时间：2022-09-07 01:42:13
0.Summary
Network science is an interdisciplinary academic field which studies the qualitative and quantitative laws of complex networks.The paper mainly establish a model to find the connections between papers and discover the most important paper in the journal citation networks.
1.Model establishment
1.1 Degree Centrality（DC）
The degree of the research paper is the number of the connections which the node owes. DC is divided into outdegree centrality DC（out） and indegree centrality DC（in）. The indegree of a paper equals to the times which other papers reference this paper in the network.And higher indegree centrality shows the paper is an important knowledge source of the network.
1.2 Closeness Centrality（CC）
Similarly， Closeness Centrality is divided into outdegree Closeness Centrality CC（out） and indegree Closeness Centrality CC（in）. If the value of Closeness Centrality is large， the possibility that the paper lying in the center of network will be big.
1.3 Betweenness Centrality（BC）
For each pair of vertices（j，k），compute the shortest paths between them. More compactly the betweenness can be represented as：
The paper with high Betweenness Centrality may have more influence.
1.4 Eigenvector Centrality（EC）
Last but not the least， the Eigenvector Centrality of a paper is measured comprehensively by the importance of other papers connected with the paper.Therefore，letaijbe the parameter indicating how much papericontributes to paperj.xis centrality vector， andAis Matrix with a N* N array， so：
In this fomula， is a diagonal matrix composed of characteristic roots，X is a Matrix with a N*N array whose column is n eigenvectors of.The Eigenvector Centrality can measure whether a paper is the center of network from an overall perspective.
2.Model solutions and analysis
This paper choose some set of foundational papers in the emerging field of network science from the attached list .At first， number the papers from 1 to 16.Then find the connections between these papers by searching the google scholar website.And get a Table 1 as follow：
Table 1 Connections between papers from the attached list
At the same time，we calculate centrality indicators of 16 papers. The top 5 papers in every indicator are listed in the Table 2.
Table 2 Top 5 papers in each indicator
From Table 2 we can discover only paper 14 and paper 4 ranking top 5 in all indicators.Paper 14 ranking the first one in DC（in） and CC（in）.Paper 4 ranking the second place in DC（in） and CC（in）. We have already knew higher indegree centrality shows that the paper is an important knowledge source of the network. So paper 14，Collective dynamics of `small-world' networks written by Watts，D.and Strogatz，S.is the most influential paper in network science.■
【References】
[1]Tzeng G H，Huang J J 2011 Multiple Attribute Decision Making：Meth-ods and Applications （CRC：Boca Raton London New York）：69.
[2]Chen Changkun1，2，Li Zhi1 and Sun Yunfeng，Study on Character istics of D isaster Information Transm ission Based on Complex Networks，Journal of Catastrophology，2008.12.
[3]Alberl.R，and Barabasi，A-L Statistical mechanics of comples networks Reviws of Modern Physics，74：47-97，2002.