Method for generating directed weighted network model based on triple reciprocity mechanism
By proposing a directed weighted network model generation method based on the triple reciprocity mechanism, the problem of the independence of edge direction and weight in existing technologies is solved, and the realism and robustness of the network structure are achieved. This method is applicable to network generation and security protection in fields such as social networks and financial transactions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF FINANCE & ECONOMICS
- Filing Date
- 2026-01-12
- Publication Date
- 2026-04-10
AI Technical Summary
Existing methods for generating directed weighted networks struggle to simultaneously model edge directionality, weights, and higher-order structural constraints, leading to inconsistencies between theory and practice and a lack of ability to preserve the structural properties of real networks.
A directed weighted network model generation method based on the triple reciprocity mechanism is adopted. By constructing a directed weighted network model that includes interactions between nodes, initializing parameters, and iteratively optimizing it using the EM algorithm, the expected weights of the connections between nodes are calculated by combining community affiliation and the conditional Poisson distribution of the triple reciprocity terms, thus generating a directed weighted network.
It effectively captures local reciprocity patterns and global ternary attributes, and the generated networks perform well in link prediction and infectious disease simulation. It provides network structure inference and completion support, and enhances the robustness and anti-propagation ability of the network, making it suitable for cybersecurity and public health security.
Smart Images
Figure CN121835938A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of directed weighted network model generation, and in particular to a directed weighted network model generation method based on a triad reciprocity mechanism. BACKGROUND
[0002] In complex system modeling, directed weighted networks are widely used to express the relationships between entities with directionality and strength, such as social influence propagation, neural signal conduction, and financial transactions. Traditional undirected or unweighted network models cannot accurately depict the structural characteristics of these real systems, especially in social networks, where relationships are often asymmetric and of varying strength, making it a research hotspot to build a generative model that can consider both the directionality and weight of edges.
[0003] Existing directed weighted network generation methods mainly develop along two routes: one is the topology-driven method, such as the weighted random block model, which extends the classic model to introduce directionality and weight modeling; the other is the feature-driven method based on node attributes, which attempts to predict edge weights using the intrinsic characteristics of nodes. However, most methods model directionality and weight as independent dimensions, failing to reveal their common nature in structural evolution, especially ignoring the collaborative evolution mechanism of reciprocity and triadic closure structures that are prevalent in networks.
[0004] Reciprocity manifests as the mutual influence of bidirectional edges, while triadic closure reflects the potential social embeddedness among shared neighbors. Numerous empirical studies have shown that these high-order structures are closely related to the generation probability and weight of edges. For example, in social networks, if nodes A and B are connected to node C, the likelihood of an edge forming between B and C significantly increases. This structural dependence phenomenon indicates that the formation of an edge is not an isolated event, but is closely related to its surrounding structure.
[0005] However, most existing generative models can only model reciprocity or triadic structure separately, making it difficult to capture their interaction uniformly; some methods attempt to combine both, but often rely on post-processing strategies to adjust the network structure, leading to inconsistencies between theory and reality, and lack of ability to maintain the structural properties of real networks. To address the above problems, there is an urgent need for a new probabilistic generative model that can model the directionality, weight, and high-order structural constraints of edges simultaneously, to achieve more realistic and credible network synthesis. SUMMARY
[0006] The purpose of the present application is to overcome the deficiencies of the prior art and provide a directed weighted network model generation method based on a triad reciprocity mechanism.
[0007] To achieve the above purpose, the present application provides a directed weighted network model generation method based on a triad reciprocity mechanism, comprising: Step 1, constructing a directed weighted network model containing inter-node interaction, and initializing parameters of the directed weighted network model, the parameters including community belonging vectors of nodes, affinity matrix between communities, and triadic reciprocity coefficient; Step 2, obtaining original interaction data from an actual network, estimating potential structural information of each node, and iteratively optimizing parameters of the directed weighted network model by using an EM algorithm; Step 3, according to the parameters of the iteratively optimized directed weighted network model, jointly considering community belonging relationship between nodes and shared neighbor information, and using conditional Poisson distribution with a triadic reciprocity term to calculate expected weight of connection between nodes; Step 4, based on the expected weight, constructing an adjacency matrix of a target network, sampling edges, and generating corresponding edge weights, to realize generation of the directed weighted network model.
