A Weighted Evolving Network with Community Size Preferential Attachment

Community structure is an important characteristic in real complex network.It is a network consists ofgroups of nodes within which links are dense but among which links are sparse.In this paper, the evolving network includenode, link and community growth and we apply the community size preferential attachment and strength preferentialattachment to a growing weighted network model and utilize weight assigning mechanism from BBV model.Theresulting network reflects the intrinsic community structure with generalized power-law distributions of nodes'degreesand strengths.

Unified Model for Generation Complex Networks with Utility Preferential Attachment

In this paper, based on the utility preferential attachment, we propose a new unified model to generate different network topologies such as scale-free, small-world and random networks. Moreover, a new network structure named super scale network is found, which has monopoly characteristic in our simulation experiments. Finally, the characteristics of this new network are given.

Preferential attachment network model with aging and initial attractiveness

In this paper,we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes.The network evolves with the addition of a new node per unit time,and each new node has m new links that with probability Π_(i) are connected to nodes i already present in the network.In our model,the preferential attachment probability Π_(i) is proportional not only to k_(i)+A,the sum of the old node i's degree ki and its initial attractiveness A,but also to the aging factor τ_(i)^(−α),whereτi is the age of the old node i.That is,Π_(i)∝(k_(i)+A)τ_(i)^(−α).Based on the continuum approximation,we present a mean-field analysis that predicts the degree dynamics of the network structure.We show that depending on the aging parameter α two different network topologies can emerge.For α<1,the network exhibits scaling behavior with a power-law degree distribution P(k)∝k^(−γ) for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m.Moreover,the average degree k(ti,t)at time t for any node i that is added into the network at time ti scales as k(t_(i),t)∝t_(i)^(−β) where 1/β is a linear function of A/m.For α>1,such scaling behavior disappears and the degree distribution is exponential.

EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK

In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.

A novel scale-free network model based on clique growth

A novel scale-flee network model based on clique （complete subgraph of random size） growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P（d） is 2m^2m1^-3（d-m1 ＋ 1）^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P（k） is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.

Modeling and Robustness of Knowledge Network in Supply Chain

The growth and evolution of the knowledge network in supply chain can be characterized by dynamic growth clustering and non-homogeneous degree distribution.The networks with the above characteristics are also known as scale-free networks.In this paper,the knowledge network model in supply chain is established,in which the preferential attachment mechanism based on the node strength is adopted to simulate the growth and evolution of the network.The nodes in the network have a certain preference in the choice of a knowledge partner.On the basis of the network model,the robustness of the three network models based on different preferential attachment strategies is investigated.The robustness is also referred to as tolerances when the nodes are subjected to random destruction and malicious damage.The simulation results of this study show that the improved network has higher connectivity and stability.

MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

Growing Small-World Networks Based on a Modified BA Model

We modify the （Barabgsi-Albert） BA model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new node are made locally to the old node and its nearest neighbours. It is found that this model can produce small-world networks with power-law degree distributions. Properties of our model, including the degree distribution, clustering, average path length and degree correlation coefficient are compared with that of the BA model. Since most real networks are both scalefree and small-world networks, our model may provide a satisfactory description for empirical characteristics of real networks.

Manufacturing enterprise collaboration network:An empirical research and evolutionary model

With the increasingly fierce market competition,manufacturing enterprises have to continuously improve their competitiveness through their collaboration and labor division with each other,i.e.forming manufacturing enterprise collaborative network(MECN)through their collaboration and labor division is an effective guarantee for obtaining competitive advantages.To explore the topology and evolutionary process of MECN,in this paper we investigate an empirical MECN from the viewpoint of complex network theory,and construct an evolutionary model to reproduce the topological properties found in the empirical network.Firstly,large-size empirical data related to the automotive industry are collected to construct an MECN.Topological analysis indicates that the MECN is not a scale-free network,but a small-world network with disassortativity.Small-world property indicates that the enterprises can respond quickly to the market,but disassortativity shows the risk spreading is fast and the coordinated operation is difficult.Then,an evolutionary model based on fitness preferential attachment and entropy-TOPSIS is proposed to capture the features of MECN.Besides,the evolutionary model is compared with a degree-based model in which only node degree is taken into consideration.The simulation results show the proposed evolutionary model can reproduce a number of critical topological properties of empirical MECN,while the degree-based model does not,which validates the effectiveness of the proposed evolutionary model.

Markov chain-based analysis of a modified Cooper-Frieze model

From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.

DESIGN METHODOLOGY OF NETWORKED SOFTWARE EVOLUTION GROWTH BASED ON SOFTWARE PATTERNS

Recently, some new characteristics of complex networks attract the attentions of scientist, in different fields, and lead to many kinds of emerging research directions. So far, most of the researcl work has been limited in discovery of complex network characteristics by structure analysis in large-scale software systems. This paper presents the theoretical basis, design method, algorithms and experiment results of the research. It firstly emphasizes the significance of design method of evolution growth for network topology of Object Oriented （OO） software systems, and argues that the selection and modulation of network models with various topology characteristics will bring un-ignorable effect on the process, of design and implementation of OO software systems. Then we analyze the similar discipline of ＂negation of negation and compromise＂ between the evolution of network models with different topology characteristics and the development of software modelling methods. According to the analysis of the growth features of software patterns, we propose an object-oriented software network evolution growth method and its algorithms in succession. In addition, we also propose the parameter systems for OO software system metrics based on complex network theory. Based on these parameter systems, it can analyze the features of various nodes, links and local-world, modulate the network topology and guide the software metrics. All these can be helpful to the detailed design, implementation and performance analysis. Finally, we focus on the application of the evolution algorithms and demonstrate it by a case study. Comparing the results from our early experiments with methodologies in empirical software engineering, we believe that the proposed software engineering design method is a computational software engineering approach based on complex network theory. We argue that this method should be greatly beneficial for the design, implementation, modulation and metrics of functionality, structure and performance in large-scale OO software complex system.

A longitudinal network analysis of social dynamics in rooks corvus frugilegus： repeated group modifications do not affect social network in captive rooks

Numerous studies have investigated the remarkable variation of social features and the resulting structures across species. Indeed, relationships are dynamic and vary in time according to various factors such as environmental conditions or individuals attributes. However, few studies have investigated the processes that stabilize the structures within a given species, and the behavioral mechanisms that ensure their coherence and continuity across time. Here, we used a dynamic actor-based model, RSiena, to investigate the consistency of the temporal dynamic of relationships of a group of captive rooks facing recurrent modifications in group composition （i.e., the loss and introduction of individuals）. We found that changes in relationships （i.e., formation and removal） followed consistent patterns regardless of group composition and sex-ratio. Rooks preferentially interacted with paired congeners （i.e., unpopular attachment） and were more likely to form rela- tionships with individuals bonded to a current social partner （i.e., ＂friends of friends＂, or triadic closure）. The sex of individuals had no effect on the dynamic of relationships. This robust behav- ioral mechanisms formed the basis of inter-connected networks, composed of sub-structures of in- dividuals emerging from the enmeshment of dyadic and triadic motifs. Overall, the present study reveals crucial aspects of the behavioral mechanisms shaping rooks social structure, suggesting that rooks live in a well-integrated society, going far beyond the unique monogamous pair-bond.