Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method

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1 Journal of Systems Science and Information Oct., 2017, Vol. 5, No. 5, pp DOI: /JSSI Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method Hongxing YAO School of Finance and Economics, Jiangsu University, Zhenjiang , China; Faculty of Science, Jiangsu University, Zhenjiang , China Yunxia LU Faculty of Science, Jiangsu University, Zhenjiang , China Abstract In this paper, we analyze the 180 stocks which have the potential influence on the Shanghai Stock Exchange (SSE). First, we use the stock closing prices from January 1, 2005 to June 19, 2015 to calculate logarithmic the correlation coefficient and then build the stock market model by threshold method. Secondly, according to different networks under different thresholds, we find out the potential influence stocks on the basis of local structural centrality. Finally, by comparing the accuracy of similarity index of the local information and path in the link prediction method, we demonstrate that there are best similarity index to predict the probability for nodes connection in the different stock networks. Keywords correlation coefficient; local structural centrality; potentially influential stocks; local information similarity index; path similarity index 1 Introduction Under circumstances of big data age, the stock market is a virtual economy and is closely related to our lives. As early as 2007, Zhuang, et al. [1,2], according to the stock in Shanghai stock market, established the correlation coefficient network of stock price fluctuation. So it is found that almost the stock networks possess the small-world property, the high clustering property and the scale-free property. This new idea broke the limitations of traditional models. Over the recent years, various measures such as degree [3], betweenness [4], closeness [5] and eigenvector centralities have been proposed to rank nodes in the network. Local metric like degree centrality is simple but less effective. Global metrics such as betweenness and closeness centrality perform well in ranking nodes, but are of high computational complexity. Furthermore it is hard to get the complete networks structure for most large-scale networks nowadays. Si, et al. [6] researched the centrality of complex network and put forward the method of peeling off. Gao, et al. [7] also considered the topological connections among the neighbors and Received November 9, 2016, accepted February 7, 2017 Supported by the National Nature Science Foundation of China ( , )

2 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 447 proposed local structural centrality (LSC). Through experiments on artificial networks generated by BA [8,9] network model and LFR network model [10], they show that their method can outperform other centrality measures in scale-free networks with different sizes and different community structure. Actually, the topological connections among the neighbors are also very important. For nodes with the same local centrality, the one with denser connected neighbors is supposed to have stronger influence ability since denser connected neighbors get more chance to influence each other. In this paper, with different thresholds, we use the local structural centrality (LSC) to analyze the influence of the stock. However, with the development of stock network, network evolution analysis is an important part of stock network analysis [11]. Network evolution analysis refers to the size of correlation between stocks changed in different periods of time. In the era of information explosion, data mining techniques are so important that it can increase cognition and insight to help us capture now and forecast future if we could find the hidden relationship from the vast data. Link prediction aims to infer the existence of links between nodes, including prediction of existent yet unknown links and future links [12]. Prediction of the future network structure plays an important role in avoiding investment risks. A large number of link prediction methods have already been proposed in recent years. Many of them assume that two nodes are more likely to be connected if they are similar. The similarities of nodes can be measured by the different scales information in network. The link among nodes indicates the price fluctuation of the corresponding stock within some specified period of time in the stock market. Kleinberg, et al. [13] presented systematically the link prediction problem, and compared the performance of several similarity indexes (Common Neighbors [14], Jaccar Index [15], Adamic-Adar Index [16], priority link [17], etc.) in the link prediction. Sarukkai, et al. [18] presented that link prediction method based on Markov chain. Newman, et al. [19] found that many complex networks have hierarchical structureswhich can predict the missing link, and so on. Lü, et al. [20] elaborated the similarity index based on local information in the complex network link prediction. Wang, et al. [21 23] obtained the actual process of link prediction from two cases of static and dynamic by the BBS network in the scale free network. The AUC evaluation served as the standard to explore the accuracy of similarity index link prediction. Zhang, et al. [24] reviewed the link prediction. Recently, link prediction has become one of the hottest topics in many branches of subjects due to its wide applications. For example link prediction is widely applied in data mining technology, and measuring the possibility of the connection between nodes in future complex network. So in this paper, with AUC as the evaluation criteria to compare the accuracy of the similarity index of local information and path [25,26], we select the appropriate similarity index of the stock network. We try to understand the influence of the potential influential stock in the whole stock market and analyze the change rule and the investor s investment preference, so as to reach the goal of planning risk. Following parts are organized as following. We briefly build stock market model in Section 2 and analyze nodes by using our local structural centrality measure in Section 3. In Section 4, we introduce the similarity index of the local information and path in link prediction. We present the experimental analysis in Section 5. Finally in Section 6, we expose the conclusions of the work.

