CN112991070A - Multi-layer stock right penetrating method for financial stock right knowledge large graph - Google Patents

Multi-layer stock right penetrating method for financial stock right knowledge large graph Download PDF

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CN112991070A
CN112991070A CN202110281306.9A CN202110281306A CN112991070A CN 112991070 A CN112991070 A CN 112991070A CN 202110281306 A CN202110281306 A CN 202110281306A CN 112991070 A CN112991070 A CN 112991070A
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洪亮
欧阳晓凤
陈昊冉
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Wuhan University WHU
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Abstract

The invention provides a multilayer equity penetration method of a financial equity knowledge map, which is characterized in that a penetration type multilayer equity network taking a given financial institution as a center is found out from the financial equity knowledge map; based on the sequence traversal, the central node gradually expands and calculates the maximum share holding ratio from each shareholder node to the central node and the number of layers of the path with the maximum share holding ratio, and the generation of the penetration type multilayer equity network is supported; and finally, calculating the final stock holding ratio from each stockholder node to the central node in the penetration type multilayer stock right network, and finding out the actual stock control stockholder of the central node. The invention can solve the calculation problem of the shortest path in the knowledge graph with the loop, is applied to the financial field, and efficiently and accurately supports the discovery of a penetration type multilayer equity network, a key equity path hierarchy and an actual stock holder in the equity network.

Description

Multi-layer stock right penetrating method for financial stock right knowledge large graph
Technical Field
The invention belongs to the field of computer algorithms, and particularly relates to a multi-layer equity penetration method for a financial equity knowledge large graph, which is applied to the field of finance.
Background
The financial stock right knowledge map is essentially a large-scale financial stock right knowledge map, contains a large amount of semantic information and knowledge association, and consists of associated nodes and edges. In the financial stock right knowledge map, each node represents a financial institution or a business entity, and each edge represents an holding or management relationship and the like between the entities. The equity network presents a complex equity structure with numerous shareholder sources and nested layer upon layer, the equity structure is an important characteristic in the financial field, a penetrating multilayer equity network can be efficiently found from the complex equity network, and the actual shareholder in the layer of the equity network is identified.
The stock right is the share of stock holding of the stockholder to the extent that the company can be controlled, and thus the right to the company for administration and control is obtained, and is divided into absolute stock holding, that is, the stock holding proportion exceeds 50%, and relative stock holding, that is, the stock holding proportion is less than 50%, but effective stock holding can be realized. Seemingly, the large stockholder has the rights of stock in the listed companies, but only one ring in the actual stockholder's stock-controlling link is affected by the actual stockholder. With the continuous development of enterprise grouping mode, the relationship between enterprises becomes more complex, actual stock control shareholders are hidden outside the shareholders layer by layer, and the high-level shareholding right structure has great risk. How to identify the actual stockholders hidden by enterprises by utilizing the multi-level complex equity network becomes the key of financial risk early warning.
At present, in order to calculate the final share holding ratio of an external shareholder to an enterprise and identify a hidden actual shareholder, the existing method mainly adopts a relational database such as MySQL to store data, and traverses a shareholder network by using a breadth-first search algorithm (BFS algorithm) until all leaf nodes are found, so as to form a final shareholder network subgraph. The shareholder network subgraph can be represented as a contiguous matrix, Briosci F et al propose an Integrated Ownership Share (IOS) model, determine the final Share holding ratio of any one shareholder to one financial institution or enterprise by back-pushing the Share holding ratio inwards through sparse matrix operation, calculate the value of the company of the group and the comprehensive Ownership Share held by the external shareholder by analyzing the equity network composed of legal independent companies with crossed shares, and demonstrate the link between the process of increasing risk capital and the separation of Ownership from the control of the business group. And determining the actual stock control shareholder according to the final stock holding ratio obtained by the IOS model.
At present, the work of discovering and analyzing financial risk structures from the perspective of knowledge association is lacked, and the full-scale equity network cannot be subjected to penetrating equity structure discovery. With the rapid increase of the number of enterprises, the constructed financial stock right knowledge large graph reaches hundred million scale, and the existing stock holding proportion calculation model has higher time complexity and is difficult to support the query and analysis of the large-scale financial stock right knowledge large graph. Therefore, the innovation points of the invention are as follows:
the financial institutions, the non-financial institutions and the stock right relationship among the financial institutions are uniformly organized and expressed into a financial stock right knowledge map based on knowledge association, and the problems discovered by key risk characteristic structures in the financial stock right network are converted into the knowledge association discovery problems in the financial stock right knowledge map.
The inquiry analysis algorithm with higher time efficiency is provided, the shareholder level and the final stock holding proportion of an enterprise can be determined through one-time traversal, actual stock control shareholders are identified, and penetrating multi-layer equity network inquiry and analysis among financial institutions in a million-level triple financial equity knowledge map is supported efficiently.
Disclosure of Invention
In view of the above, the technical problems to be solved by the present invention are: the method provides a complex traversal algorithm for incremental stock right calculation, can accurately and efficiently find out a penetrating multilayer stock right network taking a given financial institution as a center in a financial stock right knowledge large graph, and identifies the actual stock control stockholder of a center node.
