scholarly journals Context dependent preferential attachment model for complex networks

2015 ◽  
Vol 436 ◽  
pp. 499-508 ◽  
Author(s):  
Pradumn Kumar Pandey ◽  
Bibhas Adhikari
Keyword(s):  
Complex Networks ◽  
Preferential Attachment ◽  
Context Dependent ◽  
Attachment Model

scholarly journals EMERGENCE OF MULTISCALING IN HETEROGENEOUS COMPLEX NETWORKS

2007 ◽  
Vol 18 (10) ◽  
pp. 1591-1607 ◽  
Author(s):  
A. SANTIAGO ◽  
R. M. BENITO
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Threshold Model ◽  
Specific Form ◽  
Numerical Evidence ◽  
Attachment Model ◽  
Attachment Mechanism

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the threshold model, a preferential attachment model where the affinity between node states biases the attachment probabilities of links. We show that the degree densities exhibit a power-law multiscaling which points to a signature of heterogeneity in preferential attachment networks. This translates into a power-law scaling in the degree distribution, whose exponent depends on the specific form of heterogeneity in the attachment mechanism.

Models of network formation

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Distribution ◽  
Network Formation ◽  
Preferential Attachment ◽  
Network Size ◽  
Large Network ◽  
Citation Networks ◽  
Airline Networks ◽  
Attachment Model ◽  
Delivery Networks

This chapter describes models of the growth or formation of networks, with a particular focus on preferential attachment models. It starts with a discussion of the classic preferential attachment model for citation networks introduced by Price, including a complete derivation of the degree distribution in the limit of large network size. Subsequent sections introduce the Barabasi-Albert model and various generalized preferential attachment models, including models with addition or removal of extra nodes or edges and models with nonlinear preferential attachment. Also discussed are node copying models and models in which networks are formed by optimization processes, such as delivery networks or airline networks.

Clustering Coefficient of a Spatial Preferential Attachment Model

2018 ◽  
Vol 98 (1) ◽  
pp. 304-307 ◽  
Author(s):  
L. N. Iskhakov ◽  
M. S. Mironov ◽  
L. A. Prokhorenkova ◽  
B. Kamiński ◽  
P. Prałat
Keyword(s):  
Preferential Attachment ◽  
Clustering Coefficient ◽  
Attachment Model

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 Nonuniform Distribution of Nodes in the Spatial Preferential Attachment Model

2015 ◽  
Vol 12 (1-2) ◽  
pp. 121-144 ◽  
Author(s):  
Jeannette Janssen ◽  
Paweł Prałat ◽  
Rory Wilson
Keyword(s):  
Preferential Attachment ◽  
Nonuniform Distribution ◽  
Attachment Model

scholarly journals Phase Transitions for Random Geometric Preferential Attachment Graphs

2015 ◽  
Vol 47 (2) ◽  
pp. 565-588 ◽  
Author(s):  
Jonathan Jordan ◽  
Andrew R. Wade
Keyword(s):  
Phase Transitions ◽  
Preferential Attachment ◽  
Geometric Model ◽  
Degree Sequence ◽  
Spatial Proximity ◽  
Nearest Neighbour ◽  
Intermediate Regime ◽  
On Line ◽  
Attachment Model ◽  
Preferential Rule

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the resulting graph as the relative strengths of these two components of the attachment rule are varied.Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence mimics the standard Barabási-Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence mimics a purely geometric model, the on-line nearest-neighbour graph, for which we prove some extensions of known results. We also show the presence of an intermediate regime, with behaviour distinct from both the on-line nearest-neighbour graph and the Barabási-Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence.

scholarly journals Fitting the linear preferential attachment model

2017 ◽  
Vol 11 (2) ◽  
pp. 3738-3780 ◽  
Author(s):  
Phyllis Wan ◽  
Tiandong Wang ◽  
Richard A. Davis ◽  
Sidney I. Resnick
Keyword(s):  
Preferential Attachment ◽  
Attachment Model
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