Trade subject indirect interaction relationship analysis method based on medium subgraph

Abstract

The invention discloses a medium subgraph-based trade subject indirect interaction relationship analysis method, which comprises the following steps of: constructing a trade logistics weighted directed graph in combination with a trade database and a logistics transportation record, converting the trade logistics weighted directed graph into a trade logistics weighted undirected graph or a trade logistics weighted undirected graph, extracting a medium subgraph from the trade logistics weighted undirected graph or the trade logistics weighted undirected graph or the trade logistics weighted undirected graph or the trade logistics weighted undirected graph, and extracting the medium subgraph from the trade logistics weighted undirected graph or the trade logistics weighted undirected graph; the method comprises the steps of obtaining a medium sub-graph total set, traversing and calculating generalized competition and homogeneous function relation strength of each medium sub-graph in the medium sub-graph total set, constructing a strength threshold value, performing normalization processing on the generalized competition and homogeneous function relation strength of each medium sub-graph, and performing comparison to obtain a coexistence association mode. According to the mode and the strength, two visualization tools of the node and the node pair space and the generalized competition homogeneous function space are constructed. The method can effectively reveal the implicit indirect relationship between the trade subjects, quantitatively analyze the relationship strength, identify the coexistence association mode, and provide support for the structure analysis and strategy optimization of the trade logistics network.

Description

Technical Field

[0001] The present invention relates to the field of trade logistics network analysis, and particularly to a method for analyzing the indirect interaction relationship of trade entities based on a mediator subgraph. Background Art

[0002] In the analysis of the trade logistics network TLNS, revealing the indirect interaction relationship between trade entities is of great significance for understanding the network structure and optimizing resource allocation. Traditional research has mainly focused on the direct relationship between nodes, such as bilateral trade flows, but lacks a systematic analysis of the indirect relationship formed through mediator nodes. In the prior art, there is no extraction method for indirect relationships based on network subgraphs, making it difficult to comprehensively depict the generalized competition relationship among trade entities due to sharing mediator nodes.

[0003] In addition, the existing methods do not consider the relative importance of the interaction between nodes, lack a means of quantifying the strength of indirect relationships and a recognition framework for coexistence association patterns, resulting in the inability to deeply analyze the implicit interaction mechanism of trade entities in the network. In view of the above deficiencies, there is an urgent need for an analysis method that can effectively extract indirect relationships, quantify the relationship strength and identify the coexistence pattern of nodes, so as to fill the technical gap in the research of indirect relationships in the trade logistics network and provide theoretical support for trade strategy formulation and network optimization. Therefore, a method for analyzing the indirect interaction relationship of trade entities based on a mediator subgraph is proposed herein. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for analyzing the indirect interaction relationship of trade entities based on a mediator subgraph to solve the problems mentioned in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solutions: A method for analyzing the indirect interaction relationship of trade entities based on a mediator subgraph, comprising the following steps: S1. Combining a trade database and logistics transportation records, constructing a weighted directed graph of trade logistics, and converting the weighted directed graph of trade logistics into a weighted undirected graph or a weighted one-way graph of trade logistics according to the research strategy; S2. Performing mediator subgraph extraction processing on the weighted undirected graph or the weighted one-way graph of trade logistics to obtain a total set of mediator subgraphs; S3. Traversing each mediator subgraph in the total set of mediator subgraphs, and calculating the strength of the generalized competition relationship and the strength of the homogeneous function relationship corresponding to each mediator subgraph; S4. Construct the intensity thresholds of the generalized competition relationship and the intensity threshold of the homogeneous functional relationship, normalize the intensity of the generalized competition relationship and the intensity of the homogeneous functional relationship corresponding to each media subgraph respectively, and compare the intensity of the generalized competition relationship and the intensity of the homogeneous functional relationship corresponding to each normalized media subgraph with their respective intensity thresholds to obtain the coexistence association pattern corresponding to each media subgraph; S5. Construct the node-to-node pair space and the generalized competition homogeneous functional space for the total set of media subgraphs according to the coexistence association pattern, the intensity of the generalized competition relationship, and the intensity of the homogeneous functional relationship corresponding to each media subgraph.

[0006] Preferably, the method for constructing the trade logistics weighted directed graph by combining the trade database and the logistics transportation records: Extract the bilateral trade flows and bilateral trade volumes between each trading entity in the trade database and the logistics transportation records, and use each trading entity including regions, enterprises, cities, and ports as nodes , Number the nodes, and each trading entity has a unique node number , construct a directed edge connection from node to node to connect the trading entities that are used as nodes. The directed edge includes and , indicates that the trade flow between node and node is from node to node , indicates that the trade flow between node and node is from node to node . The direction of the directed edge strictly follows the trade flow, and use the bilateral trade volume between each trading entity as the edge weight. The edge weight includes and , indicates the magnitude of the trade volume from node to node , indicates the magnitude of the trade volume from node to node . Mark the corresponding edge weight for the directed edge to obtain the trade logistics weighted directed graph , is the node set composed of all nodes in the trade logistics weighted directed graph , including each trading entity, is the edge set composed of all directed edges in the weighted directed graph of trade logistics, including the trade flow directions and connections between various trade entities. is which includes the edge weight set corresponding to all directed edges in the weighted directed graph of trade logistics, where is the directed edge corresponding edge weight.