The technical scheme adopted by the invention for solving the technical problems is a multi-layer equity penetration method of a financial equity knowledge large graph, which is characterized by comprising the following steps of:
step 1: constructing a financial stock right knowledge big graph through a plurality of nodes, a plurality of edges and weights on the edges;
step 1, the financial stock right knowledge map is as follows:
G(V，E)
V＝{vi，i∈[1，K]}
Figure BDA0002978553950000021
wherein, V represents the node set in the financial stock right knowledge large graph, E represents the edge set in the financial stock right knowledge large graph, K represents the number of the nodes in the financial stock right knowledge large graph, i.e. | V | ═ K, V |, ViRepresenting the ith node in the financial stock right knowledge map, namely the ith financial industry entity, V represents the entity set of the financial industry, E represents the stock holding relationship among the nodes,
Figure BDA0002978553950000022
the method is characterized in that a shareholding relationship is formed between the ith node and the jth node in the financial stock right knowledge graph, namely the jth node holds the stock right of the ith node, the ith node and the jth node are adjacent nodes, and each edge is provided with a plurality of edges
Figure BDA0002978553950000023
The share ratio with an associated weight representing this edge is expressed as
Figure BDA0002978553950000024
Step 2: randomly selecting any one non-isolated node as a central node from the financial stock right knowledge map in the step 1, processing the central node in the financial stock right knowledge map in the step 1 through a breadth-first traversal algorithm to obtain a plurality of first-order neighbor nodes of the central node, and constructing a single-order penetration type multilayer stock right network according to the central node and the plurality of first-order neighbor nodes of the central node;
in step 2, any node is defined as: the ith central node, i.e. vi；
Step 2, a plurality of first-order neighbor node sets of the central node are defined as:
Figure BDA0002978553950000031
i∈[1，K]k represents the number of nodes in the financial stock right knowledge large graph;
the neighbor node in step 2 is defined as:
Figure BDA0002978553950000032
Figure BDA0002978553950000033
the jth neighbor node represents the ith central node, the neighbor node is in h order, h represents the ergodic hierarchy, and D represents the number of multi-order neighbor nodes of the ith central node;
step 2, the first-order neighbor node is expressed as:
Figure BDA0002978553950000034
a jth neighbor node representing an ith central node, the neighbor node being in a first order;
and step 3: in the single-order penetration type multilayer strand right network in the step 2, a strand holding path set of a central node and each first-order neighbor node is constructed, and the final strand holding proportion of each first-order neighbor node and the central node is calculated;
the single holding path in step 3 is represented as:
p＝<v0，v1，v2，…，vU>
wherein v is0Denotes the start of the path, and vUThe end point of the path is shown, and U represents the length of the path;
the product of the stock ratio on the path p is used as the stock ratio of the path:
Figure BDA0002978553950000035
step 3 the central node viWith each first-order neighbor node
Figure BDA0002978553950000036
The single holdup path of (A) may be expressed as
Figure BDA0002978553950000037
I.e. starting from
Figure BDA0002978553950000038
To the end point viA strand holding ratio of the path of (1)
Figure BDA0002978553950000039
Step 3 the central node viWith each first-order neighbor node
Figure BDA00029785539500000310
The set of holding paths is:
Figure BDA00029785539500000311
i∈[1，K]，j∈[1，D]
wherein K represents the number of nodes in the financial stock right knowledge graph, N is the number of paths between the central node and j first-order neighbor nodes of the central node,
Figure BDA00029785539500000312
a kth path representing the central node and the jth first-order neighbor node of the central node, k ∈ [1, N]，N≥1，
Figure BDA00029785539500000313
To represent
Figure BDA00029785539500000314
The share ratio of;
and 3, the final share holding ratio of the central node to the jth first-order neighbor node of the central node is as follows:
Figure BDA0002978553950000041
wherein the content of the first and second substances,
Figure BDA0002978553950000042
representing the share weight ratio of the kth path of the central node and the jth first-order neighbor node of the central node, wherein N is the jth first-order neighbor of the central node and the central nodeThe number of paths of the node;
and 4, step 4: in the single-order penetration type multilayer strand right network in the step 2, the converted strand right proportion of all strand holding paths from the neighbor node to the central node is calculated through the weight on the logarithm conversion side, namely the strand right proportion, and the minimum converted strand right proportion is selected as the first-order maximum strand holding path converted strand right proportion from the node to the central node;
the function of the weight on the converted edge described in step 4 is:
Figure BDA0002978553950000043
wherein
Figure BDA0002978553950000044
The weight of the representative edge is the stock holding ratio, and v isuIs a path
Figure BDA0002978553950000045
Any one of the nodes above;
in step 4, the conversion share right ratio of the single holding path from the neighbor node to the central node is as follows:
Figure BDA0002978553950000046
Figure BDA0002978553950000047
wherein U is the length of the path;
step 4, the first-order maximum holding path conversion share ratio calculation formula:
Figure BDA0002978553950000048
wherein the content of the first and second substances,
Figure BDA0002978553950000049
denoted as the kth path
Figure BDA00029785539500000410
The conversion stock ratio of (1);
and 5: taking the hop count of the path where the maximum share holding path conversion right proportion is positioned in the step 4 as the final level of the node
Figure BDA00029785539500000411
Obtaining each first-order neighbor node in the first-order traversal
Figure BDA00029785539500000412
With the central node viThe functional characteristics of (1);
in step 5, the traversal order is defined as h, and the current traversal is first order, so that h is 1, and the neighbor nodes are adjacent to each other
Figure BDA00029785539500000413
The final holding ratio of (2) is equal to the first-order final holding ratio, and the maximum holding path switching right ratio is equal to the first-order maximum holding path switching right ratio, so that:
Figure BDA0002978553950000051
the function characteristic of the step 5 is as follows:
Figure BDA0002978553950000052
wherein
Figure BDA0002978553950000053
Expressed as a ratio of the final stock holding,
Figure BDA0002978553950000054
expressed as the maximum holdup path switch equity proportion,
Figure BDA0002978553950000055
expressed as a final level;
step 6: taking the outermost node as a starting node of the next traversal, further searching the degree-of-entry adjacent node of the outermost node, and constructing a multi-order penetrating multilayer equity network;
the outermost node in step 6 is defined as:
Figure BDA0002978553950000056
representing a central node viAt the neighbor nodes of the h-1 level,
wherein h represents the current traversal order, and h is more than or equal to 2;
step 6 of outermost layer junction
Figure BDA0002978553950000057
Represented as
Figure BDA0002978553950000058
And 7: in the multi-order penetration type multilayer equity network in the step 6, calculating the final share holding proportion from each outermost node to the central node in the current penetration type multilayer equity network in sequence; the final share proportion of the current hierarchy from the outermost node to the central node is obtained by multiplying the share proportion from the outermost node to the out-degree neighbor node by the final share proportion of the previous hierarchy of the neighbor node, and the final share proportion of the outermost node is obtained by accumulating the final share proportions of all the hierarchies;
the outermost node in the step 7 is defined as:
Figure BDA0002978553950000059
Figure BDA00029785539500000510
the first neighbor node represents the ith central node, the neighbor node is in h order, h represents the ergodic hierarchy, and D represents the number of multi-order neighbor nodes of the ith central node;
