scholarly journals On Bollobás‐Riordan random pairing model of preferential attachment graph

2020 ◽  
Author(s):  
Boris Pittel
Keyword(s):  
Preferential Attachment ◽  
Random Pairing ◽  
Pairing 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.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals Visualizing Spatial Economic Supply Chains to Enhance Sustainability and Resilience

2021 ◽  
Vol 13 (3) ◽  
pp. 1512
Author(s):  
Yicheol Han ◽  
Stephan J. Goetz ◽  
Claudia Schmidt
Keyword(s):  
Supply Chains ◽  
Preferential Attachment ◽  
Material Balance ◽  
Service Industries ◽  
Firm Location ◽  
Commodity Flows ◽  
Geographic Space ◽  
Different Types ◽  
Gravity Equations ◽  
General Method

This article presents a spatial supply network model for estimating and visualizing spatial commodity flows that used data on firm location and employment, an input–output table of inter-industry transactions, and material balance-type equations. Building on earlier work, we proposed a general method for visualizing detailed supply chains across geographic space, applying the preferential attachment rule to gravity equations in the network context; we then provided illustrations for U.S. extractive, manufacturing, and service industries, also highlighting differences in rural–urban interdependencies across these sectors. The resulting visualizations may be helpful for better understanding supply chain geographies, as well as business interconnections and interdependencies, and to anticipate and potentially address vulnerabilities to different types of shocks.

Study on Association between Height, Weight, Iodine Supplementation and Thyroid Volume

2021 ◽  
pp. 1-25
Author(s):  
Lanchun Liu ◽  
Lixiang Liu ◽  
Ming Li ◽  
Yang Du ◽  
Peng Liu ◽  
...  
Keyword(s):  
Iodine Deficiency ◽  
Linear Models ◽  
Thyroid Volume ◽  
Salt Iodization ◽  
Iodine Supplementation ◽  
Random Pairing ◽  
Level Data ◽  
The Mean ◽  
Salt Iodine ◽  
The Difference

Abstract The policy of Universal Salt Iodization (USI) could reduce population’s thyroid volume (TVOL) in iodine deficiency areas. Conversely, the improved growth and developmental status of children might increase the TVOL accordingly. Whether the decreased TVOL by USI conceals the increase effect of height and weight on TVOL is unclear. The aim of this study was to analyse the association between height, weight, iodine supplementation and TVOL. Five national Iodine Deficiency Disorder surveys were matched into four pairs according to the purpose of analysis. County-level data of both detected by paired surveys were incorporated, 1: 1 random pairing method was used to match counties or individuals. The difference of TVOL between different height, weight, different iodine supplementation measures groups and the association between TVOL and them were studied. The mean height and weight of children aged 8-10 years increased from 129.9cm and 26.9kg in 2002 to 136.2cm and 32.1kg in 2019; while the median TVOL decreased from 3.10ml to 2.61ml. Iodine supplementation measures can affect TVOL; after exclude iodine effects, the median TVOL was increased with the height and weight. On the other side, after excluding the influence of height and weight, the median TVOL remained decreased. Only age, weight and salt iodine were significant associated with TVOL in multiple linear models. Development of height and weight in children is the evidence of improved nutrition. The decreased TVOL caused by iodized salt measures conceals the increase effect of height and weight on TVOL. Age, weight, and salt iodine affect TVOL significantly.

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 Likelihood-based approach to discriminate mixtures of network models that vary in time

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Naomi A. Arnold ◽  
Raul J. Mondragón ◽  
Richard G. Clegg
Keyword(s):  
Network Model ◽  
Change Point ◽  
Network Science ◽  
Preferential Attachment ◽  
Network Models ◽  
Explanatory Models ◽  
Growth Mechanisms ◽  
Artificial Data ◽  
Network Growth ◽  
Over Time

AbstractDiscriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms such as preferential attachment and triangle closure, with a wealth of explanatory models based on these. These models are deliberately simple, commonly with the network growing according to a constant mechanism for its lifetime, to allow for analytical results. We use a likelihood-based framework on artificial data where the network model changes at a known point in time and demonstrate that we can recover the change point from analysis of the network. We then use real datasets and demonstrate how our framework can show the changing importance of network growth mechanisms over time.

What Influences Relationship Formation in a Global Civil Society Network? An Examination of Valued Multiplex Relations

2021 ◽  
pp. 009365022110161
Author(s):  
Adam J. Saffer ◽  
Andrew Pilny ◽  
Erich J. Sommerfeldt
Keyword(s):  
Communication Network ◽  
Civil Society ◽  
Real World ◽  
Network Formation ◽  
Preferential Attachment ◽  
Interorganizational Networks ◽  
Communication Research ◽  
Relationship Formation ◽  
Interorganizational Communication ◽  
Strength Of Ties

Recent interorganizational communication research has taken up the question: why are networks structured the way they are? This line of inquiry has advanced communication network research by helping explain how and why networks take on certain structures or why certain organizations become positioned advantageously (or not). Yet, those studies assume relationships among organizations are either present or absent. This study considers how the strength of ties and multiplex relationships among organizations may reveal a more complex explanation for why networks take on certain structures. Our results challenge some long held assumptions about the mechanisms that influence network formation. For instance, our results offer important insights into the consequences of closure mechanisms, the applicability of preferential attachment to real-world networks, and the nuances of homophily in network formation on multidimensional relationships in a communication network. Implications for interorganizational networks are discussed.

scholarly journals np-Pair Correlations in the Isovector Pairing Model

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1405
Author(s):  
Feng Pan ◽  
Yingwen He ◽  
Lianrong Dai ◽  
Chong Qi ◽  
Jerry P. Draayer
Keyword(s):  
Binding Energy ◽  
Occupation Number ◽  
Mean Field ◽  
Energy Difference ◽  
Binding Energies ◽  
Pair Correlations ◽  
Isospin Symmetry Breaking ◽  
Pairing Model ◽  
Proton Pairing ◽  
Spin Basis

A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SUΛ(2) ⊗ SUI(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0+ ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J = 0+ excited states of the even–even and odd–odd N∼Z ds-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron–proton pairing contribution to the binding energy in the ds-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd–odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated.

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