[0007] Preferably, the method of converting the weighted directed graph of trade logistics into a weighted undirected graph or a weighted unidirectional graph of trade logistics according to the research strategy: If the research strategy is an undirected strategy, then the weighted directed graph of trade logistics is converted into a weighted undirected graph of trade logistics and traverse each node pair in the weighted directed graph of trade logistics The nodes and satisfy and For each node pair among the two nodes and the existing directed edges and corresponding edge weights and are calculated through the combined two-way edge weight formula to obtain the undirected edge weight corresponding to each node pair Delete the two nodes among each node pair and in the weighted directed graph of trade logistics and existing directed edges, and replace them with an undirected edge corresponding to the two-way interaction of the node pair and mark the corresponding undirected edge weight is the total interaction volume of the node pair Based on this, the weighted undirected graph of trade logistics is obtained. is the in the weighted directed graph of trade logistics and remains unchanged. is the set of all undirected edges in the weighted undirected graph of trade logistics. is the set of undirected edge weights corresponding to all undirected edges in the weighted undirected graph of trade logistics; The calculation of the combined two-way edge weight formula is: Among them, is the weight of the undirected edge ; and respectively represent the magnitude of the trade volume from node to node and the magnitude of the trade volume from node to node ; If the research strategy is a unidirectional strategy, then the weighted directed graph of trade logistics is transformed into a weighted unidirectional graph of trade logistics . Traverse each node pair in the weighted directed graph of trade logistics . Nodes and satisfy and . For each node pair among the two nodes and with existing directed edges and , the corresponding edge weights and are calculated through the flow asymmetry index formula to obtain the normalized difference of the two-way flow symmetry for each node pair ; The result interval is . The closer the value is to 1, the more the trade volume between nodes and tends to be in the same direction as ; The closer it is to , the more the trade volume between nodes and tends to be in the same direction as ; The closer it is to 0, it indicates that the magnitudes of the trade volume between nodes and in the direction and direction are closer; Select each node pair with a normalized difference in two-way flow symmetry less than 0.5 and greater than -0.5 and without a single directionality. Delete the two nodes in each node pair and with existing directed edges and , meanwhile, screen node pairs with a single directionality where the normalized difference in the symmetry of each two-way traffic is less than or equal to 0.5 or greater than or equal to -0.5 , for each node pair with a single directionality among the two nodes and the existing directed edges and the corresponding edge weights and are calculated through the traffic difference formula between node pairs to obtain the unidirectional edge weight corresponding to each node pair with a single directionality , reflecting the magnitude of the net trade volume in the dominant direction of the two nodes , delete the existing directed edges and among the two nodes in each node pair with a single directionality in the trade logistics weighted directed graph and replace them with a single unidirectional edge and or and , and label the corresponding unidirectional edge weight or , to obtain the trade logistics weighted unidirectional graph , , is the trade logistics weighted directed graph among , remain unchanged, is the set of all unidirectional edges in the trade logistics weighted unidirectional graph, is the set of unidirectional edge weights corresponding to all unidirectional edges in the trade logistics weighted unidirectional graph; The formula for the traffic asymmetry index is: ; where is the normalized difference in the symmetry of two-way traffic, and respectively represent the magnitude of the trade volume from node to node and the magnitude of the trade volume from node to node ; The formula for the traffic difference between node pairs is: ; where and respectively represent the magnitude of the trade volume from node to node and the magnitude of the trade volume from node to node The size of the trade volume, and respectively represent the net trade volume size from node to node and the net trade volume size from node to node ; The undirected strategy does not distinguish the direction of edges and emphasizes the total interaction scale between nodes; The unidirectional strategy analyzes the inflow and outflow of nodes.

[0008] Preferably, the method for extracting the mediation subgraph set from the trade logistics weighted undirected graph includes the following steps: S011. Screen nodes with a node degree greater than or equal to 2 from the trade logistics weighted undirected graph , that is, mediation points; S012. Extract the neighbor node set of the mediation points from the trade logistics weighted undirected graph , where represents the j-th neighbor node of , pair the neighbor nodes in the neighbor node set to obtain mediation-related node pairs , the number of mediation-related node pairs is , and accordingly construct the mediation-related node pair set ; S013. Combine each mediation-related node pair in the mediation-related node pair set with the mediation point respectively to form the mediation subgraph node set . At the same time, according to the mediation subgraph node set , extract two undirected edges corresponding to the mediation subgraph node set from the trade logistics weighted undirected graph and and the corresponding edge weights and to obtain the mediation subgraph edge set and the mediation subgraph edge weight set , and construct the mediation subgraph , is the l-th undirected mediation subgraph of the i-th mediation point, is the l-th subgraph node set of the i-th mediation point, is the l-th subgraph edge set of the i-th mediation point, is the l-th subgraph edge weight set of the i-th mediation point; S014. Traverse the weighted undirected graph of trade logistics for each intermediate point and repeat S011, S012, and S013 for each intermediate point in sequence to obtain all intermediate subgraphs corresponding to each intermediate point: , Let the set of subgraphs of the i-th intermediate point be denoted as, and merge all the intermediate subgraphs corresponding to all intermediate points to obtain the total set of intermediate subgraphs ; The intermediate subgraph includes an intermediate subgraph node set, an intermediate subgraph edge set, and an intermediate subgraph edge weight set. The intermediate subgraph node set includes intermediate points and intermediate-associated node pairs.