and 7, defining the neighbor nodes of the outmost node out degree as:
Figure BDA00029785539500000511
Figure BDA00029785539500000512
d represents the number of multi-order neighbor nodes of the ith central node;
Figure BDA00029785539500000513
the z-th out-degree neighbor node of the jth h-order node representing the ith central node, wherein z belongs to [1, R ]]R represents the outermost node
Figure BDA00029785539500000514
The number of out-of-degree neighbor nodes;
the h-order final holding ratio of the central node and the jth h-order neighbor node of the central node in the step 7 is as follows:
Figure BDA0002978553950000061
wherein R is the outermost node
Figure BDA0002978553950000062
The number of out-of-degree neighbor nodes,
Figure BDA0002978553950000063
representing outermost nodes
Figure BDA0002978553950000064
From the z-th out-degree neighbor node to the central node viThe final holdup ratio in the h-1 pass,
Figure BDA0002978553950000065
then represents the outermost node
Figure BDA0002978553950000066
Hold its z thThe outgoing neighbor nodes hold the strand proportion;
the final stock holding proportion of the outermost layer node in the step 7 is equal to the sum of the final stock holding proportions of the hierarchies to which the same node of each hierarchy belongs, and the calculation formula is as follows:
Figure BDA0002978553950000067
wherein when the outermost nodes are in multiple levels, e.g. viTo vi，jWhen there are multiple paths, the layer sequence will be traversed for multiple times, i.e. the layer sequence will be traversed for multiple times
Figure BDA0002978553950000068
The nodes are also presented in the h-1 level, therefore, the final share ratio of the current level is calculated for the nodes, and the final share ratios of the nodes presented in a plurality of levels are accumulated to obtain the final share ratio of the nodes. H represents the order set that the jth neighbor node of the ith central node appears in different levels;
step 7, the final stock holding proportion aims at points without loops in the penetration type multilayer stock right network, and if points with loops are met, the step 8 is carried out only aiming at the points with loops;
and 8: in the multi-level penetrating multi-level equity network described in step 6, if the node is in the loop, the correction coefficient c needs to be calculated, and the node is calculated to the central node viMultiplying the share weight proportion of the share-holding path in the loop by a correction coefficient to obtain the share weight proportion of the loop node;
the loop node set in step 8 is defined as Vloop(vi) Nodes in a loop
Figure BDA0002978553950000069
j∈[1，D]D is the number of multi-order neighbor nodes of the ith central node,
Figure BDA00029785539500000610
indicating the presence of a central node viThe jth neighbor node of (a) and the node is in the loop;
the correction coefficient calculation formula in step 8 is:
Figure BDA00029785539500000611
wherein the content of the first and second substances,
Figure BDA00029785539500000612
the share ratio is expressed as the share ratio of the loop path, and the share ratio of the loop path is obtained only by multiplying the share ratio in the path containing the loop, namely the product of all side weights in the loop path, namely the share ratio of the loop path is divided by 1 to subtract the share ratio of the loop;
the final strand holding ratio calculation formula of the loop in the step 8 is as follows:
Figure BDA0002978553950000071
wherein the content of the first and second substances,
Figure BDA0002978553950000072
Figure BDA0002978553950000073
the z-th out-degree neighbor node of the j-th node in the loop representing the ith central node, M represents the number of nodes in the loop, and z belongs to [1, R ]]R represents the outermost node
Figure BDA0002978553950000074
The number of out-of-degree neighbor nodes;
and step 9: in the multi-level penetrative multi-tiered equity network described in step 7, the outermost node goes to the central node viCalculating the conversion share right proportion of the maximum holding path; then the minimum conversion share ratio is selected as the maximum share holding path from the node to the central node according to the conversion share holding ratio from the outermost node to the neighbor node and the maximum share holding path conversion share ratio of the neighbor nodeConverting the stock ratio by path;
the outermost layer of the nodes in step 9 are
Figure BDA0002978553950000075
The neighbor nodes of the outmost node out degree are defined as:
Figure BDA0002978553950000076
z∈[1，R]r represents the outermost node
Figure BDA0002978553950000077
The number of out-of-degree neighbor nodes;
the maximum holding path conversion share ratio calculation formula in step 9 is:
Figure BDA0002978553950000078
wherein the content of the first and second substances,
Figure BDA0002978553950000079
representing outermost nodes
Figure BDA00029785539500000710
Node of arrival-departure neighbor
Figure BDA00029785539500000711
The conversion holdup ratio of (1); wherein the outermost nodes
Figure BDA00029785539500000712
Because there are many routes between two nodes, it will appear in h-1 level too;
Figure BDA00029785539500000713
the maximum share holding path conversion share right proportion of the jth neighbor node representing the ith central node in the h-1 level;
step 10: converting the maximum holding path in the step 9 into the share right proportion
Figure BDA00029785539500000714
The hop count of the path is used as the final level of the node
Figure BDA00029785539500000715
Get each node
Figure BDA00029785539500000716
The functional characteristics of (1);
the nodes in step 10
Figure BDA00029785539500000717
Is characterized by the following function:
Figure BDA00029785539500000718
step 11: repeating the calling steps 6-10, and after each round of calling, h +1, stopping traversing until the current outermost node has no leaf node, so as to obtain a final penetration type multilayer equity network, wherein the final node with the largest stock holding proportion of the leaf nodes is the actual stock control shareholder of the central node;
the leaf node set at the outermost layer of the penetration type multi-layer equity network in the step 11 is represented as: vleaf(vi)；
Actual stockholder V set forth in step 11controlI.e. having the maximum final stock holding ratio
Figure BDA0002978553950000081
A node of (a);
wherein the maximum final stock holding ratio
Figure BDA0002978553950000082
The calculation formula of (2) is as follows:
Figure BDA0002978553950000083
wherein the content of the first and second substances,
Figure BDA0002978553950000084
represents the nodes in the outermost leaf node set, j belongs to [1, D ]]，
Figure BDA0002978553950000085
The j-th neighbor node of the ith central node is represented and is an outermost leaf node, and D is represented as the number of multi-order neighbor nodes of the ith central node;
compared with the prior art, the multi-layer equity penetration method based on the financial equity knowledge large graph disclosed by the invention has the following beneficial effects:
the method is characterized in that a knowledge map technology is adopted, the intricate and complex structural information and the rich semantic information in the financial industry are fused to generate a financial stock right knowledge map, and an efficient algorithm is provided for identifying the actual stock holder by combining the semantic information;
by adopting an optimization technology, the ratio of the hierarchy to the final stock holding can be determined only by one-time traversal in the query process, and the penetration of a common path with a loop is supported, so that the method has strong applicability;
the method has lower time complexity, the increase rate of the query time is obviously lower than that of the existing algorithm along with the increase of the number of the stock right query layers, and the method has stronger expandability, can support the query and analysis of the penetrating multilayer stock right network of the financial stock right knowledge big graph under the big data environment, and effectively identifies the actual stock holder.
Drawings
The accompanying drawings are included to provide an understanding of the present disclosure and are incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and together with the examples serve to explain the principles of the disclosure and not to limit the disclosure.
