scholarly journals Clustering Properties of Spatial Preferential Attachment Model

2018 ◽  
pp. 30-43 ◽  
Author(s):  
Lenar Iskhakov ◽  
Bogumił Kamiński ◽  
Maksim Mironov ◽  
Paweł Prałat ◽  
Liudmila Prokhorenkova
Keyword(s):  
Preferential Attachment ◽  
Attachment Model

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 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

scholarly journals A generalized preferential attachment model for business firms growth rates

2007 ◽  
Vol 57 (2) ◽  
pp. 127-130 ◽  
Author(s):  
F. Pammolli ◽  
D. Fu ◽  
S. V. Buldyrev ◽  
M. Riccaboni ◽  
K. Matia ◽  
...  
Keyword(s):  
Growth Rates ◽  
Preferential Attachment ◽  
Attachment Model

scholarly journals Sublinear Random Access Generators for Preferential Attachment Graphs

2021 ◽  
Vol 17 (4) ◽  
pp. 1-26
Author(s):  
Guy Even ◽  
Reut Levi ◽  
Moti Medina ◽  
Adi Rosén
Keyword(s):  
Random Graph ◽  
Preferential Attachment ◽  
Random Access ◽  
Graph Model ◽  
Efficient Estimation ◽  
Sublinear Algorithms ◽  
Tree Model ◽  
Random Graph Model ◽  
Time Space ◽  
Attachment Model

We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space, and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space, and random bits, especially when only a small number of queries are actually issued. Instead, we propose a setting where one generates parts of the sampled graph on-the-fly, in response to queries, and therefore requires amounts of time, space, and random bits that are a function of the actual number of queries. Yet, the responses to the queries correspond to a graph sampled from the distribution in question. Within this framework, we focus on two random graph models: the Barabási-Albert Preferential Attachment model (BA-graphs) ( Science , 286 (5439):509–512) (for the special case of out-degree 1) and the random recursive tree model ( Theory of Probability and Mathematical Statistics , (51):1–28). We give on-the-fly generation algorithms for both models. With probability 1-1/poly( n ), each and every query is answered in polylog( n ) time, and the increase in space and the number of random bits consumed by any single query are both polylog( n ), where n denotes the number of vertices in the graph. Our work thus proposes a new approach for the access to huge graphs sampled from a given distribution, and our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph’s nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their on such graphs.

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