[0009] Preferably, the method for extracting intermediate subgraphs from the weighted unidirectional graph of trade logistics to obtain the total set of intermediate subgraphs includes the following steps: S021. Screen the nodes that connect two nodes as the starting point from the weighted unidirectional graph of trade logistics as intermediate points, that is, there exists such that and ; or the nodes that are connected by two nodes as the end point are used as intermediate points, that is, there exists such that and ; ; S022. Extract the set of neighbor nodes of the intermediate points from the weighted unidirectional graph of trade logistics , where ' represents the j-th neighbor node of . Combine the neighbor nodes in the set of neighbor nodes in pairs to obtain intermediate-associated node pairs . The number of intermediate-associated node pairs is ., is the out-degree or in-degree of node . Based on this, construct the set of intermediate-associated node pairs ; S023. Combine each intermediate-associated node pair in the set of intermediate-associated node pairs with the intermediate point respectively to form the intermediate subgraph node set . At the same time, according to the intermediate subgraph node set , extract two undirected edges and and the corresponding edge weights and from the weighted unidirectional graph of trade logistics , or two undirected edges and and the corresponding edge weights and , to obtain the edge set of the media point subgraph and the edge weight set of the media point subgraph , or and the edge weight set of the media point subgraph , construct the media subgraph , is the l - th undirected media subgraph of the i - th media point, is the node set of the l - th subgraph of the i - th media point, is the edge set of the l - th subgraph of the i - th media point, is the edge weight set of the l - th subgraph of the i - th media point; S024. Traverse each media point of the trade logistics weighted unidirectional graph ' , for each media point , repeat S021, S022, and S023 in sequence to obtain all the media subgraphs corresponding to each media point: , represents the subgraph set of the i - th media point. Merge all the media subgraphs corresponding to all media points to obtain the total media subgraph set .

[0010] Preferably, the method for calculating the generalized competition relationship strength and the homogeneous function relationship strength corresponding to each media subgraph: Calculating the generalized competition relationship strength corresponding to each media subgraph is used to quantify the competition strength of media - associated node pairs for media point resources. Based on the relative importance and similarity of the two nodes to the media point, calculating the homogeneous function relationship strength corresponding to each media subgraph is used to quantify the evaluation of the functional similarity of the media point to two associated nodes, based on the relative importance and similarity of the associated node pairs to the media point; For each media subgraph, calculate respectively through the comprehensive importance CI formula and the proportional similarity CS formula to obtain the comprehensive importance degree and the proportional similarity degree of the generalized competition relationship in the media subgraph. Calculate the generalized competition relationship strength through the GCR strength formula using the comprehensive importance degree and the proportional similarity degree of the generalized competition relationship in the media subgraph; The comprehensive importance CI formula is: ; where, is the comprehensive importance degree of the generalized competition relationship in the media subgraph, and respectively represent and The edge weight of an arbitrary connecting edge, i is the number of the intermediate point, j and k are the numbers of the associated nodes of the intermediate point, and l is the serial number of the intermediate subgraph. and respectively represent and the total weight of all possible connecting edges. represents the type of the intermediate subgraph; The formula for the proportional similarity CS is: ; where is the degree of proportional similarity of the generalized competition relationship, and respectively represent and the edge weight of an arbitrary connecting edge, i is the number of the intermediate point, j and k are the numbers of the associated nodes of the intermediate point, and l is the serial number of the intermediate subgraph. and respectively represent and the total weight of all possible connecting edges. represents the type of the intermediate subgraph; The formula for the GCR strength is: ; where represents the strength of the generalized competition relationship of the intermediate subgraph, is the degree of proportional similarity of the generalized competition relationship, is the comprehensive importance degree of the generalized competition relationship in the intermediate subgraph; For each intermediate subgraph, the comprehensive importance degree of the homogeneous functional relationship and the proportional similarity degree of the homogeneous functional relationship in the intermediate subgraph are calculated respectively through the comprehensive importance HI formula and the proportional similarity HS formula, and the strength of the homogeneous functional relationship is calculated through the HFR strength formula; The formula for the comprehensive importance HI is: ; where is the comprehensive importance degree of the homogeneous functional relationship in the intermediate subgraph, and respectively represent and the edge weight of an arbitrary connecting edge, i is the number of the intermediate point, j and k are the numbers of the associated nodes of the intermediate point, and l is the serial number of the intermediate subgraph. represents the intermediate point the total weight of all possible connecting edges. represents the type of mediator sub - graph; The HS formula for the proportional similarity is as follows: ; Where, is the proportional similarity degree of the homogeneous functional relationship, and respectively represent and the edge weights of any one connection edge, i is the mediator point number, j and k are the associated node numbers of the mediator point, l is the mediator sub - graph serial number, represents the type of mediator sub - graph; The formula for the HFR intensity is as follows: ; Where, represents the homogeneous functional relationship intensity of the mediator sub - graph, is the proportional similarity degree of the homogeneous functional relationship, is the comprehensive importance degree of the homogeneous functional relationship in the mediator sub - graph.

