【正文】 數(shù)和較小的平均路徑長度的網(wǎng)絡(luò)。為了計(jì)算網(wǎng)絡(luò)的平均路徑長度，我們需要得到網(wǎng)絡(luò)的最大連通子圖，網(wǎng)絡(luò)的最大連通子圖我們?cè)谏险虑蟮茫鐖D13。利用pajek軟件中的Net/Pathes between 2 vertices/distribution of distances/from all vertices對(duì)圖13的最大連通子圖求平均路徑長度，求的結(jié)果如圖21。利用Pajek中的Net/Vector/Clustering Coefficients/CC1菜單命令，可對(duì)以上網(wǎng)絡(luò)求得其各個(gè)節(jié)點(diǎn)的聚類系數(shù)。求的結(jié)果如圖22。Pajek中，分別有兩個(gè)輸出結(jié)果，一個(gè)是partition文件，它表示網(wǎng)絡(luò)中連接各個(gè)節(jié)點(diǎn)的鄰居的邊數(shù)。另一個(gè)為vector文件，它表示網(wǎng)絡(luò)中各個(gè)節(jié)點(diǎn)的聚類系數(shù)。 節(jié)點(diǎn)的聚類系數(shù)反映了該節(jié)點(diǎn)鄰點(diǎn)的聯(lián)系的程度 ，聚類系數(shù)越大，說明該點(diǎn)的鄰接點(diǎn)之間的聯(lián)系越緊密。圖21最大連通子圖的平均路徑長度圖22網(wǎng)絡(luò)的聚類系數(shù)圖23 具有相同節(jié)點(diǎn)和平均度的隨機(jī)網(wǎng)絡(luò)聚類系數(shù)股票網(wǎng)絡(luò)的最大連通子圖有134個(gè)節(jié)點(diǎn)，具有134個(gè)節(jié)點(diǎn)的隨機(jī)網(wǎng)絡(luò)的平均路徑長度為lnN=ln134=，,說明兩只完全沒有聯(lián)系的股票之間大多數(shù)要通過5到6只股票才能有聯(lián)系，圖21同時(shí)表明SH600111與SH600162兩只股票關(guān)系最遠(yuǎn)，路徑長度達(dá)到15。而具有相同節(jié)點(diǎn)和平均度數(shù)的隨機(jī)網(wǎng)絡(luò)聚類系數(shù)如上圖23。所以建立的網(wǎng)絡(luò)模型具有較大的聚類系數(shù)也有較大的平均路徑長度，與小世界網(wǎng)絡(luò)模型的較小的平均路徑長不相符合。所以建立的股票網(wǎng)絡(luò)不具備小世界特性。圖24刪除幾個(gè)度數(shù)較大的中心節(jié)點(diǎn)后的聚類系數(shù)根據(jù)圖 22，24所示，刪除幾個(gè)度數(shù)較大的節(jié)點(diǎn)之后得到的網(wǎng)絡(luò)小世界聚類系數(shù)增大，網(wǎng)絡(luò)聚類系數(shù)減小。對(duì)比兩組數(shù)據(jù)發(fā)現(xiàn)增大或者減小的數(shù)值不是很大，說明大多數(shù)的節(jié)點(diǎn)聚類系數(shù)沒有發(fā)生變化，網(wǎng)絡(luò)系統(tǒng)比較穩(wěn)定。5 總結(jié)通過對(duì)上面的研究與分析，上海股票市場(chǎng)中股票網(wǎng)絡(luò)的度分布有疏有密，存在一些度數(shù)比較大的節(jié)點(diǎn)對(duì)于與他們相連的區(qū)域的影響比較大，其他節(jié)點(diǎn)對(duì)于股票網(wǎng)絡(luò)的影響比較小。通過對(duì)網(wǎng)絡(luò)聚類系數(shù)以及平均路徑長度研究發(fā)現(xiàn)，股票網(wǎng)絡(luò)的聚類系數(shù)和平均路徑長度都比較大，與小世界網(wǎng)絡(luò)的較小的平均路徑長度不相符合。股票網(wǎng)絡(luò)中大多數(shù)節(jié)點(diǎn)聚類系數(shù)較大，度的大小大多數(shù)小于10，沒有度數(shù)過大的節(jié)點(diǎn)，表明股票網(wǎng)絡(luò)系統(tǒng)比較穩(wěn)定，受到干擾的影響較小。刪除幾個(gè)度數(shù)較大的節(jié)點(diǎn)之后得到的網(wǎng)絡(luò)聚類系數(shù)沒有多大變化，說明大多數(shù)的節(jié)點(diǎn)聚類系數(shù)沒有發(fā)生變化，網(wǎng)絡(luò)系統(tǒng)比較穩(wěn)定。以上的結(jié)論對(duì)于投資者選擇合理的投資方式有很大的幫助。通過幾個(gè)月的研究，我掌握了股票網(wǎng)絡(luò)的基本研究思路，熟悉了復(fù)雜網(wǎng)絡(luò)的基本原理，對(duì)股票網(wǎng)絡(luò)進(jìn)行了建模與分析。在這個(gè)過程中，我自主學(xué)習(xí)復(fù)雜網(wǎng)絡(luò)的相關(guān)知識(shí)，鍛煉了自己的獨(dú)立思考的能力，積累了寶貴的經(jīng)驗(yàn)。參考文獻(xiàn)，李翔，陳關(guān)榮．復(fù)雜網(wǎng)絡(luò)理論及其應(yīng)用[M]．清華大學(xué)出版社，2006：147． A L．Linked：The New Science of Networks[M]．Massachusetts：Persus Publishing，2002． D J．The‘new’science of networks[J]．Annual Review of Sociology，2004，30：243270．4. Erdos P,Renyi A．On the evolution of random graphs．Pual．Math．1nst．Hung．Acad．Sci．，1960，5：1760． S．The small world problem[J]．Psychology Today,May 1967，6067． A L,Albert R．Emergence of scaling in random networks[J]．Science, 1 999，286：509．5 12． Boginskia，Sergiy Butenkob，PanosM. Pardalosa. Statistical analysis of financial networks[J]. Computational Statistics amp。 