[0008] Further, the step 1 specifically includes: constructing a directed weighted network model represented as wherein, is a node set containing N nodes, is an asymmetric adjacency matrix, represents an interaction weight from node to node , the directed weighted network model includes two complementary mechanisms, the first mechanism is modeled by potential out-edge community belonging vector and in-edge community belonging vector , affinity relationship between K communities is represented by , the second is a triadic reciprocity mechanism, binary indicator variables , are used to represent existence of edges of common neighbor of node and node respectively, and are weighted by triadic reciprocity coefficient , a joint likelihood function is constructed, under given a set of potential parameters , dependence relationship caused by triadic structure is considered explicitly, and the expression is as follows: ; wherein, is the dependence relationship caused by triadic structure, represents product of all node triads , represents interaction weight and binary indicator variable under parameter 、 The probability of both occurring simultaneously is specifically expressed as: ; in, Indicates interaction weight factorial, For natural index, conditional strength parameter Defined as: ; Through a Bayesian probability model and use To quantify the contributions of the two complementary mechanisms, Jensen's inequality is used to analyze the Bayesian probability model. The derivation is performed, and then Lagrange multipliers are introduced. and By imposing constraints on the maximization process, the core variational lower bound of the directed weighted network model is obtained. The expression is: ; in, The weights are for binary classification Bayesian weights.
[0009] Furthermore, the iterative optimization of the parameters of the directed weighted network model in step 2 specifically includes: The parameters of the directed weighted network model are updated using edge set information and pseudo-likelihood estimation. A log-likelihood function containing community terms and triple terms is constructed and iteratively updated using the EM algorithm. The iterative formula for each parameter is obtained by differentiating the pseudo-likelihood function. Through each iteration, the parameter values are continuously updated as the likelihood value increases.
[0010] Furthermore, the reciprocity parameter The update method is as follows: .
[0011] Furthermore, the aforementioned Affinity between communities The update method is as follows: .
[0012] Furthermore, the outbound community affiliation vector and the inbound community affiliation vector The update expression is as follows: ; ; ; .
[0013] Furthermore, step 3 specifically includes: Generate the network weight matrix using the optimized parameters. The details are as follows: ;
[0014] in, for Affinity matrix between communities; Add a sparsity constraint, sparsity coefficient The definition is as follows: ;
[0015] in, The expected total number of edges is represented by the sparsity coefficient. Network weight matrix Updated to: Introducing a ternary reciprocity coefficient Update the network weight matrix Adjust to expected weights: , This is the transpose of the matrix.
[0016] Furthermore, step 4 specifically includes: Based on the expected weight The strength at the node With nodes and nodes With nodes Generate edges between them: ,in, For nodes With nodes The edge between, For nodes With nodes The weights between them All are nodes With nodes The weights between them Indicates strength, calculates the expected value of edge generation. The weights of the edges are assigned based on the expected values generated by the edges, and follow a Poisson distribution: .
[0017] Beneficial Effects: This invention integrates binary reciprocity and ternary closure mechanisms to simultaneously generate directional edges and weights in directed weighted networks, effectively capturing local reciprocity patterns and global ternary attributes, thus demonstrating excellent performance in maintaining network structure realism. Experimental results on multiple real-world network datasets show that the model can accurately predict the existence of edges in link prediction tasks, providing strong support for network structure inference and completion. Furthermore, the generated network exhibits good anti-spread capabilities in infectious disease simulations; by optimizing the network topology, it can effectively suppress the spread of infectious diseases, providing a new strategy for public health security and information dissemination control. In terms of network security, the generated network can enhance its robustness against attacks by identifying key nodes, providing a theoretical basis for network security protection. Attached Figure Description
[0018] Figure 1 This is a schematic diagram illustrating the probability formation of edges connecting nodes; Figure 2 This is a schematic diagram of the model learning and generative network process. Detailed Implementation
[0019] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solutions of the present invention, and it should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.