[0011] Preferably, the method for constructing the generalized competition relationship intensity threshold and the homogeneous functional relationship intensity threshold: For each mediator sub - graph in the total set of mediator sub - graphs, the corresponding generalized competition relationship intensity and the homogeneous functional relationship intensity are respectively sorted in descending order, represents the generalized competition relationship intensity of the nth mediator sub - graph of the lth mediator point, represents the homogeneous functional relationship intensity of the nth mediator sub - graph of the lth mediator point, obtaining a descending sequence of generalized competition relationship intensity and a descending sequence of homogeneous functional relationship intensity; If the number of elements n in the descending sequences of generalized competition relationship and homogeneous functional relationship intensity is odd, then the generalized competition relationship intensity threshold is the mid - th generalized competition relationship intensity in the middle position of the descending sequence of generalized competition relationship intensity, and the homogeneous functional relationship intensity threshold is the mid - th homogeneous functional relationship intensity in the middle position of the descending sequence of homogeneous functional relationship intensity, and the value of mid is the value of (n + 1) / 2 rounded down; If the number of elements n in the descending sequences of generalized competition relationship and homogeneous functional relationship intensity is even, then the generalized competition relationship intensity threshold is the average value of the mid1 - th and mid2 - th generalized competition relationship intensities in the two middle positions of the descending sequence of generalized competition relationship intensity, and the homogeneous functional relationship intensity threshold is the average of the homogeneous functional relationship strengths at the two middle positions in the descending sequence of homogeneous functional relationship strengths, where the value of mid1 is n / 2 and mid2 is n / 2 + 1.

[0012] Preferably, the method for obtaining the coexistence association pattern corresponding to each medium subgraph: Calculate the generalized competition relationship strength and homogeneous functional relationship strength corresponding to each medium subgraph respectively through the normalization formula, so that the generalized competition relationship strength and homogeneous functional relationship strength corresponding to each medium subgraph are scaled to the interval [0, 1], and obtain the generalized competition relationship strength corresponding to each medium subgraph after normalization processing and homogeneous functional relationship strength ; Compare the generalized competition relationship strength and homogeneous functional relationship strength corresponding to each medium subgraph after normalization processing with their respective strength thresholds; If and , then the corresponding coexistence association pattern is a stable bidirectional dependence pattern; If and , then the corresponding coexistence association pattern is an associated node dominant pattern; If and , then the corresponding coexistence association pattern is a bidirectional independent edge pattern; If and , then the corresponding coexistence association pattern is a medium node monopoly pattern; The normalization formula is: ; Among them, is the value after normalization processing, is the maximum value, is the minimum value, is the value to be normalized.

[0013] Preferably, the method for constructing the node-to-node pair space and generalized competition homogeneous function space for the total set of medium subgraphs: For each mediator sub - graph in the total set of mediator sub - graphs, using the mediators in the mediator sub - graph node set of each mediator sub - graph as the abscissa and the mediator - related node pairs in the mediator sub - graph node set of each mediator sub - graph as the ordinate, each mediator sub - graph is mapped to a unique corresponding coordinate position on the rectangular coordinate system, and the corresponding co - existence association pattern, normalized generalized competition relationship strength, and homogeneous function relationship strength are marked at the coordinate position. Based on this, a node - to - node - pair space NNPS is constructed. The constructed node - to - node - pair space is a two - dimensional table, where the rows represent mediator - related node pairs, the columns represent mediators, and each cell corresponds to a mediator sub - graph, containing its relationship strength and pattern information, visually showing: the node pairs connected by mediators, the difference in relationship strength of different node pairs under the same mediator, and the distribution characteristics of the co - existence pattern in the dimension from mediator to node pair; For each mediator sub - graph in the total set of mediator sub - graphs, using the normalized generalized competition relationship strength corresponding to each mediator sub - graph as the abscissa and the normalized homogeneous function relationship strength corresponding to each mediator sub - graph as the ordinate, each mediator sub - graph is mapped to a unique corresponding coordinate position on the rectangular coordinate system. Based on this, a generalized competition - homogeneous function space CHS is constructed. The constructed generalized competition - homogeneous function space is a two - dimensional scatter plot. For the generalized competition - homogeneous function space, based on the generalized competition relationship strength threshold and the homogeneous function relationship strength threshold, the generalized competition - homogeneous function space can be divided into four sub - spaces: high - high, high - low, low - high, and low - low, representing 4 types of node co - existence association patterns. At the same time, for the generalized competition - homogeneous function space, the kernel density estimation method can be used to create a probability distribution map to analyze the overall distribution characteristics of mediator sub - graphs in the CHS; The kernel density estimation is a non - parametric estimation method used to estimate the probability density function of a random variable; The node - to - node - pair space and the generalized competition - homogeneous function space are visualization tools for the analysis and display of indirect relationships between nodes in the trade logistics network TLNS. The visualization tools refer to the probability distribution map, two - dimensional scatter plot, and two - dimensional table.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention constructs an indirect relationship analysis framework, filling a technical gap. Existing technologies mostly focus on the direct relationships between trading entities and lack a systematic analysis of indirect relationships formed through third - party mediators. The present invention introduces mediator sub - graphs as the smallest structural units, processes the original network through undirected or unidirectional strategies, systematically extracts the triple structures mediated by mediators, and for the first time constructs an extraction and analysis framework for indirect relationships in the trade logistics network, filling the technical gap in the research of indirect relationships. It can comprehensively reveal the generalized competition relationships and homogeneous function relationships generated by trading entities due to sharing mediators, and deepen the understanding of the implicit interaction mechanism of the network.