Data Analysis，2005,2(48):431443. H J,Lee Y,Kahng B,et scalefree network in financial correlations [J].Phys Soc Jpn, 2002,71(9):21332136. Eom，Okyu Kwon，WooSung Jung and Seunghwan Kim. The effect of a market factor on information flow between stocks using minimal spanning tree[J]. Physica A:Statistieal Meehanics and its APPlieations, 2010,389 (8). Zhou,Didier Somette. A case study of speculative financial bubbles in the South African stock market20032006[J]. Physica A:Statistical Mechanics and its application，2009 ,388(6). Seleuk，F(xiàn)inancial earthquakes，aftershoeks and scaling in emerging stock markets[J].Physica A:Statistical and Theoretieal Physics, 2004, 333. ，Benjamin M. Tabakb，F(xiàn)iliPe . Can we predict crashes ,The case of the Brazilian stock market[J]. Physiea A:Statistical Meehanics and its Applications , 2009, 388(8). Eun Lee, Jae Woo Lee, Byoung Hee networks in a stock market[J]. Computer Physics Communications，2007,177, l2.，閡志鋒，陳師陽．上海證券市場(chǎng)的復(fù)雜網(wǎng)絡(luò)特性分析[J]．東北大學(xué)學(xué)報(bào)(自然科學(xué)版)，2007，128（7）．，Xin Tian Zhuang and Shuang network analysis of the Chinese stock market[J]. Physica A:Statistical Mechanics and its Applications , 2009, 388(14). Ying，Zhang Research on the Scaling Properties of Financial Time Series[J].Physica A:Statistical Mechanics and its Applications, 2009, 388(11). Xintian，Yuan on scale crossover phenomenon and its characteristics of stock markets in China[J]. Journal of Systems Engineering，2009.，高巖．基于復(fù)雜網(wǎng)絡(luò)理論的證券市場(chǎng)網(wǎng)抗毀性分析[J]．金融理論與實(shí)踐，2008(6)．，王存睿，劉向東，張慶靈．基于網(wǎng)絡(luò)權(quán)重的多社團(tuán)網(wǎng)絡(luò)結(jié)構(gòu)劃分算法[J]．復(fù)雜系統(tǒng)與復(fù)雜性科學(xué)，2009，6（3）．，狄增如，樊瑛．二分網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)的比較性定義[J]．復(fù)雜系統(tǒng)與復(fù)雜性科學(xué)，2009，6（4）．，張鵬，狄增如，樊瑛．復(fù)雜網(wǎng)絡(luò)中的社團(tuán)結(jié)構(gòu)[J]．復(fù)雜系統(tǒng)與復(fù)雜性科學(xué)，2008，5（3）．，沈軼．網(wǎng)絡(luò)的模塊矩陣及其社團(tuán)結(jié)構(gòu)指標(biāo)[J]．物理學(xué)報(bào)，2010．，劉亞冰．復(fù)雜網(wǎng)絡(luò)中的社團(tuán)結(jié)構(gòu)算法綜述[J]．電子科技大學(xué)學(xué)報(bào)，2009，38．Stock Network Modeling and Analysis
GAO HuiminNanjing University of Information Science and Technology，nanjing 210044ABSTRACTAt present，taking advantage of plex network theory to better understand and explain various phenomena in stock markets has roused great interest among scholars home and abroad. Complex network theory is the emerging research focus in recent years，its applied research also has a wide range of areas，and the financial stock market is an important area of research of plex network theory. In this, we use the plex network theory methods to do the following work. Taking the Shanghai stock market as the research object, in the Shanghai stock market panies as nodes, through the correlation coefficient calculating their contact, select the appropriate threshold value, by MATLAB software programming by adjacency matrix, then Pajek software was used to establish the stock network model simulation. Through the analysis of the network39。s degree distribution and clustering coefficient, get the stock network has scalefree and smallworld properties.Keywords: stock。 plex networks。 modeling and analysis 附錄一Matlab軟件編寫股票網(wǎng)絡(luò)度分布程序[A,txt]= xlsread(39。39。)B = corrcoef(A)idb = find(B )。B (idb)=[0]。idb=find(B )。B (idb)=[1]x= B diag(diag(B))x=load(39。D:\pajek\39。)。x=sum(x)。pp=zeros(2,1)。qq=1。for i=1:501if x(i)~=0pp(qq)=x(i)。qq=qq+1。endend[alpha, xmin, D]=plfit(pp)。h = plplot(pp,xmin,alpha)