[0020] like Figure 1 and Figure 2 As shown, this embodiment of the invention provides a method for generating a directed weighted network model based on a triple reciprocity mechanism, including: Step 1: Construct a directed weighted network model that includes interactions between nodes, and initialize the parameters of the directed weighted network model. These parameters include the node's community affiliation vector, the affinity matrix between communities, and the ternary reciprocity coefficient. Specifically: The directed weighted network model is represented as follows: ,in, Given a set of N nodes, It is an asymmetric adjacency matrix; see [link / reference]. Figure 1 , Indicates from node To the node The interactive weights of the directed weighted network model include two complementary mechanisms. The first mechanism utilizes the potential out-edge community affiliation vector. and the inbound community affiliation vector Modeling, The affinity between communities is The second type is a ternary reciprocity mechanism, which uses binary indicator variables. , To represent nodes respectively and nodes with mutual neighbors The existence of edges, and determined by the ternary reciprocity coefficient. Weighted, a joint likelihood function is constructed based on the above parameters given a set of latent parameters. Under the given conditions, the dependency relationship caused by the ternary structure is explicitly considered, resulting in the expression: ;
[0021] in, The dependency relationship is caused by the ternary structure. Represents the triplet for all nodes Perform the product. Indicates in the parameter Lower Interaction Weight and binary indicator variables 、 The probability of both occurring simultaneously is specifically expressed as: ;
[0022] in, Indicates interaction weight factorial, It is the natural index.
[0023] Conditional strength parameters Defined as: ;
[0024] To maximize this likelihood function and to more easily handle the logarithmic summation term, a Bayesian probability model is needed. , To quantify the contributions of these two mechanisms, and using Jensen's inequality to derive the model, a rigorous theoretical lower bound is established. Furthermore, because the established likelihood function depends on... and Introducing Lagrange multipliers and By imposing constraints on the maximization process, we obtain the core variational lower bound of the directed weighted network model. The expression (the final likelihood function) is: ;
[0025] in, The weights are for binary classification Bayesian weights.
[0026] Step 2: Obtain raw interaction data from the actual network, estimate the potential structural information of each node, and iteratively optimize the parameters of the directed weighted network model using the EM algorithm. Specifically, update the parameters of the directed weighted network model using edge set information and pseudo-likelihood estimation. Construct a log-likelihood function containing community terms and ternary terms, and iteratively update it using the EM algorithm. Obtain the iterative formula for each parameter by differentiating the pseudo-likelihood function. Through each iteration, continuously update the parameter values as the likelihood value increases.
[0027] The obtained likelihood function about Taking the derivative and setting the gradient to 0, we obtain the reciprocity parameter. The update method is as follows: .
[0028] Likelihood function Regarding the affinity between communities Taking the derivative and setting the gradient to 0, we get Affinity between communities The update method is as follows: .
[0029] For ease of expression, the log-likelihood was then rewritten as about , and The function. This form allows us to explicitly extract the part containing constraint terms and impose constraints in the model. The outbound community affiliation vector is obtained. and the inbound community affiliation vector The update expression is as follows: ;
[0030] ;
[0031] To meet the demand and The normalization constraint, i.e. and It can be deduced that and The expression: ;
[0032] .
[0033] By using the parameter update formula above, we finally obtain the parameter value that maximizes the likelihood function, and then use... and Parameters are used to generate network edge sets with reciprocal ternary structures.
[0034] Step 3: Based on the parameters of the iteratively optimized directed weighted network model, and combining the community affiliation relationships and shared neighbor information between nodes, calculate the expected weights of the connections between nodes using a conditional Poisson distribution with ternary reciprocity terms. Specifically, the generated network can fit the community structure and reciprocity characteristics of real networks. This is based on the model's input, including attributes related to community structure. , Affinity matrix and reciprocity coefficient The optimized parameters are used to generate the network weight matrix. The details are as follows: ;
[0035] To introduce sparsity into the network, a sparsity constraint is added, with sparsity coefficients... The definition is as follows: ;
[0036] in, The expected total number of edges is represented by the sparsity coefficient. Network weight matrix Updated to: Introducing a ternary reciprocity coefficient Update the network weight matrix Adjust to expected weights: , This is the transpose of the matrix.
[0037] Step 4: Construct the adjacency matrix of the target network based on the expected weights, sample the edges, and generate the corresponding edge weights to generate the directed weighted network model. Specifically, based on the expected weights... The strength at the node With nodes and nodes With nodes Generate edges between them: ,in, For nodes With nodes The edge between, For nodes With nodes The weights between them All are nodes With nodes The weights between them Indicates strength, calculates the expected value of edge generation. The weights of the edges are assigned based on the expected values generated by the edges, and follow a Poisson distribution: For details, please refer to Figure 2 By maximizing the likelihood function value through a directed weighted network of real inputs, the optimal parameter values are obtained, including the community structure attributes u and v, the affinity matrix w, and the reciprocity coefficient. Finally, the parameters are combined to assign common nodes, weight values, and directed edges to the generated directed weighted network.