[0015] 2. The present invention proposes a method for measuring the strength of relationships based on relative importance, which differs from the limitations of existing technologies that rely on absolute values. By comprehensively evaluating importance and proportional similarity, combined with natural logarithm correction, it accurately quantifies the strength of indirect relationships. This method takes into account both local interactions and the overall network structure, considering the product of the relative importance of mediating nodes to associated nodes in generalized competition relationships, and evaluating the similarity of the functional contributions of associated nodes to mediating nodes in homogeneous functional relationships. It can more accurately reflect the actual dependence and functional associations between nodes, providing a more scientific quantification tool for complex network analysis.

[0016] 3. The present invention can identify co - existing association patterns and reveals deep - level interaction mechanisms. Based on the strong - weak combinations of generalized competition and homogeneous functional relationships, it first defines four co - existing association patterns, namely stable two - way dependence, associated - node dominance, two - way independent edge, and mediating - node monopoly. By using the median threshold to divide the pattern boundaries, it realizes the classification and identification of the dependence, dominance, edge, and monopoly relationships between nodes. This pattern framework goes beyond simple binary - relationship analysis and can reveal the role positioning of trading entities in the network, providing a new perspective for understanding the hierarchical structure and dynamic interactions of trade logistics networks.

[0017] 4. The present invention provides multi - dimensional visualization tools to support intuitive analysis and decision - making. It constructs two visualization strategies, NNPS and CHS. NNPS accurately locates the node composition, relationship strength, and patterns of each mediating sub - graph through a two - dimensional table, which is suitable for detailed analysis of small - scale networks. CHS shows the relationship strength distribution and pattern clustering through scatter plots and kernel density estimation, supporting the analysis of the macroscopic pattern of large - scale networks. The two tools complement each other, transforming abstract indirect relationships into intuitive visualization results, facilitating researchers and decision - makers to quickly identify key nodes, core relationships, and potential risks, and providing an efficient analysis means for formulating trade strategies and optimizing resource allocation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for description in the embodiments or the prior art. Obviously, the following - described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0019] Figure 1 It is the flowchart of the steps of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] To make the objectives, technical solutions, and advantages of the present invention more clear, the following will provide a detailed description of the technical solutions of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other implementation manners obtained by those of ordinary skill in the art without creative efforts belong to the scope protected by the present invention.

[0021] An embodiment is as follows Figure 1 As shown, a method for analyzing the indirect interaction relationship of trading entities based on a mediator subgraph includes the following steps: S001. Combine the trade database and logistics transportation records to construct a trade logistics weighted directed graph, and according to the research strategy, convert the trade logistics weighted directed graph into a trade logistics weighted undirected graph or a trade logistics weighted one-way graph; S002. Perform mediator subgraph extraction processing on the trade logistics weighted undirected graph or the trade logistics weighted one-way graph to obtain the total set of mediator subgraphs; S003. Traverse each mediator subgraph in the total set of mediator subgraphs, and calculate the generalized competition relationship strength and homogeneous function relationship strength corresponding to each mediator subgraph; S004. Construct a generalized competition relationship strength threshold and a homogeneous function relationship strength threshold, respectively perform normalization processing on the generalized competition relationship strength and the homogeneous function relationship strength corresponding to each mediator subgraph, and compare the normalized generalized competition relationship strength and homogeneous function relationship strength corresponding to each mediator subgraph with their respective strength thresholds to obtain the coexistence association pattern corresponding to each mediator subgraph; S5. According to the coexistence association pattern, generalized competition relationship strength, and homogeneous function relationship strength corresponding to each mediator subgraph, construct a node and node pair space and a generalized competition homogeneous function space for the total set of mediator subgraphs.

