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.

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.