3 448 YAO H X, LU Y X. 2 To Build Stock Network Market In this paper, we select the daily closing price of SSE 180 stocks from January 1, 2005 to June 19, 2015 because those stocks are in large scale and good liquidity. Network nodes represent a single stock and edges among nodes represent the price fluctuations between stocks in a particular period. 2.1 Correlation Between Stocks There are N stocks in the stock market and here i and j are the labels of stocks. ρ ij is the correlation coefficient of logarithm different of corresponding closing price data in stock i and j: < Y i Y j > < Y i >< Y j > ρ ij =, (1) (< Yi 2 > < Y i > 2 )(< Yj 2 > < Y j > 2 ) Y i (t) = lnp i (t) lnp i (t 1). (2) Here, P i (t) is the relevant closing price of stock i at day t, and < > is the statistical average of a variable. We use Matlab to calculate the correlation coefficient and draw the Figure 1. The correlation coefficient is concentrated on Moreover, less stocks correlation coefficient are negative. This shows that the connection between stocks is generally weak in the stock market. P x F x C x Figure 1 Relative and cumulative Frequency of correlation coefficient 2.2 Matrix Determination and Network Construction In order to establish the stock network, we determine the n n stock distance matrix {d ij } first. The element d ij is viewed as the distance between stock and stock and it is defined by D ij = 2(1 ρ ij ). (3)

4 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method Network Construction Through the Threshold Method by According to the threshold method, the adjacency matrix a ij of stock market is determined 0, i = j or d ij > τ, a ij = 1, else. Here τ is the threshold. Through the different threshold value, it can get the corresponding stock market. When the threshold value is 0.6, 0.89 and 1, we analyze the stock market structure. If the threshold is 0.6, there are 180 nodes and 10 edges. If the threshold is 0.89, the edge is 272. If the threshold is 1, the edge is 912. Due to the threshold is 0.6, the correlation among the nodes is the strongest. But it ignores the weak correlation so that the network is too simple. When the threshold is greater than 1, the increase of complexity makes it difficult to calculate, and the correlation among the nodes is also declined. Therefore, this paper chooses the research on the stock network market with a threshold value of 0.89 in Figure 2. (4) Figure 2 Stock network market for τ = 0.89

5 450 YAO H X, LU Y X. Figure 3 Local structural centrality 3 The Analysis of Stock Nodes In order to better understand the local structural centrality in Figure 3. Intuitively, node 7 has stronger influential ability than node 1. They have the same degree (k(7) = k(1) = 4) but the different local structural centrality (C LSC (7) = 16.9, C LSC (1) = with α = 0.7). Because nodes 2 and 9 are respective the nearest neighbor of node 1 and 7, and the influence of node 9 is stronger than that of node 2. Due to node 13 and node 14, neighbors of node 9, are connected with each other, the denser connection of node 13 and node 14 is higher than node 11 and node 12, so the influence of node 9 is higher than that of node 2. The local structural centrality is to take into account both the number of nearest and the next nearest neighbors, and the topological connections among neighbors. This method is defined as: C LSC = u Γ 1(v) = u Γ 1(v) Q(u), (5) ( αn(u) + (1 α) w Γ 2(u) c w ). (6) Where Γ 1 (v) is the number of nearest of node v, N(u) = Γ 2 (u) is the number of nearest and the next nearest neighbors of node u, c w represents the local clustering coefficient of node and is a tunable balance parameter between 0 and 1. c w is defined as: c w = e k(k 1). (7) Here, k is the number of nearest of node w, and e represents the number of edges that exist between the nearest neighbors the node w. By understanding the basic knowledge of local structural centrality, we gain the potentially influential stocks from the SSE 180. On this basis, the stocks are divided into financial categories (I), non-ferrous metals (II), real estate (III), engineering (IV), construction (V), and other categories (VI). When the threshold is 0.6, 0.89, 1, 1.02, 1.04, and 1.06, we use the local structural centrality to rank the nodes and keep the top-30 stocks in Table 1.