FIG. 1: is a flow chart of the method of the present invention.
FIG. 2: the financial equity knowledge provided for an embodiment of the present invention is illustrated schematically.
FIG. 3: the looped financial equity knowledge provided for an embodiment of the present invention is illustrated schematically.
Detailed Description
The invention is further illustrated with reference to the following specific examples and the accompanying figures 1-3.
The invention provides a multi-layer equity penetration method based on a financial equity knowledge large graph, which comprises the following steps as shown in figure 1:
step 1: constructing a financial stock right knowledge big graph through a plurality of nodes, a plurality of edges and weights on the edges;
step 1, the financial stock right knowledge map is as follows:
G(V，E)
V＝{vi，i∈[1，K]}
Figure BDA0002978553950000091
wherein V represents a set of nodes in the financial stock right knowledge map, E represents a set of edges in the financial stock right knowledge map, K-60,599,124 represents the number of nodes in the financial stock right knowledge map, i.e. | V | -K, ViRepresenting the ith node in the financial stock right knowledge map, namely the ith financial industry entity, V represents the entity set of the financial industry, E represents the stock holding relationship among the nodes,
Figure BDA0002978553950000092
the method is characterized in that a shareholding relationship is formed between the ith node and the jth node in the financial stock right knowledge graph, namely the jth node holds the stock right of the ith node, the ith node and the jth node are adjacent nodes, and each edge is provided with a plurality of edges
Figure BDA0002978553950000093
The share ratio with an associated weight representing this edge is expressed as
Figure BDA0002978553950000094
Step 2: randomly selecting any one non-isolated node as a central node from the financial stock right knowledge map in the step 1, processing the central node in the financial stock right knowledge map in the step 1 through a breadth-first traversal algorithm to obtain a plurality of first-order neighbor nodes of the central node, and constructing a single-order penetration type multilayer stock right network according to the central node and the plurality of first-order neighbor nodes of the central node;
in step 2, any node is defined as: the ith central node, i.e. vi；
Step 2, a plurality of first-order neighbor node sets of the central node are defined as: n is a radical of1(vi)，i∈[1，K]K represents the number of nodes in the financial stock right knowledge large graph, and K is 60,599,124;
the neighbor node in step 2 is defined as:
Figure BDA0002978553950000095
Figure BDA0002978553950000096
the jth neighbor node represents the ith central node, the neighbor node is in h order, h represents the ergodic hierarchy, and D represents the number of multi-order neighbor nodes of the ith central node;
step 2, the first-order neighbor node is expressed as:
Figure BDA0002978553950000097
a jth neighbor node representing an ith central node, the neighbor node being in a first order;
and step 3: in the single-order penetration type multilayer strand right network in the step 2, a strand holding path set of a central node and each first-order neighbor node is constructed, and the final strand holding proportion of each first-order neighbor node and the central node is calculated;
the single holding path in step 3 is represented as:
p＝<v0，v1，v2，…，vU>
wherein v is0Denotes the start of the path, and vUThe end point of the path is shown, and U represents the length of the path;
the product of the stock ratio on the path p is used as the stock ratio of the path:
Figure BDA0002978553950000101
step 3 the central node viWith each first-order neighbor node
Figure BDA0002978553950000102
The single holdup path of (A) may be expressed as
Figure BDA0002978553950000103
I.e. starting from
Figure BDA0002978553950000104
To the end point viA strand holding ratio of the path of (1)
Figure BDA0002978553950000105
Step 3 the central node viWith each first-order neighbor node
Figure BDA0002978553950000106
The set of holding paths is:
Figure BDA0002978553950000107
i∈[1，K]，j∈[1，D]
wherein K represents the number of nodes in the financial stock right knowledge graph, N is the number of paths between the central node and j first-order neighbor nodes of the central node,
Figure BDA0002978553950000108
a kth path representing the central node and the jth first-order neighbor node of the central node, k ∈ [1, N]，N≥1，
Figure BDA0002978553950000109
To represent
Figure BDA00029785539500001010
The share ratio of;
and 3, the final share holding ratio of the central node to the jth first-order neighbor node of the central node is as follows:
Figure BDA00029785539500001011
wherein the content of the first and second substances,
Figure BDA00029785539500001012
representing the share weight ratio of the kth path of the central node and the jth first-order neighbor node of the central node, wherein N is the number of paths of the central node and the jth first-order neighbor node of the central node;
and 4, step 4: in the single-order penetration type multilayer strand right network in the step 2, the converted strand right proportion of all strand holding paths from the neighbor node to the central node is calculated through the weight on the logarithm conversion side, namely the strand right proportion, and the minimum converted strand right proportion is selected as the first-order maximum strand holding path converted strand right proportion from the node to the central node;
the function of the weight on the converted edge described in step 4 is:
Figure BDA00029785539500001013
wherein
Figure BDA00029785539500001014
The weight of the representative edge is the stock holding ratio, and v isuIs a path
Figure BDA00029785539500001015
Any one of the nodes above;
in step 4, the conversion share right ratio of the single holding path from the neighbor node to the central node is as follows:
Figure BDA0002978553950000111
Figure BDA0002978553950000112
wherein U is the length of the path;
step 4, the first-order maximum holding path conversion share ratio calculation formula:
Figure BDA0002978553950000113
wherein the content of the first and second substances,
Figure BDA0002978553950000114
denoted as the kth path
Figure BDA0002978553950000115
The conversion stock ratio of (1);
and 5: taking the hop count of the path where the maximum share holding path conversion right proportion is positioned in the step 4 as the final level of the node
Figure BDA0002978553950000116
Obtaining each first-order neighbor node in the first-order traversal
Figure BDA0002978553950000117
With the central node viThe functional characteristics of (1);
in step 5, the traversal order is defined as h, and the current traversal is first order, so that h is 1, and the neighbor nodes are adjacent to each other
Figure BDA0002978553950000118
The final holding ratio of (2) is equal to the first-order final holding ratio, and the maximum holding path switching right ratio is equal to the first-order maximum holding path switching right ratio, so that:
Figure BDA0002978553950000119
the function characteristic of the step 5 is as follows:
Figure BDA00029785539500001110
wherein
Figure BDA00029785539500001111
Expressed as a ratio of the final stock holding,
Figure BDA00029785539500001112
expressed as the maximum holdup path switch equity proportion,
Figure BDA00029785539500001113
expressed as a final level;
step 6: taking the outermost node as a starting node of the next traversal, further searching the degree-of-entry adjacent node of the outermost node, and constructing a multi-order penetrating multilayer equity network;
the outermost node in step 6 is defined as:
Figure BDA00029785539500001114
representing a central node viAt the neighbor nodes of the h-1 level,
wherein h represents the current traversal order, and h is more than or equal to 2;
