The Degree Distribution of Generalized Collaboration Networks with Preferential Attachment

2013 ◽  
Author(s):  
Lei Min ◽  
Zhang Ye ◽  
Zhu Min ◽  
Jing Ping
Keyword(s):  
Degree Distribution ◽  
Preferential Attachment ◽  
Collaboration Networks

scholarly journals MODELLING COLLABORATION NETWORKS BASED ON NONLINEAR PREFERENTIAL ATTACHMENT

2007 ◽  
Vol 18 (02) ◽  
pp. 297-314 ◽  
Author(s):  
TAO ZHOU ◽  
BING-HONG WANG ◽  
YING-DI JIN ◽  
DA-REN HE ◽  
PEI-PEI ZHANG ◽  
...  
Keyword(s):  
Empirical Data ◽  
Degree Distribution ◽  
Alternative Model ◽  
Free Parameter ◽  
Preferential Attachment ◽  
Average Distance ◽  
Small World ◽  
Clustering Coefficient ◽  
Collaboration Networks ◽  
Scale Free

In this paper, we propose an alternative model for collaboration networks based on nonlinear preferential attachment. Depending on a single free parameter "preferential exponent", this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.

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 The degree distribution of simple generalized collaboration networks

2009 ◽  
Vol 58 (10) ◽  
pp. 6682
Author(s):  
Zhao Qing-Gui ◽  
Kong Xiang-Xing ◽  
Hou Zhen-Ting
Keyword(s):  
Degree Distribution ◽  
Collaboration Networks

scholarly journals A quality-of-service-aware dynamic evolution model for space–ground integrated network

2017 ◽  
Vol 13 (8) ◽  
pp. 155014771772864 ◽  
Author(s):  
Zhuo Yi ◽  
Xuehui Du ◽  
Ying Liao ◽  
Lifeng Cao
Keyword(s):  
Quality Of Service ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Evolution Model ◽  
Dynamic Evolution ◽  
Power Law Distribution ◽  
Integrated Network ◽  
Complex Network Theory

Space–ground integrated network, a strategic, driving, and irreplaceable infrastructure, guarantees the development of economic and national security. However, its natures of limited resources, frequent handovers, and intermittently connected links significantly reduce the quality of service. To address this issue, a quality-of-service-aware dynamic evolution model is proposed based on complex network theory. On one hand, a quality-of-service-aware strategy is adopted in the model. During evolution phases of growth and handovers, links are established or deleted according to the quality-of-service-aware preferential attachment following the rule of better quality of service getting richer and worse quality of service getting poor or to die. On the other hand, dynamic handover of nodes and intermittent connection of links are taken into account and introduced into the model. Meanwhile, node heterogeneity is analyzed and heterogeneous nodes are endowed with discriminate interactions. Theoretical analysis and simulations are utilized to explore the degree distribution and its characteristics. Results reveal that this model is a scale-free model with drift power-law distribution, fat-tail and small-world effect, and drift character of degree distribution results from dynamic handover. Furthermore, this model exerts well fault tolerance and attack resistance compared to signal-strength-based strategy. In addition, node heterogeneity and quality-of-service-aware strategy improve the attack resistance and overall quality of service of space–ground integrated network.

GROWING HIERARCHICAL SCALE-FREE NETWORKS BY MEANS OF NONHIERARCHICAL PROCESSES

2007 ◽  
Vol 17 (07) ◽  
pp. 2447-2452 ◽  
Author(s):  
S. BOCCALETTI ◽  
D.-U. HWANG ◽  
V. LATORA
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Rate Equations ◽  
Scale Free ◽  
Scale Free Networks ◽  
Degree Correlations ◽  
Law Degree ◽  
Hierarchical Scale

We introduce a fully nonhierarchical network growing mechanism, that furthermore does not impose explicit preferential attachment rules. The growing procedure produces a graph featuring power-law degree and clustering distributions, and manifesting slightly disassortative degree-degree correlations. The rigorous rate equations for the evolution of the degree distribution and for the conditional degree-degree probability are derived.

Assortativity and act degree distribution of some collaboration networks

2007 ◽  
Vol 383 (2) ◽  
pp. 687-702 ◽  
Author(s):  
Hui Chang ◽  
Bei-Bei Su ◽  
Yue-Ping Zhou ◽  
Da-Ren He
Keyword(s):  
Degree Distribution ◽  
Collaboration Networks

scholarly journals Exploring the topology and dynamic growth properties of co-invention networks and technology fields

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0256956
Author(s):  
Pablo E. Pinto ◽  
Guillermo Honores ◽  
Andrés Vallone
Keyword(s):  
Preferential Attachment ◽  
Small World ◽  
Individual Characteristics ◽  
Collaboration Networks ◽  
Technological Diversification ◽  
Sudden Rise ◽  
Growth Properties ◽  
Dynamic Growth ◽  
The Individual ◽  
Inventor Networks

This study investigates the topology and dynamics of collaboration networks that exist between inventors and their patent co-authors for patents granted by the USPTO from 2007–2019 (2,241,201 patents and 1,879,037 inventors). We study changes in the configurations of different technology fields via the power-law, small-world, preferential attachment, shrinking diameter, densification law, and gelling point hypotheses. Similar to the existing literature, we obtain mixed results. Based on network statistics, we argue that the sudden rise of large networks in six technology sectors can be understood as a phase transition in which small, isolated networks form one giant component. In two other technology sectors, such a transition occurred much later and much less dramatically. The examination of inventor networks over time reveals the increased complexity of all technology sectors, regardless of the individual characteristics of the network. Therefore, we introduce ideas associated with the technological diversification of inventors to complement our analysis, and we find evidence that inventors tend to diversify into new fields that are less mature. This behavior appears to be correlated with the compliance of some of the expected network rules and has implications for the emerging patterns among the different collaboration networks under consideration here.

Directed preferential attachment models: Limiting degree distributions and their tails

2020 ◽  
Vol 57 (1) ◽  
pp. 122-136
Author(s):  
Tom Britton
Keyword(s):  
Explicit Expression ◽  
Empirical Evidence ◽  
Explicit Form ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Outgoing Edge ◽  
Tail Probabilities ◽  
Attachment Model ◽  
Birth Processes

AbstractThe directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node.

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