[0022] Furthermore, the working principle of the present invention is illustrated through the following embodiments: Assume taking the global major region crude oil trade data in 2023 as an example to elaborate the specific implementation process of the method of the present invention. The involved nodes include Region A , Region B , Region C , Region D and Region E .

[0023] Extract the bilateral trade flow and trade volume from the UN Comtrade database to construct a trade logistics weighted directed graph , where , contains , , etc., W includes , etc. For example, if Region A exports 1 million tons of crude oil to Region C, then the trade logistics weighted directed graph has a directed edge , and is 1 million, and if Region C exports 0 tons of crude oil to Region A, then the trade logistics weighted directed graph has a directed edge , and is 0; if Region B exports 500,000 tons of crude oil to Region C, then the trade logistics weighted directed graph has a directed edge , and is 500,000, and if Region C imports 100,000 tons of crude oil from Region B, then the trade logistics weighted directed graph has a directed edge , and is 100,000; taking the unidirectionalization strategy as an example, convert the trade logistics weighted directed graph into a trade logistics weighted unidirectional graph, calculate the flow asymmetry index, taking the node pair , as an example, is (100 - 0) / (100 + 0), that is, 1. Since is 1 which is greater than 0.5, retain the unidirectional edge , 's weight is 1 million tons, is (50 - 10) / (50 + 10), approximately 0.67. Since is 0.67 which is greater than 0.5, retain the unidirectional edge , 's weight is 400,000 tons. Accordingly, the trade logistics weighted unidirectional graph , includes , etc. unidirectional edges; Taking the undirected network as an example, assume that the Region C node of the trade logistics weighted unidirectional graph has neighbor nodes , and , and the node degree is 3 which is greater than 2, then determine as the intermediate point, , and the combined node pairs are , and , forming the intermediate association node pair set . Taking the node pair as an example, the node set , the edge set , the weight set , assume The weight is 600,000 tons, and based on this, a mediator subgraph is constructed.

[0024] Calculate the relationship strength for the mediator subgraph. For the generalized competition relationship GCR of the mediator subgraph, under the assumption The total trade volume is 1.5 million tons, Under the condition that the total trade volume is 1.1 million tons, it is approximately 0.36, it is approximately 0.82, is , approximately -1.22; for the homogeneous functional relationship HFR of the mediator subgraph, under the assumption Under the condition that the total trade volume is 2 million tons, it is 0.15, it is 0.75, is , approximately -2.10.

[0025] Assume that for all mediator subgraphs, the GCR strength range is [-2, 0], and the HFR strength range is [-3, -1]. Then, after normalization, it is 0.45, it is 0.39. Assume that if the generalized competition relationship strength threshold is 0.3 and the homogeneous functional relationship strength threshold is 0.4, then is greater than 0.4 and is greater than 0.3, and it is determined as a stable two-way dependence mode, that is, region A and region B form resource competition and functional dependence through region C.

[0026] Construct NNPS, with the horizontal axis being the mediator point , and the vertical axis being the node pair . Mark the GCR as 0.39 and the HFR as 0.45 for the coordinates , and the mode is stable two-way dependence; construct CHS, with the horizontal axis being the GCR value of 0.39 and the vertical axis being the HFR value of 0.45, falling into the first quadrant with high GCR and high HFR, corresponding to the stable two-way dependence mode. The probability density plot shows that the data points in this area are dense, indicating the importance of the oil transactions between region C and region A and between region B and region C for the crude oil market in region C.

[0027] ​The above embodiments strictly follow the logic of the claims, fully demonstrating the entire process from data modeling to pattern recognition, and reflecting the specific application and technical advantages of the present invention in the actual trade network. The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than limiting them; modifying the technical solutions recorded in the foregoing embodiments, or equivalently replacing some of the technical features therein, does not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application, and should all be included within the protection scope of the present application.

Claims

1. A method for analyzing the indirect interaction relationship of trading entities based on mediator subgraphs, characterized in that, It includes the following steps: S1. Combine the trade database and logistics transportation records to construct a weighted directed graph of trade logistics, and according to the research strategy, convert the weighted directed graph of trade logistics into a weighted undirected graph of trade logistics or a weighted unidirectional graph of trade logistics; S2. Perform media subgraph extraction processing on the weighted undirected graph of trade logistics or the weighted unidirectional graph of trade logistics to obtain the total set of media subgraphs; S3. Traverse each media subgraph in the total set of media subgraphs, and calculate the generalized competition relationship intensity and homogeneous function relationship intensity corresponding to each media subgraph; S4. Construct the generalized competition relationship intensity threshold and the homogeneous function relationship intensity threshold, respectively normalize the generalized competition relationship intensity and the homogeneous function relationship intensity corresponding to each media subgraph, and compare the normalized generalized competition relationship intensity and the homogeneous function relationship intensity corresponding to each media subgraph with their respective intensity thresholds to obtain the coexistence association pattern corresponding to each media subgraph; S5. According to the coexistence association pattern, generalized competition relationship intensity and homogeneous function relationship intensity corresponding to each media subgraph, construct a node and node pair space and a generalized competition homogeneous function space for the total set of media subgraphs.