step 6 of outermost layer junction
Figure BDA00029785539500001115
Represented as
Figure BDA00029785539500001116
And 7: in the multi-order penetration type multilayer equity network in the step 6, calculating the final share holding proportion from each outermost node to the central node in the current penetration type multilayer equity network in sequence; the final share proportion of the current hierarchy from the outermost node to the central node is obtained by multiplying the share proportion from the outermost node to the out-degree neighbor node by the final share proportion of the previous hierarchy of the neighbor node, and the final share proportion of the outermost node is obtained by accumulating the final share proportions of all the hierarchies;
the outermost node in the step 7 is defined as:
Figure BDA0002978553950000121
j∈[1，D]，
Figure BDA0002978553950000122
the jth neighbor node represents the ith central node, the neighbor node is in h order, h represents the ergodic hierarchy, and D represents the number of multi-order neighbor nodes of the ith central node;
and 7, defining the neighbor nodes of the outmost node out degree as:
Figure BDA0002978553950000123
Figure BDA0002978553950000124
d represents the number of multi-order neighbor nodes of the ith central node;
Figure BDA0002978553950000125
the z-th out-degree neighbor node of the jth h-order node representing the ith central node, wherein z belongs to [1, R ]]R represents the outermost node
Figure BDA0002978553950000126
The number of out-of-degree neighbor nodes;
the h-order final holding ratio of the central node and the jth h-order neighbor node of the central node in the step 7 is as follows:
Figure BDA0002978553950000127
wherein R is the outermost node
Figure BDA0002978553950000128
The number of out-of-degree neighbor nodes,
Figure BDA0002978553950000129
representing outermost nodes
Figure BDA00029785539500001210
From the z-th out-degree neighbor node to the central node viThe final holdup ratio in the h-1 pass,
Figure BDA00029785539500001211
then represents the outermost node
Figure BDA00029785539500001212
Holding the share holding proportion of the z-th out-degree neighbor node;
the final stock holding proportion of the outermost layer node in the step 7 is equal to the sum of the final stock holding proportions of the hierarchies to which the same node of each hierarchy belongs, and the calculation formula is as follows:
Figure BDA00029785539500001213
wherein when the outermost nodes are in multiple levels, e.g. viTo vi，jWhen there are multiple paths, the layer sequence will be traversed for multiple times, i.e. the layer sequence will be traversed for multiple times
Figure BDA00029785539500001214
The nodes are also presented in the h-1 level, therefore, the final share ratio of the current level is calculated for the nodes, and the final share ratios of the nodes presented in a plurality of levels are accumulated to obtain the final share ratio of the nodes. H represents the order set that the jth neighbor node of the ith central node appears in different levels;
step 7, the final stock holding proportion aims at points without loops in the penetration type multilayer stock right network, and if points with loops are met, the step 8 is carried out only aiming at the points with loops;
and 8: the multi-stage penetrating multi-layer strand in step 6In the weight network, if the node is in the loop, the correction coefficient c needs to be calculated, and the node is calculated to the central node viMultiplying the share weight proportion of the share-holding path in the loop by a correction coefficient to obtain the share weight proportion of the loop node;
the loop node set in step 8 is defined as Vloop(vi) Nodes in a loop
Figure BDA0002978553950000131
j∈[1，D]D is the number of multi-order neighbor nodes of the ith central node,
Figure BDA0002978553950000132
indicating the presence of a central node viThe jth neighbor node of (a) and the node is in the loop;
the correction coefficient calculation formula in step 8 is:
Figure BDA0002978553950000133
wherein the content of the first and second substances,
Figure BDA0002978553950000134
the share ratio is expressed as the share ratio of the loop path, and the share ratio of the loop path is obtained only by multiplying the share ratio in the path containing the loop, namely the product of all side weights in the loop path, namely the share ratio of the loop path is divided by 1 to subtract the share ratio of the loop;
the final strand holding ratio calculation formula of the loop in the step 8 is as follows:
Figure BDA0002978553950000135
wherein the content of the first and second substances,
Figure BDA0002978553950000136
Figure BDA0002978553950000137
the z-th out-degree neighbor node of the j-th node in the loop representing the ith central node, M represents the number of nodes in the loop, and z belongs to [1, R ]]R represents the outermost node
Figure BDA0002978553950000138
The number of out-of-degree neighbor nodes;
and step 9: in the multi-level penetrative multi-tiered equity network described in step 7, the outermost node goes to the central node viCalculating the conversion share right proportion of the maximum holding path; selecting the minimum conversion share ratio as the maximum share path conversion share ratio from the node to the central node according to the conversion share ratio from the outermost node to the neighbor node and the maximum share path conversion share ratio of the neighbor node;
the outermost layer of the nodes in step 9 are
Figure BDA0002978553950000139
The neighbor nodes of the outmost node out degree are defined as:
Figure BDA00029785539500001310
z∈[1，R]r represents the outermost node
Figure BDA00029785539500001311
The number of out-of-degree neighbor nodes;
the maximum holding path conversion share ratio calculation formula in step 9 is:
Figure BDA0002978553950000141
wherein the content of the first and second substances,
Figure BDA0002978553950000142
representing outermost nodes
Figure BDA0002978553950000143
Node of arrival-departure neighbor
Figure BDA0002978553950000144
The conversion holdup ratio of (1); wherein the outermost nodes
Figure BDA0002978553950000145
Because there are many routes between two nodes, it will appear in h-1 level too;
Figure BDA0002978553950000146
the maximum share holding path conversion share right proportion of the jth neighbor node representing the ith central node in the h-1 level;
step 10: converting the maximum holding path in the step 9 into the share right proportion
Figure BDA0002978553950000147
The hop count of the path is used as the final level of the node
Figure BDA0002978553950000148
Get each node
Figure BDA0002978553950000149
The functional characteristics of (1);
the nodes in step 10
Figure BDA00029785539500001410
Is characterized by the following function:
Figure BDA00029785539500001411
step 11: repeating the calling steps 6-10, and after each round of calling, h +1, stopping traversing until the current outermost node has no leaf node, so as to obtain a final penetration type multilayer equity network, wherein the final node with the largest stock holding proportion of the leaf nodes is the actual stock control shareholder of the central node;
the leaf node set at the outermost layer of the penetration type multi-layer equity network in the step 11 is represented as: vleaf(vi)；
Actual stockholder V set forth in step 11controlI.e. having the maximum final stock holding ratio
Figure BDA00029785539500001412
A node of (a);
wherein the maximum final stock holding ratio
Figure BDA00029785539500001413
The calculation formula of (2) is as follows:
Figure BDA00029785539500001414
wherein the content of the first and second substances,
Figure BDA00029785539500001415
represents the nodes in the outermost leaf node set, j belongs to [1, D ]]，
Figure BDA00029785539500001416
And D represents the number of multi-order neighbor nodes of the ith central node.
