On The Basis Of Empirical Analysis Of Mathematics Cooperative Network

The system complexity is the cutting-edge direction in systems science.lt mainly researches the changes of the whole system’s structure and function caused by the interaction between various subsystems, it focus on the macro-level changes resulted from the micro-level changes.People always calls it as "21st century science". Researches about system complexity has been across many fields,such as society,politics, military, economy,management,engineering, biology and so on. With the further in-depth understanding of the theory and application of systems complexity, researchers pay more attention to how the interaction of the subsystems’running in the miro-level influence to the function of the entire system and evolution of the whole system,in recently years,researchers from different fields has expand their study of complex networks on the marco and micro levels with the overall and individual perspective.Collaborative networks is a hot research field of complex network analysis and belongs to a research direction in social network analysis. While the scientific research cooperation network is one of the earlier collaborative networks which are payed more attention to.The scientific research cooperation network is consituted by relationship of mutual cooperation between scientists and institutions. In this network, the scientists or research institutions are abstracted into a point, the cooperative relationship between them (for example, publishing a paper together,working together to complete a project) are abstracted into edge,then this complex network is scientific research cooperation network. The collaborative networks of scientist is the abstract description of the interaction of scientists.By describing the evolution of cooperation network,analyzing the connection structure of the relationship between scientists, people can analyze the the cooperative network evolution mechanism, the mutual influence between scientists, the mode of transmission of new knowledge and new ideas; they can propose many suggestions on how to enhance the influence of scientists in the relevant fields, how to increase output capacity and how to promote the scientific development.Publishing papers is an important way to show results of scientific research, the number of papers is an important indicator to measure the outputs. So this thesis researches the topology of the collaborative networks in Pure Mathematics field by researching the published papers in10famous journal and then analyzes the high yield authors,the high-impactauthor, and their citation identity, citation image. The achievement of this thesis is as follows:First,systematically analyzing the authors which published papers on the10top international journals during the1981to2011, and detailly decomposing the cooperative mode of these authors,decriping the graph of the collaboration networks,making the statistics on the distribution of the sub-networks in the entire network.identifying the network-specific parameters,the properties of the largest connected sub-network.By making the statistic on the node degree distribution and making its fitting curve,finding that the power-law index of the function lies in the range[2,3],in the line with the power-law distribution features,this shows that the network fits to the typical scale-free characteristics; Calculating the deameter,average distance of the network, finding the network has the small world effect and the mode of authors collaboration is mainly the indirect cooperation;calculating the clustering coefficient of the network,and finding that a moderately large nodes which is the representive of the authors in pure mathematics are the Fields Medal and the Wolf Prize winner;finding that the cooperation the collaboration density of the network is lower,and the potentiality of the cooperation between researchers in pure mathematics is higher.Second,citation identiy and citation image is the part of the citation analysis theory, but is different from the method of citation analysis. This study builds two new concepts,the citation identity of a group of authors and the citation image of a group of authors. According to the detailed analysis,finding that most of the top50high yield of authors obtained higher citation frequency;the highly cited journals which are cited by the groups included the10top journals we choosed as the sample,it has once again proven highly influential in these journals, and selecting them as a sample has some convincing; By analyzing the citation image and citation identity,it finds that they shows a centralized,decentralized law,and the minority authors obtain the large number of citation,while the majority obtain the less citation.Third, we used a self-designed citation count function to show that this phenomenon:the citation frequency of the highly cited author and the number of his published papers has relation,and the authors influence is as a bridge linking between them,in the meantime,the three affect each other.Fourth,we find that most of the core people and the high-impact figures of the cooperationcooperation network,are the Fields Medal, and the Wolf Prize winners, the two are famous mathematic awards. And their research fields distribut in algebra, geometry and analysis,which are three mathematical field of pure mathematics research.This highlights the importance of basic research in the20th century.Fifth, the mathematics organizations play a very important role in the mathematician’s research activities.it finds that the majority of the highly influenced authors of the groups are members of the American Mathematical Society, which indicates that this group is very active in the mathematical scientific research;it also finds another influential school of Bourbaki school, they get high cites,this mathematical group plays a certain role for mathematical research activities.Sixth, highly influenced journals, highly influenced authors and high citation frequency, the internationally renowned mathematics awards (Fields Medal example), presents a positive correlation to some extent. Influence of the journals is usually obtained by high cited frequency, of course, not all from the cites, but to large extent. High cited number always is obtained by citing some papers and works of famous people,meanwhile these famous mathematicians usually are the international famous mathematical awards due to their outstanding contribution. The relationship between them is not unilateral, actually is bilateral.