BA Model Research Articles

Complex Network Evolution Model Based on Node Attraction

This paper studied the evolution law of the real-world networks, and then proposed a complex network model based on node attraction with tunable parameters in order to solve the problems existing in BA model and the original node attraction model. The model considered the effects of preferential attachments by the changes of degree and node attraction in the evolution process of networks. Theory research and simulation analysis show that we can more flexible adjust the evolution process of network through adjusting model parameters, therefore make it more accord with the network topology and statistical characteristics of real-world networks.

Duality between preferential attachment and static networks on hyperbolic spaces

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate scale-free networks. We show that there is actually a duality between a class of growing spatial networks based on preferential attachment on the sphere and a class of static random networks on the hyperbolic plane. Both classes of networks have the same scale-free degree distribution as the Barabasi-Albert model. As a limit of this correspondence, the Barabasi-Albert model is equivalent to a static random network on an hyperbolic space with infinite curvature.

Nonlinear dynamic evolution and control in a new scale-free networks modeling

The nonlinear evolving and controlling in complex networks are an important way to understand the dynamic mechanism for real networks. In order to explore universality of scale-free systems, we propose an extended network model based on Barabasi–Albert model by developing and decaying networks. The novel network evolves by growing and optimizing processes, such as the addition of new nodes and edges, or deletion of edges at every time step. Meanwhile, in order to describe more realistic phenomena of reality, we introduce the fitness to reflect the competition and local event of inner anti-preferential mechanism to delete the edges. We calculate analytically the degree distribution and find that the Barabasi–Albert model is only one of its special cases and the model self-organizes into scale-free networks, moreover, the numerical simulations are in good agreement with the analytical conclusions. The results imply that this extended model has more comprehensive and universal simulation and reflection in complex network topology characters and evolution with practices and applications.

Measurement and Control of Operational Risk of Banking Industry based on Complex Network

Operational risk has been great challenges of commercial banks and financial institutions since losses caused by operational risk have been significantly greater than ever before. In order to control and manage operational risk better,clear awareness of the operational risk conduction mechanism is helpful to further understand the whole dynamic process of the risks affecting the business. Traditional researches focus on the method to measure the risk more accurately, but few studies took into account the conduction mechanism of operational risk. This paper constructs operational risk network to simulate the contagion process of operational risk and put forward new measurement model based on complex network. First, properties of the operational risk network is analyzed, and risk spreading process in the network is described. Then, a load model is established to explain the conduction mechanism of operational risk factors. Next, a new measurement method of operational risk based on BA model is presented to make Monte Carlo simulation and calculate the amount of operational risk losses in the operational risk network. Also, this model is used to simulate the affecting factors in the operational risk network. The simulation results show that the degree of operational risk network as well as the selection of initial node plays an important role on losses, and thus some control recommendations based on the simulation results is given. Finally, a framework of operational risk management system is designed to apply this research result into practice.

Analysis and Control of Beliefs in Social Networks

In this paper, we investigate the problem of how beliefs diffuse among members of social networks. We propose an information flow model (IFM) of belief that captures how interactions among members affect the diffusion and eventual convergence of a belief. The IFM model includes a generalized Markov Graph (GMG) model as a social network model, which reveals that the diffusion of beliefs depends heavily on two characteristics of the social network characteristics, namely degree centralities and clustering coefficients. We apply the IFM to both converged belief estimation and belief control strategy optimization. The model is compared with an IFM including the Barabasi-Albert model, and is evaluated via experiments with published real social network data.

Information Dissemination and Control Models in Complex Network

In order to well understand and control the information dissemination in the complex network, Increasing Trust SI model and SIP model have been built to represent the peoples' interaction during information dissemination. By introducing and computing the trust degree of the net nodes, the process of information dissemination can be truly represented following increasing trust rule. Simulation experiments reveal that the informations can be quickly broken out in ER model, NW model and BA model due to the small world characteristic of complex networks. To prevent bad information disseminating, SIP model with Persuasion mechanism is presented. It can be effect when immune nodes with P status persuade their neighber disseminator with the truth. Simulation experiments show that not all nodes in the network will be disseminated and all will lose the trust on the bad information. Exceptionally, the best effection is in BA network with free-scale. The results of this paper can be used for analysis and management of information dissemination on complex networks. DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.3662

NLL: A Complex Network Model with Compensation for Enhanced Connectivity

The canonical scale-free model to describe complex networks is BA model with an power-law exponent γ = 3. Researchers further propose DS model (1 <; γ ≤ 4) to consider link failure besides node growth in preferential attachment. However, both models assume globally preferential attachment which is difficult to achieve in real networks. This paper proposes a new scale-free model, i.e. Neighborhood Log-on and Log-off model (NLL) which considers locally preferential connectivity. NLL incorporates both node growth and removal in topology evolvement. Unlike BA and DS, NLL adds compensation mechanism to enhance connectivity. The analysis shows that NLL has 1 <; γ ≤ 3. We conduct simulations to evaluate NLL performance and show that, NLL has short average path length and large clustering coefficient, compared with BA and DS models.