2. The method for analyzing the indirect interaction relationship of trading entities based on a mediating subgraph according to claim 1, wherein The method of combining the trade database and logistics transportation records to construct a weighted directed graph of trade logistics: Extract the bilateral trade flows and bilateral trade volumes between various trading entities in the trade database and logistics records. Take each trading entity as a node, and based on the bilateral trade flows between the trading entities, construct directed edges to connect the trading entities as nodes, and use the bilateral trade volumes between the trading entities as the edge weights. Label the corresponding edge weights for the directed edges to obtain a weighted directed graph of trade logistics .

3. The method for analyzing the indirect interaction relationship of trading entities based on a mediating subgraph according to claim 2, wherein The method of converting the weighted directed graph of trade logistics into a weighted undirected graph of trade logistics or a weighted unidirectional graph of trade logistics according to the research strategy: If the research strategy is an undirected strategy, the weighted directed graph of trade logistics is transformed into a weighted undirected graph of trade logistics. Each node pair in the weighted directed graph of trade logistics is traversed, and for the edge weights corresponding to the directed edges existing between the two nodes in each node pair, they are calculated through the formula for combining two-way edge weights to obtain the undirected edge weights corresponding to each node pair. The directed edges existing between the two nodes in each node pair in the weighted directed graph of trade logistics are replaced with undirected edges, and the corresponding undirected edge weights are marked to obtain the weighted undirected graph of trade logistics ; If the research strategy is a unidirectional strategy, the trade logistics weighted directed graph is transformed into a trade logistics weighted unidirectional graph. Each node pair in the trade logistics weighted directed graph is traversed, and the edge weights corresponding to the directed edges existing between the two nodes in each node pair are calculated through the flow asymmetry index formula to obtain the normalized difference in the two-way flow symmetry of each node pair. Node pairs without a single directionality with a normalized difference in two-way flow symmetry less than 0.5 and greater than -0.5 are screened out, and the directed edges existing between the two nodes in each node pair without a single directionality are deleted from the trade logistics weighted directed graph. At the same time, node pairs with a single directionality with a normalized difference in two-way flow symmetry less than or equal to 0.5 or greater than or equal to -0.5 are screened out, and the edge weights corresponding to the directed edges existing between the two nodes in each node pair with a single directionality are calculated through the flow difference formula between node pairs to obtain the unidirectional edge weights corresponding to each node pair with a single directionality. The directed edges existing between the two nodes in each node pair with a single directionality in the trade logistics weighted directed graph are replaced with unidirectional edges, and the corresponding unidirectional edge weights are marked to obtain the trade logistics weighted unidirectional graph ; The undirected strategy does not distinguish the direction of the edges and emphasizes the total interaction scale between nodes; The unidirectional strategy is to analyze the inflow and outflow of nodes.

4. The method for analyzing the indirect interaction relationship of trading entities based on a mediating subgraph according to claim 3, wherein The method of performing media subgraph extraction processing on the weighted undirected graph of trade logistics to obtain the total set of media subgraphs includes the following steps: S011. Select nodes with a node degree greater than or equal to 2 from the weighted undirected graph of trade logistics , which are the intermediate points ; ​ S012. Extracting media points from the weighted undirected graph of trade logistics and the set of neighbor nodes thereof Pair up the neighbor nodes in the set of neighbor nodes to obtain media-related node pairs, and construct a set of media-related node pairs based on this ; S013. Combine each media-associated node pair in the set of media-associated node pairs with the media points respectively to form a set of media subgraph nodes . At the same time, according to the set of media subgraph nodes , extract the set of media subgraph edges and the set of media subgraph edge weights corresponding to the set of media subgraph nodes from the trade logistics weighted undirected graph to construct a media subgraph ; S014. Traverse each media point of the weighted undirected graph of trade logistics, and successively repeat S011, S012, and S013 for each media point to obtain all media subgraphs corresponding to each media point ; merge all the media subgraphs corresponding to all media points to obtain the total set of media subgraphs ; ; The media subgraph includes a media subgraph node set, a media subgraph edge set, and a media subgraph edge weight set. The media subgraph node set includes media points and media-associated node pairs.

5. The method for analyzing the indirect interaction relationship of trading entities based on a mediating subgraph according to claim 3, wherein The method of performing media subgraph extraction processing on the weighted unidirectional graph of trade logistics to obtain the total set of media subgraphs includes the following steps: S021. From the weighted unidirectional graph of trade logistics filter out the nodes that connect two nodes as the starting point or are connected by two nodes as the ending point , that is, the intermediate points ; S022. Extracting the intermediate points from the weighted unidirectional graph of trade logistics and the set of neighbor nodes thereof, combining the neighbor nodes in the set of neighbor nodes in pairs to obtain intermediate associated node pairs, and constructing a set of intermediate associated node pairs accordingly ; ; S023. Associating the media node pair set Each media-related node pair in is combined with the media point to form a media point subgraph node set At the same time, according to the set of intermediate point subgraph nodes , from the weighted one-way graph of trade logistics Extracting the set of nodes of the mediating subgraph The corresponding media point subgraph edge set and the set of edge weights of the intermediate point subgraph , construct the media subgraph ; S024. Traverse the weighted unidirectional graph of trade logistics For each media point, repeat S021, S022, and S023 in sequence for each media point to obtain all media subgraphs corresponding to each media point Merge all the media subgraphs corresponding to all media points to obtain the total set of media subgraphs .

