Network model of deviation from power-law distribution in complex network

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

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A dynamic power-law sexual network model of gonorrhoea outbreaks

10.1101/322875 ◽

2018 ◽

Author(s):

Lilith K Whittles ◽

Peter J White ◽

Xavier Didelot

Keyword(s):

Network Model ◽

Power Law ◽

Dynamic Network ◽

Great Promise ◽

Model Parameters ◽

Power Law Distribution ◽

Time Model ◽

Dynamic Network Model ◽

The Impact ◽

Over Time

AbstractHuman networks of sexual contacts are dynamic by nature, with partnerships forming and breaking continuously over time. Sexual behaviours are also highly heterogeneous, so that the number of partners reported by individuals over a given period of time is typically distributed as a power-law. Both the dynamism and heterogeneity of sexual partnerships are likely to have an effect in the patterns of spread of sexually transmitted diseases. To represent these two fundamental properties of sexual networks, we developed a stochastic process of dynamic partnership formation and dissolution, which results in power-law numbers of partners over time. Model parameters can be set to produce realistic conditions in terms of the exponent of the power-law distribution, of the number of individuals without relationships and of the average duration of relationships. Using an outbreak of antibiotic resistant gonorrhoea amongst men have sex with men as a case study, we show that our realistic dynamic network exhibits different properties compared to the frequently used static networks or homogeneous mixing models. We also consider an approximation to our dynamic network model in terms of a much simpler branching process. We estimate the parameters of the generation time distribution and offspring distribution which can be used for example in the context of outbreak reconstruction based on genomic data. Finally, we investigate the impact of a range of interventions against gonorrhoea, including increased condom use, more frequent screening and immunisation, concluding that the latter shows great promise to reduce the burden of gonorrhoea, even if the vaccine was only partially effective or applied to only a random subset of the population.

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Structural Properties of the Brazilian Air Transportation Network

Anais da Academia Brasileira de Ciências ◽

10.1590/0001-3765201520140155 ◽

2015 ◽

Vol 87 (3) ◽

pp. 1653-1674 ◽

Cited By ~ 7

Author(s):

GUILHERME S. COUTO ◽

ANA PAULA COUTO DA SILVA ◽

LINNYER B. RUIZ ◽

FABRÍCIO BENEVENUTO

Keyword(s):

Structural Properties ◽

Complex Network ◽

Power Law ◽

Global Economy ◽

Transportation Network ◽

Small World ◽

Air Transportation ◽

Power Law Distribution ◽

National Network ◽

Operational Problem

The air transportation network in a country has a great impact on the local, national and global economy. In this paper, we analyze the air transportation network in Brazil with complex network features to better understand its characteristics. In our analysis, we built networks composed either by national or by international flights. We also consider the network when both types of flights are put together. Interesting conclusions emerge from our analysis. For instance, Viracopos Airport (Campinas City) is the most central and connected airport on the national flights network. Any operational problem in this airport separates the Brazilian national network into six distinct subnetworks. Moreover, the Brazilian air transportation network exhibits small world characteristics and national connections network follows a power law distribution. Therefore, our analysis sheds light on the current Brazilian air transportation infrastructure, bringing a novel understanding that may help face the recent fast growth in the usage of the Brazilian transport network.

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STRENGTH DISTRIBUTION IN DERIVATIVE NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183105007765 ◽

2005 ◽

Vol 16 (07) ◽

pp. 1097-1105 ◽

Cited By ~ 2

Author(s):

LUCIANO DA FONTOURA COSTA ◽

GONZALO TRAVIESO

Keyword(s):

Complex Networks ◽

Complex Network ◽

Lower Limit ◽

Network Model ◽

Power Law ◽

Neuronal Networks ◽

Strength Distribution ◽

Node Degree ◽

Upper Limit ◽

The Difference

This article describes a complex network model whose weights are proportional to the difference between uniformly distributed "fitness" values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e., the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent γ<1 if the fitness has an upper limit and γ>1 if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.

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Co-Movement in Stock Markets Based on Directed Complex Network

International Journal of Economics and Finance ◽

10.5539/ijef.v8n2p179 ◽

2016 ◽

Vol 8 (2) ◽

pp. 179

Author(s):

Zhen Du ◽

Pujiang Chen ◽

Na Luo ◽

Yingjie Tang

Keyword(s):

Complex Network ◽

Power Law ◽

Degree Distribution ◽

Path Length ◽

Stock Exchange ◽

Small World ◽

Clustering Coefficient ◽

Power Law Distribution ◽

Scale Free ◽

Set Up

<p>In this paper, directed complex network is applied to the study of A shares in SSE (Shanghai Stock Exchange). In order to discuss the intrinsic attributes and regularities in stock market, we set up a directed complex network, selecting 450 stocks as nodes between 2012 and 2014 and stock yield correlation connected as edges. By discussing out-degree and in-degree distribution, we find essential nodes in stock network, which represent the leading stock,. Moreover, we analyze directed average path length and clustering coefficient in the condition of different threshold, which shows that the network doesn’t have a small- world effect. Furthermore, we see that when threshold is between 0.08 and 0.15, the network follows the power-law distribution and behaves scale-free.</p>

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The structure of co-publications multilayer network

Computational Social Networks ◽

10.1186/s40649-021-00089-w ◽

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.

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Sublinear domination and core–periphery networks

Scientific Reports ◽

10.1038/s41598-021-94105-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Marios Papachristou

Keyword(s):

Network Model ◽

Power Law ◽

Real World ◽

Random Network ◽

Small World ◽

The Core ◽

Entire Network

AbstractIn this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

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Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

Nucleic Acids Research ◽

10.1093/nar/gkab072 ◽

2021 ◽

Author(s):

David A Garcia ◽

Gregory Fettweis ◽

Diego M Presman ◽

Ville Paakinaho ◽

Christopher Jarzynski ◽

...

Keyword(s):

Transcription Factor ◽

Single Molecule ◽

Power Law ◽

Dwell Time ◽

Specific Binding ◽

Power Law Distribution ◽

Single Molecule Level ◽

Binding Behavior ◽

Chromatin Template ◽

Nuclear Domains

Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

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