On the convergence rate of diffusion in the bidirectional Erdös–Rényi networks: An [formula omitted]-norm perspective

We investigate the convergence rates of diffusion in bidirectional Erdös–Rényi networks. We analytically and numerically demonstrate that the asymptotic distribution is far from a bell shape. Further, we numerically verify that the dynamical networks generated by the Barabasi–Albert model, which is a standard scale-free network model, exhibiting faster convergence of average consensus.

Structural features beneath neuronal avalanches

Recently, Friedman et al performed high-resolution measurements [1] that strongly supported an universal critical character (in the sense of statistical physics) of neuronal avalanches, despite the abnormally high frequency of large events (bumps in the distributions of size and lifetime of avalanches) deforming the pure power-law behavior expected from analogies to equilibrium critical phenomena that became manifest only for smaller events. Based on simulations of the Kinouchi-Copelli (KC) model, we have shown [2] that such bumps may not be experimental artifacts and really be typical at criticality when the topology of the neural network is the Barabasi-Albert (BA) model, leading to a scale-free degree distribution of exponent -3.0. On the other hand, those simulations could not reproduce the exponents of the power-law region of the avalanche distributions in [1] (namely, -1.7 for the size distribution and -1.9 for the lifetime distribution). Besides that, the KC dynamics on BA topology revealed that the information capacity (entropy of avalanche size distribution) did not exhibit critical optimization, in contrast with an earlier experiment [3]. In this study we investigate the KC dynamics on the Uncorrelated Configuration Model (UCM) [4]. The UCM is a kind of wiring procedure of a neural topology that can lead to scale-free degree distributions with tunable exponents and can be matched to BA model. However, even so their avalanches are not identical. While the UCM also allows the appearance of bumps on the avalanche distributions, it both shows that the information capacity may be critically optimal and exhibits quantitatively accurate values of the critical exponents for small avalanches, suggesting the UCM may be descriptive of some structural features in the systems claimed to exhibit critical dynamics.

A New Evolution Mechanism Model for B2B E-Commerce Network

To study the structure and evolution mechanism of B2B e-commerce network, the authors propose a network with several layers description of B2B e-commerce market. The empirical analysis from Alibaba.com shows that degree distribution of the network structure follows power-law. Based on modified BA (Barabasi-Albert) model, a new model is proposed, adding layers, fitness parameters, and more reasonable growth mechanism. The model reveals that, the structure of the network is stable, and the average path length and clustering coefficient are small. The authors also find that the impact of parameters is not decisive, and the emergence of scale-free nature depends on the mechanism itself.

Scale-free homophilic network

An important aspect governing the growth of complex networks is homophily, which is defined as the tendency of sites to link with others which are similar to themselves. Here, we modify the preferential attachment from Barabasi-Albert model by including a homophilic term. Comparisons are made with the Barabasi-Albert model, fitness model and our present model considering its topological properties: degree distribution, time dependence of the connectivity, shortest path length and clustering coefficient. We verify the existence of a region where the characteristics of sites play an important role in the rate of gaining links as well as in the number of links between sites with similar and dissimilar characteristics.

Cyclic Preferential Attachment in Complex Networks

Preferential Attachment (PA), which was originally proposed in the Barabasi-Albert (BA) Model, has been widely ac- cepted as a network growth model which returns in scale-free networks. Preferential attachment in the BA model operates on the assumption that a node which has more links has a better likelihood to create new links. In this work, we expand the PA mechanism by treating it as a cyclic mechanism which is linked to both direct and indirect neighbours of a node. The assumption behind this extension is that the preference of nodes is influenced by their indirect neighbours as well. We show that traditional PA can be absorbed as a special case of this new growth model, which we name ‘cyclic preferential attachment’ (CPA). We also discuss the properties of simulated networks that were generated based on CPA. Finally, we compare and contrast the CPA based networks with the traditional PA based networks and several real-world networks of similar sizes and link-to-node ratios, and show that CPA offers more flexibility in modeling real world networks.

Establishment of the Lakes and Reservoirs’ Model

This article describes the simulation method of water temperature and the model classification of water quality in lakes and reservoirs, and classic model of ecosystem dynamics of lakes and reservoirs - BA model from the water quality parameters of the relationship between two aspects of the basic equations are introduced. On this basis, establish the eutrophication of ecological models of lakes and reservoirs.

A Router-Level Topology Simulation Algorithm Based on Improved BA Model

A Router-Level Topology Simulation Algorithm Based on Improved BA Model

Formation Mechanism and Simulation Research on Innovation Clusters

With economic globalization and rapid development of science technology, a number of enterprises in the region work closely in the form of industrial clusters, with whose overall innovation capability increasing rapidly. It is in this situation that the conception of innovation cluster comes with the tide of fashion. This paper first reviews the study situation of networks; analyzing the structure of innovation clusters deeply, and then constructs an improved BA model to demonstrate the complex links among the innovation cluster nodes and explains their structural features, then simulate its formation mechanism and evolution process.