[0038] The above description is merely a preferred embodiment of the present invention. It should be noted that for those skilled in the art, other parts not specifically described are existing technology or common knowledge. Several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for generating a directed weighted network model based on a triple reciprocity mechanism, characterized in that, include: Step 1: Construct a directed weighted network model that includes interactions between nodes, and initialize the parameters of the directed weighted network model, including the community affiliation vector of the nodes, the affinity matrix between communities, and the ternary reciprocity coefficient. Step 2: Obtain raw interaction data from the actual network, estimate the potential structural information of each node, and use the EM algorithm to iteratively optimize the parameters of the directed weighted network model. Step 3: Based on the parameters of the iteratively optimized directed weighted network model, the expected weights of the connections between nodes are calculated using a conditional Poisson distribution with ternary reciprocity terms, combining the community affiliation and shared neighbor information between nodes. Step 4: Construct the adjacency matrix of the target network based on the expected weights, sample the edges, and generate the corresponding edge weights to realize the generation of the directed weighted network model.
2. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 1, characterized in that, Step 1 specifically includes: The directed weighted network model is represented as follows: ,in, Given a set of N nodes, It is an asymmetric adjacency matrix. Indicates from node To the node The interactive weights of the directed weighted network model include two complementary mechanisms. The first mechanism utilizes the potential out-edge community affiliation vector. and the inbound community affiliation vector Modeling, The affinity between communities is The second type is a ternary reciprocity mechanism, which uses binary indicator variables. , To represent nodes respectively and nodes with mutual neighbors The existence of edges, and determined by the ternary reciprocity coefficient. Weighted, constructing a joint likelihood function given a set of latent parameters Under the given conditions, the dependency relationship caused by the ternary structure is explicitly considered, resulting in the expression: ； in, The dependency relationship is caused by the ternary structure. Represents the triplet for all nodes Perform the product. The table indicates that the parameters Lower Interaction Weight and binary indicator variables 、 The probability of both occurring simultaneously is specifically expressed as: ； in, Indicates interaction weight factorial, For natural index, conditional strength parameter Defined as: ； Through a Bayesian probability model and use To quantify the contributions of the two complementary mechanisms, Jensen's inequality is used to analyze the Bayesian probability model. The derivation is performed, and then Lagrange multipliers are introduced. and By imposing constraints on the maximization process, the core variational lower bound of the directed weighted network model is obtained. The expression is: ； in, The weights are for binary classification Bayesian weights.
3. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 2, characterized in that, Step 2, which iteratively optimizes the parameters of the directed weighted network model, specifically includes: The parameters of the directed weighted network model are updated using edge set information and pseudo-likelihood estimation. A log-likelihood function containing community terms and triple terms is constructed and iteratively updated using the EM algorithm. The iterative formula for each parameter is obtained by differentiating the pseudo-likelihood function. Through each iteration, the parameter values are continuously updated as the likelihood value increases.
4. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 3, characterized in that, The reciprocity parameter The update method is as follows: 。 5. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 3, characterized in that, The Affinity between communities The update method is as follows: 。 6. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 3, characterized in that, The outgoing community affiliation vector and the inbound community affiliation vector The update expression is as follows: ； ； ； 。 7. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 2, characterized in that, Step 3 specifically includes: Generate the network weight matrix using the optimized parameters. The details are as follows: ； in, for Affinity matrix between communities; Add a sparsity constraint, sparsity coefficient The definition is as follows: ； in, The expected total number of edges is represented by the sparsity coefficient. Network weight matrix Updated to: Introducing a ternary reciprocity coefficient Update the network weight matrix Adjust to expected weights: , This is the transpose of the matrix.
8. The method for generating a directed weighted network model based on a triplet reciprocity mechanism according to claim 7, characterized in that, Step 4 specifically includes: Based on the expected weight The strength at the node With nodes and nodes With nodes Generate edges between them: ,in, For nodes With nodes The edge between, For nodes With nodes The weights between them All are nodes With nodes The weights between them Indicates strength, calculates the expected value of edge generation. The weights of the edges are assigned based on the expected values generated by the edges, and follow a Poisson distribution: .