The overall algorithm is as follows:
Figure BDA00029785539500001417
Figure BDA0002978553950000151
the specific embodiment is as follows:
as shown in the financial stock right knowledge graph of fig. 2, the edge in the graph is labeled as the stock holding relationship corresponding to the edge, and the lower part in the graph is the stock holding ratio of the edge and the weight after logarithmic conversion of the stock holding ratio. Selection of node v0As a central node. First, the final strand holding ratio, v, of a first-order adjacent node pair is calculated1As v0First order neighbor node of
Figure BDA0002978553950000161
Passing through the path
Figure BDA0002978553950000162
For v0Holding the strand in a ratio of
Figure BDA0002978553950000163
The conversion share ratio of the first-order maximum holding path is
Figure BDA0002978553950000164
Figure BDA0002978553950000165
For v0Has a final strand holding ratio of
Figure BDA0002978553950000166
Figure BDA0002978553950000167
v2As v0First order neighbor node of
Figure BDA0002978553950000168
Passing through the path
Figure BDA0002978553950000169
For v0Holding the strand in a ratio of
Figure BDA00029785539500001610
The conversion share ratio of the first-order maximum holding path is
Figure BDA00029785539500001611
Figure BDA00029785539500001612
For v0Has a final strand holding ratio of
Figure BDA00029785539500001613
v3As v0First order neighbor node of
Figure BDA00029785539500001614
Passing through the path
Figure BDA00029785539500001615
For v0Holding the strand in a ratio of
Figure BDA00029785539500001616
Figure BDA00029785539500001617
The conversion share ratio of the first-order maximum holding path is
Figure BDA00029785539500001618
Figure BDA00029785539500001619
For v0Has a final strand holding ratio of
Figure BDA00029785539500001620
Figure BDA00029785539500001621
Then, the higher-order neighbor node pairs v are calculated outwards layer by layer from the first-order adjacent nodes0And finally, the stock holding ratio is calculated until the outermost node, v, is calculated1As v0Second order neighbor node of
Figure BDA00029785539500001640
By passing
Figure BDA00029785539500001622
And
Figure BDA00029785539500001623
two path pair v0Holding strand, the holding strand ratio of the two paths is respectively
Figure BDA00029785539500001624
Figure BDA00029785539500001625
Figure BDA00029785539500001626
Convert the stock ratio to
Figure BDA00029785539500001627
Figure BDA00029785539500001628
The conversion share ratio of the second-order maximum share holding path is
Figure BDA00029785539500001629
Figure BDA00029785539500001630
Figure BDA00029785539500001631
Figure BDA00029785539500001632
The final strand holding ratio is
Figure BDA00029785539500001633
Figure BDA00029785539500001634
v1As v0Third order neighbor node of
Figure BDA00029785539500001635
By passing
Figure BDA00029785539500001636
And pair v0Holding the strand in a ratio of
Figure BDA00029785539500001637
Figure BDA00029785539500001638
Convert the equity proportion to
Figure BDA00029785539500001639
The conversion share ratio of the three-order maximum share holding path is
Figure BDA0002978553950000171
Figure BDA0002978553950000172
The final strand holding ratio is
Figure BDA0002978553950000173
Figure BDA0002978553950000174
Are all nodes v1At v0V in a different hierarchical neighbor node of1For v0Final strand holding ratio of
Figure BDA0002978553950000175
Figure BDA0002978553950000176
Transition holdup ratio of maximum holdup path
Figure BDA0002978553950000177
Hierarchy of maximum holdout paths
Figure BDA0002978553950000178
In the same way, v is calculated2、v3、v4For v0Is represented by the functional characteristics of (1), namely the final stock holding ratio, the conversion stock holding ratio of the maximum stock holding path and the maximum stock holding path level
Figure BDA0002978553950000179
Figure BDA00029785539500001710
Figure BDA00029785539500001711
Figure BDA00029785539500001712
The leaf node with the largest final holdup ratio is the central node v0Actual stockholder Vcontrol＝v4。
For the case of stock holding loop in the financial stock right knowledge map, node v is shown in FIG. 31As v0Neighbor nodes in a loop
Figure BDA00029785539500001713
In a loop<v1，v2，v1>In, Vloop(v0)＝{v1，v2}. Equity proportion of loop path
Figure BDA00029785539500001714
Calculating a correction factor for the loop
Figure BDA00029785539500001715
Node v1As a loop node
Figure BDA00029785539500001716
For v0Has a final strand holding ratio of
Figure BDA00029785539500001717
Figure BDA00029785539500001718
The multilayer equity penetration method in the financial equity knowledge map provided by the invention solves the problem of complex incremental equity calculation, is applied to the financial equity knowledge map, can discover a penetration type multilayer equity network from complex equity knowledge association, and identifies the actual stock control shareholder hidden behind the layer-upon-layer equity network.
The above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes and modifications made in accordance with the principles and concepts disclosed herein are intended to be included within the scope of the present invention.

