SBSIR model construction method and IMGPE algorithm for identifying network node influence

Abstract

The invention discloses an SBSIR model construction method and an IMGPE algorithm for identifying network node influence in the field of Internet social network modeling analysis. The method is improved on the basis of a traditional SIR. Different from a traditional infectious disease model, the SBSIR model not only considers a direct interaction relationship between users, but also introduces interest similarity as a spreading mechanism of information spreading, so that the SBSIR model is more in line with an actual spreading rule of an interest social network compared with the traditional infectious disease model. The IMGPE algorithm reconstructs the network based on interaction and interest features among users in the social network, and identifies nodes with influence in the interested social network by measuring local features and global features of the network and position features among the users.

Description

Technical Field

[0001] The present invention relates to a method for constructing an SBSIR model and an IM_GPE algorithm for identifying the influence of network nodes in the field of Internet social network modeling and analysis. Background Art

[0002] In recent years, with the rapid development of the Internet, online social networks have become an important platform for information dissemination and social interaction. In this context, Influence Maximization (IM) has gradually become one of the most popular research directions in this field. The goal of IM is to maximize the scope of information dissemination by selecting a small number of the most influential users in the network as seed nodes, so as to achieve a wider information diffusion and more effective marketing promotion. This concept originated from viral marketing, where enterprises promote products in their friends' circles by rewarding influential users.

[0003] The early research on the IM problem can be traced back to the work of Domingos and Richardson. They first formulated the problem as an optimization problem based on a Markov random field, modeling the social network as a Markov random field, where the state (active or inactive) of each node is affected by the states of its neighbors. They solved this problem by a heuristic method of maximization. On this basis, Kempe et al. first clearly defined the IM problem and proposed two classic influence propagation models: the Independent Cascade (IC) model and the Linear Threshold (LT) model. Kempe et al. proved that the IM problem is an NP-hard problem under both the IC and LT models. In addition, classic propagation models in epidemiology, such as the SIR, SIS, SIRU, and SISIR models, have also been borrowed in IM research. These models were initially used to describe the spread of infectious diseases, but their ideas and methods have also been widely applied to the study of information dissemination.

[0004] Traditional IM methods are mainly based on users' social relationship networks, that is, by analyzing the friendship relationships between users to determine the nodes with greater influence. Common methods include greedy algorithms, centrality algorithms, and heuristic methods. Kempe et al. first proposed a climbing greedy algorithm, Greedy, which constructs a seed set by gradually selecting the nodes with the greatest influence, but its computational complexity is relatively high. To improve the computational efficiency, Leskovec et al. and Amit et al. proposed the CELF method and the CELF++ method respectively, and these methods have improved the computational efficiency to a certain extent. In addition, Kempe et al. also proposed centrality methods based on node centrality, such as degree centrality, betweenness centrality, and closeness centrality, which evaluate the influence of nodes by calculating their positions and connection characteristics in the network. However, these centrality methods often only consider a single attribute of the network, such as the adjacency relationship and path information of the network, thus limiting the effectiveness of the algorithm. For this reason, researchers have proposed new methods and models. Ma et al. used the barycentric index based on the law of gravity to utilize the influence of neighboring nodes and path information to identify influential nodes. Li et al. considered the influence of network scale on this basis and proposed a generalized gravity model. Inspired by electric potential energy, Ullah et al. proposed a method based on electric potential energy centrality to identify influential nodes by balancing local information and global information in different networks through adjustable parameters.

[0005] In the IM problem, traditional epidemic models (such as SIR, SIS, SIRU, and SISIR) are widely used to simulate the information dissemination process. These models can adapt to various dissemination scenarios by introducing different node states and state transition mechanisms. For example, the SIR model divides the population into three categories: susceptible (S), infected (I), and recovered (R), and is suitable for describing the entire life cycle of information from dissemination to final stability; the SIS model allows infected individuals to recover to the susceptible state and is suitable for simulating the situation of repeated infections; the SIRU model adds an "unaware (U)" state to depict the initial stage of information dissemination; the SISIR model combines the characteristics of SIS and SIR and allows users to switch repeatedly between the susceptible and infected states to simulate the dynamic dissemination process of information.