6 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 451 Table 1 Potential influential stocks in different kinds of stocks for τ=0.89 τ sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh sh With the different threshold, the influence of the stock is arranged by the local structural centrality. When the threshold is 0.6, only 16 stocks can be ranked in Table 1. In the top- 30 stocks, when the threshold is 0.89, the financial stocks account for 24, non-ferrous metals stocks account for 3, energy stocks account for 2, and real estate stocks account for 1. When the threshold is 1, the financial stocks account for 15, non-ferrous metals stocks account for 4, energy stocks account for 4, real estate stocks account for 2, engineering construction stocks

7 452 YAO H X, LU Y X. account for 1, and other types of shares account for 4. With the increase of the threshold, the influence of financial stocks has declined. The proportion of non-ferrous metal stocks is relatively stable, but on the whole, the influence of stock is constantly strengthened. Here, the influence of Western Mining (sh601168), Chalco (sh601600), Gold Molybdenum Shares (sh601958) and Jiangxi Copper (sh600362) is rising. When the threshold is greater than 1, they rank at the forefront and reach a stable state. This indicates that non-ferrous metals stocks are the most potential impact in all stocks. When the threshold is greater than 1, the influence of energy stocks also increased. The influence of HK (sh601088) increases and then decreased slightly, but overall, its influence is rising. The influence of COSL (sh601808) continues climbing. Influential stocks in the real estate are rising, including BEIJE (sh601588), Nanjing City (sh600064), City Investment Holdings (sh600649) and Beijing City Construction (sh600266) and so on. The influence of CREC (sh601390) in the stock of construction is also rising. CA (sh601111) in the other types of stocks has the potential influence, and its influence basically maintained stable. Table 2 Potential influential stocks in different kinds of stocks for τ=0.89 Non-ferrous metals stocks Energy stocks Real estate stocks Project construction Other types of stocks Western Mining HK BEIJE CREC CA (sh601168) (sh601088) (sh601588) (sh601390) (sh601111) Chalco YZC Pacific CSCEC Baoshan Iron (sh601600) (sh600188) stocks(sh601099) (sh601668) and Steel (sh600019) Gold Molybdenum CNPC City Investment CRCC China Unicom Shares (sh601958) (sh601857) Holdings (sh600649) (sh601186) (sh600050) Jiangxi Copper SINOPEC Nanjing BBMG YOUNGOR (sh600362) (sh600028) Hi-Tech (sh600064) (sh601992) (sh600177) COSL Beijing City Daqin Railway (sh601808) Construction (sh600266) (sh601006) Golden Bridge SPH in Pudong (sh600639) (sh601607) SAIC (sh600104) When the threshold is equal to 0.89, the more influential stock nodes are basically concentrated in the financial stocks; however, their influence is decreased at a value 1 of threshold. When the threshold is greater than 1, the different types of industries all have influential stocks. However, they change into the stocks which have potential impact during the threshold is less than 1. In Table 2. When the threshold is equal to 0.89, potential influential stocks focus on the non-ferrous metals stocks, including the Western Mining (sh601168), Chalco (sh601600), Gold Molybdenum Shares (sh601958) and Jiangxi Copper (sh600362), and

8 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 453 the energy stocks, including HK (sh601088), YZC (sh600188), CNPC (sh601857), SINOPEC (sh600028) and COSL (sh601808), and the real estate stocks, including BEIJE (sh601588), Pacific stocks (sh601099), City Investment Holdings (sh600649), Nanjing Hi-Tech (sh600064), Beijing City Construction (sh600266), Golden Bridge in Pudong (sh600639), and the project construction, including CREC (SH601390), CSCEC (sh601668), CRCC (sh601186), BBMG (sh601992), and the Other types of stocks, inducing CA (sh601111), Baoshan Iron and Steel (sh600019), China Unicom (sh600050), YOUNGOR (sh600177), Daqin Railway (sh601006), SPH (sh601607), SAIC (sh600104). 4 Methods of Link Prediction For an undirected network G = (V, E), where n and m are used to denote the number of nodes and edges. The set of non-existent link is U E, where U is the universal set. Set U contains all (N(N 1)/2) possible links. For a node pair (x, y) U, the score S xy reflects the similarity between x and y. To measure the performance of similarity indices in link prediction, E is randomly divided into two parts: A training set E T a test set E P. Here E T E P = E and E T E P =. The standard metrics AUC is often used in link prediction. In fact, AUC show that the probability is the score of an edge of randomly selected higher the score of a non-existent edge of randomly selected in test set. AUC is defined as: AUC = n + 0.5n. (8) n Where if among n times of independent comparisons, there are n times that the score of link from E P is higher than the link from U E, and n times that have the same scores. 4.1 Similarity Indexes Based on Local Information Common neighbors (CN) are the simplest but only consider the nearest neighbors among the local similarity indices. For example, the basic idea of CN is that it may be more likely that two people know each other if they have one or more acquaintances in common in a social network. In the definition of similarity indices, Γ(x) and Γ(y) represents the set of neighbors of node x and y respectively. Therefore, Γ(x) Γ(y) represent the common neighbors of node x and y. A larger similarity S xy between x and y indicates that they are more likely by an edge. The definition of ten kinds of similarity index based on local information of nodes is elaborated from different perspectives in Table Similarity Index Based Path Local Path Index The advantage of similarity index based on common neighbor is low computational complexity, but the prediction accuracy is limited due to the lack of information. On the basis of the common neighbor, LP concerned the set of paths with length 2 and 3 connecting two nodes, where α is a free parameter that controls all the length-3 paths. The similarity matrix S in LP is given as follows: S = A 2 + αa 3. (9)