Claims (10)

1. A multi-layer equity penetration method of a financial equity knowledge large map is characterized by comprising the following steps:
step 1: constructing a financial stock right knowledge big graph through a plurality of nodes, a plurality of edges and weights on the edges;
step 2: randomly selecting any one non-isolated node as a central node from the financial stock right knowledge map in the step 1, processing the central node in the financial stock right knowledge map in the step 1 through a breadth-first traversal algorithm to obtain a plurality of first-order neighbor nodes of the central node, and constructing a single-order penetration type multilayer stock right network according to the central node and the plurality of first-order neighbor nodes of the central node;
and step 3: in the single-order penetration type multilayer strand right network in the step 2, a strand holding path set of a central node and each first-order neighbor node is constructed, and the final strand holding proportion of each first-order neighbor node and the central node is calculated;
and 4, step 4: in the single-order penetration type multilayer strand right network in the step 2, the converted strand right proportion of all strand holding paths from the neighbor node to the central node is calculated through the weight on the logarithm conversion side, namely the strand right proportion, and the minimum converted strand right proportion is selected as the first-order maximum strand holding path converted strand right proportion from the node to the central node;
and 5: taking the hop count of the path where the maximum share holding path conversion right proportion is positioned in the step 4 as the final level of the node
Figure FDA0002978553940000011
Obtaining each first-order neighbor node in the first-order traversal
Figure FDA0002978553940000012
With the central node viThe functional characteristics of (1);
step 6: taking the outermost node as a starting node of the next traversal, further searching the degree-of-entry adjacent node of the outermost node, and constructing a multi-order penetrating multilayer equity network;
and 7: in the multi-order penetration type multilayer equity network in the step 6, calculating the final share holding proportion from each outermost node to the central node in the current penetration type multilayer equity network in sequence; the final share proportion of the current hierarchy from the outermost node to the central node is obtained by multiplying the share proportion from the outermost node to the out-degree neighbor node by the final share proportion of the previous hierarchy of the neighbor node, and the final share proportion of the outermost node is obtained by accumulating the final share proportions of all the hierarchies;
and 8: in the multi-level penetrating multi-level equity network described in step 6, if the node is in the loop, the correction coefficient c needs to be calculated, and the node is calculated to the central node viMultiplying the share weight proportion of the share-holding path in the loop by a correction coefficient to obtain the share weight proportion of the loop node;
and step 9: in the multi-level penetrative multi-tiered equity network described in step 7, the outermost node goes to the central node viCalculating the conversion share right proportion of the maximum holding path; selecting the minimum conversion share ratio as the maximum share path conversion share ratio from the node to the central node according to the conversion share ratio from the outermost node to the neighbor node and the maximum share path conversion share ratio of the neighbor node;
step 10: converting the maximum holding path in the step 9 into the share right proportion
Figure FDA0002978553940000021
The hop count of the path is used as the final level of the node
Figure FDA0002978553940000022
Get each node
Figure FDA0002978553940000023
The functional characteristics of (1);
step 11: and h is 2, repeating the calling steps 6-10, and after each round of calling, h +1, stopping traversing until the current outermost node has no leaf node, so as to obtain a final penetration type multilayer equity network, wherein the final node with the largest stock holding proportion of the leaf nodes is the actual stock control shareholder of the central node.
2. The multi-tiered equity penetration method of the knowledge map of financial equity as claimed in claim 1, wherein said knowledge map of financial equity in step 1 is:
G(V，E)
V＝{vi，i∈[1，K]}
Figure FDA0002978553940000024
wherein, V represents the node set in the financial stock right knowledge large graph, E represents the edge set in the financial stock right knowledge large graph, K represents the number of the nodes in the financial stock right knowledge large graph, i.e. | V | ═ K, V |, ViRepresenting the ith node in the financial stock right knowledge map, namely the ith financial industry entity, V represents the entity set of the financial industry, E represents the stock holding relationship among the nodes,
Figure FDA0002978553940000025
the method is characterized in that a shareholding relationship is formed between the ith node and the jth node in the financial stock right knowledge graph, namely the jth node holds the stock right of the ith node, the ith node and the jth node are adjacent nodes, and each edge is provided with a plurality of edges
Figure FDA0002978553940000026
The share ratio with an associated weight representing this edge is expressed as
Figure FDA0002978553940000027
3. The multi-tiered equity penetration method of the financial equity knowledge map as claimed in claim 1, wherein any one of the nodes in step 2 is defined as: the ith central node, i.e. vi；
Step 2, a plurality of first-order neighbor node sets of the central node are defined as:
Figure FDA0002978553940000028
k represents the number of nodes in the financial stock right knowledge large graph;
the neighbor node in step 2 is defined as:
Figure FDA0002978553940000029
Figure FDA00029785539400000210
the jth neighbor node represents the ith central node, the neighbor node is in h order, h represents the ergodic hierarchy, and D represents the number of multi-order neighbor nodes of the ith central node;
step 2, the first-order neighbor node is expressed as:
Figure FDA00029785539400000211
the jth neighbor node representing the ith central node, and this neighbor node being at first order.
4. The multi-tiered equity penetration method according to the financial equity knowledge map of claim 1, wherein said single holding path of step 3 is represented as:
p＝<v0，v1，v2，...，vU>
wherein v is0Denotes the start of the path, and vUThe end point of the path is shown, and U represents the length of the path;
the product of the stock ratio on the path p is used as the stock ratio of the path:
Figure FDA0002978553940000031
step 3 the central node viWith each first-order neighbor node
Figure FDA0002978553940000032
The single holdup path of (A) may be expressed as
Figure FDA0002978553940000033
I.e. starting from
Figure FDA0002978553940000034
To the end point viA strand holding ratio of the path of (1)
Figure FDA0002978553940000035
Step 3 the central node viWith each first-order neighbor node
Figure FDA0002978553940000036
The set of holding paths is:
Figure FDA0002978553940000037
wherein K represents the number of nodes in the financial stock right knowledge graph, N is the number of paths between the central node and j first-order neighbor nodes of the central node,
Figure FDA0002978553940000038
a kth path representing the central node and the jth first-order neighbor node of the central node, k ∈ [1, N]，N≥1，
Figure FDA0002978553940000039
To represent
Figure FDA00029785539400000310
The share ratio of;
and 3, the final share holding ratio of the central node to the jth first-order neighbor node of the central node is as follows:
Figure FDA00029785539400000311
wherein the content of the first and second substances,
Figure FDA00029785539400000312
and expressing the share weight ratio of the k path of the central node and the jth first-order neighbor node of the central node, wherein N is the number of the paths of the central node and the jth first-order neighbor node of the central node.
5. The multi-tiered equity penetration method of a financial equity knowledge map as claimed in claim 1, wherein said function of weight on the converted edges in step 4 is:
Figure FDA00029785539400000313
wherein
Figure FDA00029785539400000314
The weight of the representative edge is the stock holding ratio, and v isuIs a path
Figure FDA00029785539400000315
Any one of the nodes above;
in step 4, the conversion share right ratio of the single holding path from the neighbor node to the central node is as follows:
Figure FDA0002978553940000041
Figure FDA0002978553940000042
wherein U is the length of the path;
step 4, the first-order maximum holding path conversion share ratio calculation formula:
Figure FDA0002978553940000043
wherein the content of the first and second substances,
Figure FDA0002978553940000044
denoted as the kth path
Figure FDA0002978553940000045
Upper conversion stock ratio.
