Weighted Network Evolution Model of Industry Technology Innovation Alliances Kno

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Abstract

On the basis of the dynamic evolution and competition of the complex network of industry alliances together with the limitations of the BBV network model， a competitive merit-based dynamic evolution model is constructed. It not only considers the addition of new nodes， but also the deletion of old nodes， the rewiring of old nodes and the deletion of old links appear in the networks. By using continuum theory and mean field theory， the corresponding evolution equation is established. The strength and degree distribution of the model still has the power-rate characteristics of scale-free networks and BBV scale-free network is a special case. The correctness of the theoretical analysis is proved by the simulation. The results show that by adjusting the parameters， it can coincide with the power-low exponent of many complex networks. Therefore， the improved model is more adaptive and authenticity.

Key words： Industry Technology innovation Coalition； BBV Model； Competitiveness； Degree Distribution； Power -low Exponent

INTRODUCTION

In recent years， the rise of complex networks makes the study of various disciplines substantial breakthroughs. Through the research on the Internet， the World Wide Web， the global aviation network， research cooperation network， social networks， biological metabolic networks etc.， it can be found that many systems in the reality can be seen as complex networks. The network nodes represent system elements and the edges represent the link between elements. People have proposed a variety of complex network model from different perspectives， in which the most famous are the ER random graph model proposed by Erd？s and Rényi （Erd？s， 1960）， the WS small-world network model proposed by Watts and Strogatz （Watts， 1998） and the BA scale-free network model proposed by Barabási and Albert （Barabási， 1999）. The BA model studied the origin of the macroscopic properties of the network from the perspective of evolution for the first time， and laid the foundation of network evolution model. The BA model indicated that growth and preferential attachment mechanism were reasons for the formation of the complex network scale-free property. This allowed people to recognize the macroscopic properties of complex networks are determined by its microscopic mechanism， thus began to study the macroscopic properties of the real network and its evolution problems.

The above-mentioned correction models are presented based on the real life network features and phenomena. They are built through the amendment and improvement of the growth and merit-based selection mechanism of the BA model. Each model has a focus， revealing the inherent nature of the corresponding network from the microscopic mechanisms to explain the macroscopic phenomena appeared in the corresponding network， which are more realistic， practical and complete than the BA model. However， these amendments models all have inadequacies： they just conceive and analyze certain types of networks from a certain point of view. They can just explain some characteristics of the corresponding network phenomenon and can’t reflect the essential attribute of all real networks reality， that is， they are not comprehensive and unified. For example， these models are not related to the actual knowledge transfer problems of the industry alliance， and can only explain part of the network they studied. This shows that these networks all have design deficiencies.

The BBV model， considering factors such as the network structure and node weights， has laid a good foundation for the weighted network’s research， but there are still certain gaps between the BBV model and the real network. Considering the actual situation of the industry alliance， it has the following inadequacies：

Firstly， the growth mechanism of the BBV model is inadequate. BBV model is a growth network model， only considering the addition of nodes and the connection with existing nodes. In the actual evolution of the industry alliance network， there exists a series of changes such as point plus， edge plus， point delete， edge delete and edge reconnect. For instance， in the process of continuous change of market economy， knowledge transfer relationship between the members of the Industry Alliance is not static. Constantly added to the network， there will be new members and old members leaving the network for some reason. It continues to have new members join the Industry Alliance Knowledge Transfer Network and old members leave the network for some reason. Moreover， the knowledge transfer connection between the old members is unstable. Individual members may create a new knowledge transfer between both or stop the knowledge transfer with partners at any time， that is， the network presents dynamic evolution with the increase of nodes. Secondly， the merit-based mechanism of the BBV model is deficient. In the BBV model， the node is preferred selected to connect edges in accordance with its strength. However， in the real network， the number of node connections and the growth rate of nodes strength are related to not only the strength of the link between nodes， but also its own “competitiveness”. For example， a new member of the industry alliance has only a few connections， that is， its node strength is lower. But if its knowledge innovation ability is strong or it owns some sort of knowledge resources advantage， lots of other members are willing to expand the exchange of knowledge and technical cooperation with it. The new member will be at a higher rate to get connected and its node strength will grow rapidly. Here we call the competitive ability of nodes as “competitive factor” （Zhou et al.， 2012）. Therefore， the weighted network， consider node competitiveness is essential. Thus， it is essential to consider nodes’ competitiveness in a weighted network.

2. THE WEIGHTED NETWORK DYNAMIC EVOLUTION MODEL

3.1 Experimental Simulation