trade ◽  
Trade Networks ◽  
Scale Free ◽  
Weighted Networks ◽  
Free Exploration ◽  
Technology Products ◽  
Attachment Mechanism

AbstractFailing to consider the strong correlations between weights and topological properties in capacity-weighted networks renders test results on the scale-free property unreliable. According to the preferential attachment mechanism, existing high-degree nodes normally attract new nodes. However, in capacity-weighted networks, the weights of existing edges increase as the network grows. We propose an optimized simplification method and apply it to international trade networks. Our study covers more than 1200 product categories annually from 1995 to 2018. We find that, on average, 38%, 38% and 69% of product networks in export, import and total trade are scale-free. Furthermore, the scale-free characteristics differ depending on the technology. Counter to expectations, the exports of high-technology products are distributed worldwide rather than concentrated in a few developed countries. Our research extends the scale-free exploration of capacity-weighted networks and demonstrates that choosing appropriate filtering methods can clarify the properties of complex networks.

scholarly journals Self-organizing topology for energy-efficient ad-hoc communication networks of mobile devices

2020 ◽  
Author(s):  
Indushree Banerjee ◽  
Martijn Warnier ◽  
Frances M. T Brazier
Keyword(s):  
Communication Network ◽  
Mobile Devices ◽  
Communication Networks ◽  
Energy Efficient ◽  
Ad Hoc ◽  
Preferential Attachment ◽  
Scale Free ◽  
Simulated Environment ◽  
Adaptive Topology ◽  
Hoc Networks

Abstract When physical communication network infrastructures fail, infrastructure-less communication networks such as mobile ad-hoc networks (MANET), can provide an alternative. This, however, requires MANETs to be adaptable to dynamic contexts characterized by the changing density and mobility of devices and availability of energy sources. To address this challenge, this paper proposes a decentralized context-adaptive topology control protocol. The protocol consists of three algorithms and uses preferential attachment based on the energy availability of devices to form a loop-free scale-free adaptive topology for an ad-hoc communication network. The proposed protocol has a number of advantages. First, it is adaptive to the environment, hence applicable in scenarios where the number of participating mobile devices and their availability of energy resources is always changing. Second, it is energy-efficient through changes in the topology. This means it can be flexibly be combined with different routing protocols. Third, the protocol requires no changes on the hardware level. This means it can be implemented on all current phones, without any recalls or investments in hardware changes. The evaluation of the protocol in a simulated environment confirms the feasibility of creating and maintaining a self-adaptive ad-hoc communication network, consisting of multitudes of mobile devices for reliable communication in a dynamic context.

scholarly journals RECIPROCITY AND THE EMERGENCE OF POWER LAWS IN SOCIAL NETWORKS

2006 ◽  
Vol 17 (07) ◽  
pp. 1067-1076 ◽  
Author(s):  
MICHAEL SCHNEGG
Keyword(s):  
Social Networks ◽  
Power Laws ◽  
Scaling Exponent ◽  
Policy Makers ◽  
Public Health Programs ◽  
Scale Free ◽  
The Past ◽  
Naturally Occurring ◽  
Growing Networks ◽  
Law Degree

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

scholarly journals HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS

2006 ◽  
Vol 17 (09) ◽  
pp. 1303-1311 ◽  
Author(s):  
SUMIYOSHI ABE ◽  
STEFAN THURNER
Keyword(s):  
Complex Network ◽  
Preferential Attachment ◽  
Hierarchical Organization ◽  
Scale Free Network ◽  
Mixing Properties ◽  
Scale Free ◽  
Free Network ◽  
Growing Network ◽  
Arbitrary Connectivity

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

scholarly journals The Formation of Social Network Assortativity: A Cultural Trait-Matching Mechanism

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wei Wang ◽  
Xiaoming Sun ◽  
Yalan Wang ◽  
Wentian Cui
Keyword(s):  
Preferential Attachment ◽  
Scale Free Network ◽  
Selection Probability ◽  
Network Nodes ◽  
Scale Free ◽  
Cultural Trait ◽  
Free Network ◽  
Matching Mechanism ◽  
Simulation Results ◽  
Attachment Mechanism

The preferential attachment mechanism that forms scale-free network cannot display assortativity, i.e., the degree of one node is positively correlated with that of their neighbors in the network. Given the attributes of network nodes, a cultural trait-matching mechanism is further introduced in this paper. Both theoretical analysis and simulation results indicate that the higher selection probability of such mechanism, the more obvious the assortativity is shown in networks. Further, the degree of nodes presents a positive logarithm correlation with that of adjacent ones. Finally, this study discusses the theoretical and practical significances of the introduction of such a cultural trait-matching mechanism.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

scholarly journals PageRank of Scale-Free Growing Networks

2006 ◽  
Vol 3 (2) ◽  
pp. 207-231 ◽  
Author(s):  
Konstantin Avrachenkov ◽  
Dmitri Lebedev
Keyword(s):  
Scale Free ◽  
Growing Networks

Effect of connection on transport between scale free networks

2017 ◽  
Vol 28 (05) ◽  
pp. 1750064 ◽  
Author(s):  
A. Ould Baba ◽  
O. Bamaarouf ◽  
A. Rachadi ◽  
H. Ez-Zahraouy
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Preferential Attachment ◽  
Electrical Conductance ◽  
Global Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Conductance Distribution

Using numerical simulations, we investigate the effects of the connectivity and topologies of network on the quality of transport between connected scale free networks. Hence, the flow as the electrical conductance between connected networks is calculated. It is found that the conductance distribution between networks follow a power law [Formula: see text] where [Formula: see text] is the exponent of the global Network of network, we show that the transport in the symmetric growing preferential attachment connection is more efficient than the symmetric static preferential attachment connection. Furthermore, the differences of transport and networks communications properties in the different cases are discussed.

scholarly journals A Novel Wireless Sensor Network Evolution Model Based on Energy-Efficiency

2017 ◽  
Vol 13 (03) ◽  
pp. 4 ◽  
Author(s):  
Hui Gao ◽  
Zhixian Yang
Keyword(s):  
Preferential Attachment ◽  
Influence Factors ◽  
Network Evolution ◽  
Evolution Model ◽  
Wireless Sensor ◽  
Font Size ◽  
Total Energy Consumption ◽  
Scale Free ◽  
Random Node ◽  
Attachment Mechanism

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; mso-fareast-font-family: SimSun; mso-fareast-theme-font: minor-fareast; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">The Barabási–Albert (BA) model is a famous complex network model that generates scale-free networks. Wireless sensor networks (WSNs) had been thought to be approximately scale-free through lots of empirical research. Based on the BA model, we propose an evolution model for WSNs. According to actual influence factors such as the remainder energy of each sensor and physical link capability of each sensor, our evolution model constructs WSNs by using a preferential attachment mechanism. Through simulation and analysis, we can prove that our evolution model would make the total energy consumption of the WSNs more efficient and have a superior random node error tolerance.</span>

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