9 454 YAO H X, LU Y X. Here A is adjacency matrix. Followed by [27], we set α = 0.01 in order to obtain a near optimal prediction accuracy. The number of local paths among various stocks is obtained. Moreover, when the path of the two nodes is shorter, the higher the score, the nodes are more likely to be connected with each other. Table 3 10 similarity indices based on local information of nodes Names Definition Katz Index Common neighbors (CN) Salaton Index (SA) S xy = Γ(x) Γ(y) S xy = Γ(x) Γ(y) k(x) k(y) Jaccard Index (JA) S xy = Γ(x) Γ(y) Γ(x) Γ(y) Sorenson Index (SO) S xy = 2 Γ(x) Γ(y) k(x)+k(y) Adamic-Adar IndexAA S xy = 1 lg k(z) z Γ(x) Γ(y) Hub Depressed Index (HDI) S xy = Γ(x) Γ(y) max{k(x)+k(y)} Hub promoted Index (HPI) S xy = Γ(x) Γ(y) min{k(x)+k(y)} Preferential Attachmet Index (PA) S xy = k(x) k(y) Resource Allocation Index (RA) S xy = Leicht-Holme-Newman Index (LHN1) 1 k(z) z Γ(x) Γ(y) S xy = Γ(x) Γ(y) k(x) k(y) Katz index considers the number of all paths in the network, and for the short path to give greater weight, while the long path to give smaller weights. The weight of the path length is exponential decay, and its mathematical expression as: S = βa + βa 2 + βa 3 + = (I βa) 1 I. (10) Here, β is the free parameter to adjust the weight of the path, and the value should be less than the reciprocal of the maximum eigenvalue of the adjacency matrix A. 5 Experimental Analyze In this paper, we study the accuracy of the similarity index by SSE 180 stocks and find potential influence stocks. 5.1 The Accuracy of the Similarity of Local Information and Path Under Different Proportion of Training Set The AUC as measured by local information and path similarity analysis of indicators were used to investigate the accuracy of various similarity index stock market and potential influence on the stock market network in different training set. As shown in Figure 4, with the increase in the proportion of the training set, the accuracy of the various indicators is in constant improvement. When the training set is 80% by Figure 4(a)(b), the similarity index of resource allocation (RA) is the best. However, in Figure 4(b), when the training set is relatively small,

10 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 455 the similarity index of the PA is the best. So, under different training sets, the accuracy of the similarity indicators is in constant change. We found that the accuracy of the Katz index is higher than the LP index in Figure 4(c). It can be found that when the training set is more than 80%, the accuracy of all kinds of indicators is basically the same Precision PA RA CN AA JA Precision PA RA CN AA JA (a) Proportion of training set (b) Proportion of training set Precision Katz LP (C) Proportion of training set Precision Katz LP (d) Proportion of training set Figure 4 Comparison of similar accuracy of each index in different training sets Table 4 Comparison of prediction accuracy of similarity index of local information based on AUC AUC Net1 Net2 Net3 Net3 Net4 Net5 Net6 Net7 CN JA SO LHN HPI HDI PA AA SA RA