6. The multi-tiered shareholding traversal method for the financial equity knowledge large map as claimed in claim 1, wherein in step 5 we define the traversal order as h, and the current traversal is first order, so h is 1, and neighbor nodes are adjacent to each other
Figure FDA00029785539400000416
The final holding ratio of (2) is equal to the first-order final holding ratio, and the maximum holding path switching right ratio is equal to the first-order maximum holding path switching right ratio, so that:
Figure FDA0002978553940000046
the function characteristic of the step 5 is as follows:
Figure FDA0002978553940000047
wherein
Figure FDA0002978553940000048
Expressed as a ratio of the final stock holding,
Figure FDA0002978553940000049
expressed as the maximum holdup path switch equity proportion,
Figure FDA00029785539400000410
represented as the final hierarchy.
7. The multi-tiered equity penetration method of a financial equity knowledge map as claimed in claim 1, wherein said outermost nodes of step 6 are defined as:
Figure FDA00029785539400000411
representing a central node viAt the neighbor nodes of the h-1 level,
wherein h represents the current traversal order, and h is more than or equal to 2;
step 6 of outermost layer junction
Figure FDA00029785539400000412
Represented as
Figure FDA00029785539400000413
8. The multi-tiered equity penetration method of a financial equity knowledge map as claimed in claim 1, wherein said outermost nodes of step 7 are defined as:
Figure FDA00029785539400000414
Figure FDA00029785539400000415
a j-th neighbor node representing the ith central node, the neighbor node being in h order, h representing the traversedA hierarchy D representing the number of multi-order neighbor nodes of the ith central node;
and 7, defining the neighbor nodes of the outmost node out degree as:
Figure FDA0002978553940000051
Figure FDA0002978553940000052
d represents the number of multi-order neighbor nodes of the ith central node;
Figure FDA0002978553940000053
the z-th out-degree neighbor node of the jth h-order node representing the ith central node, wherein z belongs to [1, R ]]R represents the outermost node
Figure FDA0002978553940000054
The number of out-of-degree neighbor nodes;
the h-order final holding ratio of the central node and the jth h-order neighbor node of the central node in the step 7 is as follows:
Figure FDA0002978553940000055
wherein R is the outermost node
Figure FDA0002978553940000056
The number of out-of-degree neighbor nodes,
Figure FDA0002978553940000057
representing outermost nodes
Figure FDA0002978553940000058
From the z-th out-degree neighbor node to the central node viThe final holdup ratio in the h-1 pass,
Figure FDA0002978553940000059
then represents the outermost node
Figure FDA00029785539400000510
Holding the share holding proportion of the z-th out-degree neighbor node;
the final stock holding proportion of the outermost layer node in the step 7 is equal to the sum of the final stock holding proportions of the hierarchies to which the same node of each hierarchy belongs, and the calculation formula is as follows:
Figure FDA00029785539400000511
wherein when the outermost nodes are in multiple levels, e.g. viTo vi，jWhen there are multiple paths, the layer sequence will be traversed for multiple times, i.e. the layer sequence will be traversed for multiple times
Figure FDA00029785539400000512
The nodes also appear in the h-1 level, so that the final share proportion of the current level is calculated for the nodes, and the final share proportion of the nodes appearing in a plurality of levels is accumulated to obtain the final share proportion of the nodes; h represents the order set that the jth neighbor node of the ith central node appears in different levels;
the final stock holding ratio stated in step 7 is for the points without loop in the penetration multi-layer stock right network, if the points with loop are encountered, the step goes to step 8 only for the points with loop.
9. The multi-tiered equity penetration method of a financial equity knowledge map as claimed in claim 1, wherein said set of loop nodes of step 8 is defined as Vloop(vi) Nodes in a loop
Figure FDA00029785539400000513
j∈[1，D]D is the number of multi-order neighbor nodes of the ith central node,
Figure FDA00029785539400000514
indicating the presence of a central node viThe jth neighbor node of (a) and the node is in the loop;
the correction coefficient calculation formula in step 8 is:
Figure FDA0002978553940000061
wherein the content of the first and second substances,
Figure FDA0002978553940000062
the share ratio is expressed as the share ratio of the loop path, and the share ratio of the loop path is obtained only by multiplying the share ratio in the path containing the loop, namely the product of all side weights in the loop path, namely the share ratio of the loop path is divided by 1 to subtract the share ratio of the loop;
the final strand holding ratio calculation formula of the loop in the step 8 is as follows:
Figure FDA0002978553940000063
wherein the content of the first and second substances,
Figure FDA0002978553940000064
Figure FDA0002978553940000065
the z-th out-degree neighbor node of the j-th node in the loop representing the ith central node, M represents the number of nodes in the loop, and z belongs to [1, R ]]R represents the outermost node
Figure FDA0002978553940000066
The number of out-of-degree neighbor nodes.
10. The multi-tiered equity penetration method of a large knowledge map of financial equities as claimed in claim 1, wherein said step 9 is performed at mostThe outer layer node is
Figure FDA0002978553940000067
The neighbor nodes of the outmost node out degree are defined as:
Figure FDA0002978553940000068
z∈[1，R]r represents the outermost node
Figure FDA0002978553940000069
The number of out-of-degree neighbor nodes;
the maximum holding path conversion share ratio calculation formula in step 9 is:
Figure FDA00029785539400000610
wherein the content of the first and second substances,
Figure FDA00029785539400000611
representing outermost nodes
Figure FDA00029785539400000612
Node of arrival-departure neighbor
Figure FDA00029785539400000613
The conversion holdup ratio of (1); wherein the outermost nodes
Figure FDA00029785539400000614
Because there are many routes between two nodes, it will appear in h-1 level too;
Figure FDA00029785539400000615
the maximum share holding path conversion share right proportion of the jth neighbor node representing the ith central node in the h-1 level;
the nodes in step 10
Figure FDA00029785539400000616
Is characterized by the following function:
Figure FDA00029785539400000617
the leaf node set at the outermost layer of the penetration type multi-layer equity network in the step 11 is represented as: vleaf(vi)；
Actual stockholder V set forth in step 11controlI.e. having the maximum final stock holding ratio
Figure FDA00029785539400000618
A node of (a);
wherein the maximum final stock holding ratio
Figure FDA0002978553940000071
The calculation formula of (2) is as follows:
Figure FDA0002978553940000072
wherein the content of the first and second substances,
Figure FDA0002978553940000073
represents the nodes in the outermost leaf node set, j belongs to [1, D ]]，
Figure FDA0002978553940000074
Figure FDA0002978553940000075
And D represents the number of multi-order neighbor nodes of the ith central node.
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