6. The method for analyzing the indirect interaction relationship of trading entities based on a mediagraph according to claim 1, characterized in that, The method of calculating the generalized competition relationship intensity and the homogeneous function relationship intensity corresponding to each media subgraph: For each media subgraph, calculate through the comprehensive importance CI formula and the proportional similarity CS formula respectively to obtain the comprehensive importance degree of the generalized competition relationship and the proportional similarity degree of the generalized competition relationship in the media subgraph. Calculate the generalized competition relationship intensity obtained by the GCR intensity formula with the comprehensive importance degree of the generalized competition relationship and the proportional similarity degree of the generalized competition relationship in the media subgraph; For each media subgraph, calculate through the comprehensive importance HI formula and the proportional similarity HS formula respectively to obtain the comprehensive importance degree of the homogeneous function relationship and the proportional similarity degree of the homogeneous function relationship in the media subgraph. Calculate the homogeneous function relationship intensity obtained by the HFR intensity formula with the comprehensive importance degree of the homogeneous function relationship and the proportional similarity degree of the homogeneous function relationship in the media subgraph.

7. The analysis method of the indirect interaction relationship of trading entities based on the mediagraph according to claim 6, wherein The method of constructing the generalized competition relationship intensity threshold and the homogeneous function relationship intensity threshold: For each mediator subgraph in the total set of mediator subgraphs, sort all the generalized competition relationship strengths and all the homogeneous functional relationship strengths corresponding to the mediator subgraph in descending order to obtain a descending sequence of generalized competition relationship strengths and a descending sequence of homogeneous functional relationship strengths; If the number of elements in the descending order sequence of the generalized competition relationship and the homogeneous function relationship strength is odd, the generalized competition relationship strength threshold is the generalized competition relationship strength at the middle position in the descending order sequence of the generalized competition relationship strength, and the homogeneous function relationship strength threshold is the homogeneous function relationship strength at the middle position in the descending order sequence of the homogeneous function relationship strength; If the number of elements in the descending sequence of the generalized competition relationship and the homogeneous function relationship strength is even, the generalized competition relationship strength threshold is the average of the generalized competition relationship strengths at the two middle positions in the descending sequence of the generalized competition relationship strength, and the homogeneous function relationship strength threshold is the average of the homogeneous function relationship strengths at the two middle positions in the descending sequence of the homogeneous function relationship strength.

8. The method for analyzing the indirect interaction relationship of trading entities based on a mediagraph according to claim 7, wherein The method for obtaining the coexistence association pattern corresponding to each mediator subgraph: The generalized competition relationship strength and the homogeneous functional relationship strength corresponding to each media sub-graph are calculated respectively through a normalization formula, so that the generalized competition relationship strength and the homogeneous functional relationship strength corresponding to each media sub-graph are scaled to the interval [0, 1], and the generalized competition relationship strength corresponding to each media sub-graph after normalization is obtained and the homogeneous functional relationship strength ; Compare the generalized competition relationship strength corresponding to each normalized mediagraph and the homogeneous functional relationship strength with their respective strength thresholds respectively; If and , the corresponding coexistence association mode is a stable two-way dependence mode; If and , the corresponding coexistence association mode is the associated node dominant mode; If and , the corresponding coexistence association mode is a two-way independent edge mode; If and , the corresponding coexistence association mode is the media node monopoly mode.

9. The method for analyzing the indirect interaction relationship of trading entities based on a media subgraph according to claim 8, characterized in that, The method for constructing the node and node pair space and the generalized competition homogeneous function space for the total set of mediator subgraphs: For each mediator subgraph in the total set of mediator subgraphs, use the mediator points in the mediator subgraph node set of each mediator subgraph as the abscissa and the mediator association node pairs in the mediator subgraph node set of each mediator subgraph as the ordinate, map each mediator subgraph to the unique corresponding coordinate position on the rectangular coordinate system, and mark the corresponding coexistence association pattern, generalized competition relationship strength and homogeneous functional relationship strength at the coordinate position, and construct the node and node pair space accordingly; For each mediator subgraph in the total set of mediator subgraphs, use the generalized competition relationship strength corresponding to each mediator subgraph as the abscissa and the homogeneous functional relationship strength corresponding to each mediator subgraph as the ordinate, map each mediator subgraph to the unique corresponding coordinate position on the rectangular coordinate system, and construct the generalized competition homogeneous function space accordingly; The node and node pair space and the generalized competition homogeneous function space are visualization tools for the analysis and display of the indirect relationships between nodes in the trade logistics network TLNS.

Images