11 456 YAO H X, LU Y X. 5.2 The Accuracy of Similarity Index in Stock Market Under Different Thresholds However, the threshold values were 0.8, 0.89, 1, 1.02, 1.04 and 1.06, respectively, corresponding to the network 1, network 2, network 3, network 4, network 5 and network 6. When the training set is 80%, the accuracy of the similarity of each index in the stock networks is evaluated by AUC in Table 4. The SSE 180 stock network market for τ = 0.89, the number of nodes is 180, the link number in the stock network market calculated by 180 (180 1) /2= The 272 connecting edges can be observed and there is no link in the remaining The third part of this paper mainly discussed the different values of the threshold, the potential influence of various sectors of the stock can be discovered. We also found that the non-ferrous metal stocks are the most potential influence on stock and only 25 potential influential stocks market analyze called network 7. This network consists of 25 nodes; therefore the number of possible link is 300. Here 31 connections edges of the network can be observed and the rest of the 269 are non-existing links. In order to ensure the accuracy of the test algorithm, we divided the edges, which accounted for 80% of the training set and test set for 20% (n=10000). We obtained Table 4 with the indexes of table 3 by AUC evaluation. We conclude that the accuracy of similarity of the RA index is the highest in the local information. 5.3 Evaluate the Influence Ability of the Stock Market Ranked by RA Similarity Indices Through the analysis of the experimental data of different networks, it is found that the resource allocation index (RA) in the stock market is the most accurate. The analysis correlation connection strength by the price fluctuation of stock network market overlooked weak correlation. Through comparing the accuracy of similarity index, RA index is much higher than others. The accuracy of each similarity index is also constant change in the different period of different networks, so we infer the mechanism of evolution through comparing the various performance indexes. On the basis of comparative analysis of the impact of different thresholds on the SSE 180 stocks, we find out 25 potential influence stocks and build the potential impact stock market for τ = 0.89 in Table 4. The results show index is the most suitable for the network in different networks through the comparison of the accuracy of the prediction of each index. Thanks to the most accuracy of RA similarity indices in the local information similarity, it can get the score to judge the possibility of the connection between nodes in Figure 5. The common neighbors of Baoshan Iron and Steel (sh600019) node and YZC (sh600188) stock node is HK (sh601088), the Western Mining (sh601168) and Chalco (sh601600) and their degrees respectively as 8, 11, 7 in Figure 5. Thus S RA = 1/8+1/11+1/7 = is obtained. Similarly, the RA similar value of stock nodes of Baoshan Iron and Steel (sh600019) and YOUNGOR (sh600177) is S RA = 1/11 = According to the prediction method of RA similarity, the possibility of the connection between Baoshan Iron and Steel (sh600019) and YZC (sh600188) is greater than the possibility of the connection between Baoshan Iron and Steel (sh600019) and the YOUNGOR (sh600177).

12 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 457 Figure 5 Potential impact of the stock market Figure 6 Comparison of path prediction accuracy based on AUC for evaluation criteria

13 458 YAO H X, LU Y X. Figure 7 The possibility of connection between various types of shares through the RA index 5.4 Favorable Path Similarity Index in Stock Market Under Different Time It is mainly about the analysis of the prediction accuracy of the path similarity index in the network 7 in Figure 6. The experimental data show that the adjustable parameters of LP, LP1 and LP2 are 0.01, 0.05 and 0.1. In each year LP, LP1, LP2, Katz the size of the basic fluctuations have the same direction and size. Comparing the accuracy of the prediction results of LP index and Katz index with the pure local information index (such as RA), it is found that the accuracy of LP index and Katz index is higher than that of RA in 2012, 2013, The accuracy of LP index and Katz index is more than 0.95, while the RA index is between , and the gap is very big from 2013 to The accuracy of RA index is higher than the LP and Katz index in the old years, which shows that the best indicators used network in different time are constantly changing. But they basically show the trend of change is consistent and the accuracy of the gap is very little, AUC as the evaluation criteria can reach more than In Table 4, it is found that the accuracy of all kinds of indexes in different network RA index is more than 0.95, which indicates that the stock market is also more and more perfect. Combining Figure 6 with Table 4, as time goes on, the accuracy of the similarity index of potential impact stock market is also in the continuous improvement. This indicates that the potential impact of the stock market is also in constant enhancement in the stock market. 5.5 Experimental Analysis Based on RA and Katz Indices We can find that the RA value is relatively large in finance, non-ferrous metals and energy class in Figure 7. Financial stocks are mainly concentrated in the financial and energy stocks, RA value exists, and the RA of other module is almost 0. That means there is no connection. Non-ferrous metal stocks are mainly concentrated in the non-ferrous metals and energy stocks, RA value is there, and the RA of other modules is almost 0. That means there is no connection. Real estate stocks, Construction stocks and other class stocks are mainly connected with themselves. But the RA value of links between the other class stocks and financial, non-ferrous