Online Social Network Evolving Model Based on Damping Factor

Recently the evolving model of network has become one of hot research topics. Since the BA model is presented, many kinds of evolving models have been proposed. However the generation mechanism of existing evolving model of online social network has certain limitation, i.e. researchers mostly focus on the factors that facilitating network growth but ignore the factors that delaying network growth. In order to resolve this limitation, a new online social network evolving model (DFEM) is proposed in this paper. In this model, the factors delaying network growth are defined as damping factor and which is divided into the decline of initial attraction, the loss of node heat, and irresistible natural factors. In addition, the damping factors, the attractive factors, and the degree of nodes are taken into consideration together in the preference link. The results of theoretical analysis and numerical simulation suggest that the degree distribution of network generated by DFEM model is more correspond with existing online social network.

Research on Industrial Clusters Networks Degree Distribution Evolving Features Based on Expected Return Factor

The key that firms constructing and maintaining the coordination relations in industrial clusters was the pursuit for profit. The pursuit dominated the evolving of industrial clusters networks structure. And it was featured in the dynamic evolving of its degree distribution. The industrial clusters networks degree distribution model was presented based on expected return factor by use of mean-field theory. Its evolving phase features were also studied by using simulation method. The main findings were as follows: (i) the model had the both properties of BA model and exponential distribution model and it was the extension of them. (ii)The industrial clusters networks degree distribution had scale-free property. The power exponent was influenced by the number of new added edges, proportion of complementary firms, expected return and its weight. Its value was larger than one. (iii)The degree distribution fluctuated regularly as the life cycle of industrial clusters. The main trend was getting more and more gentle. That was to say there would be more focal firms and not only first -come-first-rich and rich-get-richer. (iv)The exponent was larger in higher risk industrial clusters. (v)Complementary industrial clusters would more likely evolve to the central satellite type structure.

The accelerating growth of online tagging systems

Research on the growth of online tagging systems not only is interesting in its own right, but also yields insights for website management and semantic web analysis. Traditional models that describing the growth of online systems can be divided between linear and nonlinear versions. Linear models, including the BA model (Brabasi and Albert, 1999), assume that the average activity of users is a constant independent of population. Hence the total activity is a linear function of population. On the contrary, nonlinear models suggest that the average activity is affected by the size of the population and the total activity is a nonlinear function of population. In the current study, supporting evidences for the nonlinear growth assumption are obtained from data on Internet users' tagging behavior. A power law relationship between the number of new tags (F) and the population (P), which can be expressed as F ~ P ^ gamma (gamma > 1), is found. I call this pattern accelerating growth and find it relates the to time-invariant heterogeneity in individual activities. I also show how a greater heterogeneity leads to a faster growth.

CRBA: A Capacity Restricted Model Evolved from BA Model for Complex Network

It is critical to obtain a fine description of the topology of a complex network when modeling its behavior, as the network’s functionality heavily relies on its structure. Capacity Restricted model evolved from BA model (CRBA) for complex network proposed in this paper is the first attempt to date to take the node’s capacity distribution into modeling. CRBA is a universal and academic model, we learn it qualitatively and acquire several meaningful outcomes. Then we deduce a practical model from CRBA (CRBA C ) which has a constant node’s capacity distribution. We make a quantitative comparison of the properties of CRBA C with those of BA model, including the degree distribution, clustering coefficient and the average path length. Since majority of networks in practical are capacity–restricted, our model provides a better description of real-life complex networks.

Generative probabilistic models for protein–protein interaction networks—the biclique perspective

Motivation: Much of the large-scale molecular data from living cells can be represented in terms of networks. Such networks occupy a central position in cellular systems biology. In the protein–protein interaction (PPI) network, nodes represent proteins and edges represent connections between them, based on experimental evidence. As PPI networks are rich and complex, a mathematical model is sought to capture their properties and shed light on PPI evolution. The mathematical literature contains various generative models of random graphs. It is a major, still largely open question, which of these models (if any) can properly reproduce various biologically interesting networks. Here, we consider this problem where the graph at hand is the PPI network of Saccharomyces cerevisiae. We are trying to distinguishing between a model family which performs a process of copying neighbors, represented by the duplication–divergence (DD) model, and models which do not copy neighbors, with the Barabási–Albert (BA) preferential attachment model as a leading example.Results: The observed property of the network is the distribution of maximal bicliques in the graph. This is a novel criterion to distinguish between models in this area. It is particularly appropriate for this purpose, since it reflects the graph's growth pattern under either model. This test clearly favors the DD model. In particular, for the BA model, the vast majority (92.9%) of the bicliques with both sides ≥4 must be already embedded in the model's seed graph, whereas the corresponding figure for the DD model is only 5.1%. Our results, based on the biclique perspective, conclusively show that a naïve unmodified DD model can capture a key aspect of PPI networks.Contact: regevs01@cs.huji.ac.il; michall@cc.huji.ac.il; nati@cs.huji.ac.ilSupplementary information: Supplementary data are available at Bioinformatics online.