14 Analyzing the Potential Influence of Shanghai Stock Market Based on Link Prediction Method 459 metals, construction and energy stocks is very small and can be neglected. Energy stocks are connected with financial, non-ferrous metals and themselves. RA stocks sh sh sh sh Figure 8 The possibility of connection between various types of shares through the RA index In this paper, we use Matlab to calculate the eigenvalues of the adjacency matrix A, and the maximum eigenvalue is approximately equal to (β = 0.05). By the Katz index to calculate the score of the path between the various stocks, we can rank nodes in the next moment. This implies the possibility that the nodes are connected to each other. We find that the connectivity possibility of potential impact stock is very small in the overall stock market. The above shows that the influence of non-ferrous metals is great. We mainly discuss the great potential impact of non-ferrous metals stocks. The potential impact stocks in non-ferrous metals with 58 stocks are relatively small, but the fraction of the connection with the rest of the 122 stocks is smaller, which is almost negligible in Figure 8. In the next moment, the potential influence stocks in non-ferrous metal have connection with others. The potential influence stocks, Western Mining (sh601168), Chalco (sh601600), Gold Molybdenum Shares (sh601958) and Jiangxi Copper (sh600362), which belong to non-ferrous metal, have connection with other non-ferrous metal stocks and connectivity is bigger than the others. They have connection with the energy stocks including Orchid Technology (sh600123), YZC (sh600188), Panjiang shares (sh600395), HK (sh601088), Lahn (sh601699), COSL (sh601808) and CNPC (sh601857) and the connectivity is relatively large. The connectivity between them and Finance of Bank of communications (sh601328), China

15 460 YAO H X, LU Y X. Construction Bank (sh601939) and the CPIC (sh601601) is slightly larger. Through a series of analysis, we find their links obvious modular model at the next moment, the modular model of links between them and energy is the most serious. 6 Conclusions In summary, we mainly study the influence of price fluctuation of SSE 180 stocks. When the threshold value is different, we use local structural centrality to identify the various sectors of the potential impact stocks and analyze. In this paper, when the threshold is in a certain range, we have concluded that the potential influence of the non-ferrous metal stocks is the strongest and tends to be stable among all the sectors. In the second part of this paper, we mainly analyze the potential impact of stock based on link prediction and discuss the potential impact of the stock through two aspects of the local information and path similarity. Comparing the various similarities of the potential impact stocks indicators with the SSE 180 stocks, we draw that the most reasonable measure of similarity which can used to predict the probability of the network connection, so as to achieve the effect of risk aversion. References [1] Huang W Q, Zhuang X T, Yao S. Study on dynamic evolution of Chinese stock association network. Journal of Systems Engineering, 2014, 2: 29. [2] Hu S, Yang H L, Cai B L, et al. Reseach on spatial economic sectors from a perspective of a complex network. Physica A, 2013, 392: [3] Freeman L C. Centrality in social networks conceptual clarification. Social Networks, , 1(3): [4] Sabidussi G. The centrality index of a graph. Psychometrika, 1996, 31(4): [5] Katz L. A new status index derived from socio metric analysis. Psychometrika, 1953, 18(1): [6] Si X J. Study on the importance of nodes in complex networks. Xi an Electronic and Science University, [7] Gao S, Ma J, Chen Z M, et al. Ranking the spreading ability of nodes in complex networks based on local structure. Physica A, 2014, 403: [8] Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439): [9] Albert R, Barabási A L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74: [10] Lancichinetti A, Fortunato S, Radicchi F. Benchmark graphs for testing community detection algorithms. Physical Review E, 2008, 78: [11] Hu W B, Peng C, Liang J, et al. Social network event detection method based on link prediction. Journal of Software, 2015, 9: [12] Liu J, Xu B M, Xu X, et al. A link prediction algorithm based on label propagation. Journal of Computational Science, 2016, 16: [13] Liben-Nowell D, Kleinberg J. The link-prediction problem for social networks. Journal of the American Society for Information Science and Technology, 2007, 58(7): [14] Liben-Nowell D, Kleinberg J. The linle-predication problem for social networks. Journal of the American Society for Information Science and Technology, 2007, 58: [15] Jaccard P. Etude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Societe Vaudoise des Science Naturelles, 1901, 37(1901): 547. [16] Adamic L A, Adar E. Friends and neighbors on the web. Social Networks, 2003, 25(3): [17] Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439): [18] Sarukkai R R. Link prediction and path analysis using Markov chains. Computer Networks, 2000, 33(1):

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