[0006] However, these traditional infectious disease models are mainly based on the direct interaction relationships among users and are applicable to the acquaintance social mode of "word-of-mouth". They assume that information dissemination is only achieved through the contact of adjacent nodes and cannot effectively model the complex dissemination mechanisms in interest social networks. In interest social networks such as BiliBili and TikTok, users not only interact with their direct social neighbors but are also influenced by non-directly connected users with similar interests. For example, a user may be attracted by the content recommended by the system due to their interest in a certain topic and thus come into contact with the information. This dissemination mechanism breaks through the limitation of direct interaction in traditional models, making it difficult for existing methods to accurately simulate the information dissemination process in interest social networks. Summary of the Invention

[0007] The object of the present invention is to provide a method for constructing an SBSIR model and an IM_GPE algorithm for identifying the influence of network nodes, which can accurately simulate the information dissemination process in interest social networks, reconstruct the network based on the interaction and interest characteristics among users in the social network, and identify influential nodes in the interest social network by measuring the local characteristics, global characteristics, and position characteristics among users.

[0008] To achieve the above object, the present invention provides a method for constructing an SBSIR model, including the following steps:

[0009] Step 1, input the interest social network;

[0010] Step 2, calculate the potential influence of nodes and the interest similarity between nodes based on the node interest characteristics and interaction relationships;

[0011] Step 3, construct server nodes according to the potential influence of nodes and the interest similarity between nodes, and the server node set is composed of the interest neighbors of each node;

[0012] Step 4, information dissemination process;

[0013] Step 4.1, initial state setting: all nodes are in the susceptible state initially;

[0014] Step 4.2, infection process: the infected nodes disseminate information through direct connections and server recommendations, and the infection probability is jointly determined by the connection strength and interest similarity of the nodes;

[0015] Step 4.3, recovery process: the infected nodes recover to the immune state with a certain probability;

[0016] Step 4.4, termination condition: when there are no new infected nodes, the dissemination process ends.

[0017] Compared with the prior art, the beneficial effect of the present invention is that the model is improved based on the traditional SIR. Different from the traditional infectious disease model, the SBSIR model not only considers the direct interaction relationship between users, but also introduces interest similarity as the propagation mechanism of information dissemination, making it more in line with the actual propagation law of the interest social network than the traditional infectious disease model.

[0018] As a further improvement of the present invention, the specific content of step 1 is as follows.

[0019] For an interest social network, it can be modeled as G=(V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes.

[0020] As a further improvement of the present invention, the specific content of step 2 is as follows.

[0021] Based on the node interest characteristics and interaction relationships, calculate the potential influence of the node and the interest similarity between nodes. The potential influence of the node is calculated by the following formula:

[0022]

[0023] Among them, PI u represents the magnitude of the potential influence of node u, Γ u is the set of neighbor nodes of node u, d u is the degree of node u, d v is the degree of node v, and node v is other nodes except node u.

[0024] As a further improvement of the present invention, the specific content of step 3 is as follows.

[0025] Step 3.1, for each node u, calculate its interest similarity with node v and sort it in descending order. The interest similarity between nodes is calculated by cosine similarity, and the formula is as follows:

[0026]

[0027] Among them, i is the interest limit, and it has a total of c dimensions. represents the q-dimensional interest vector of node u. represents the q-dimensional interest vector of node v. By calculating the interest similarity between nodes, node pairs with similar interests can be identified.

[0028] Step 3.2, select the top PI u non-direct neighbor nodes from the sorting result as the interest neighbor set IN u of node u;

[0029] Step 3.3, record the interest neighbor sets of all nodes, and construct the server node. As a further improvement of the present invention, the input structure includes an input port, which is arranged on the outer dielectric substrate and is connected to the outer metal resonance ring through an input coupling capacitor.

[0030] To achieve the above object, the present invention also provides an IM_GPE algorithm for identifying the influence of network nodes, including the following steps:

[0031] Step 1, input the interest social network;

[0032] For an interest social network, it can be modeled as G=(V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes;

[0033] Step 2, construct the propagation matrix;

[0034] Step 3, calculate the mass of the node;

[0035] Step 4, calculate the gravitational acceleration of the node;

[0036] Step 5, calculate the relative height of the node;

[0037] Step 6, calculate the gravitational potential energy.

[0038] Compared with the prior art, the beneficial effect of the present invention is that the algorithm reconstructs the network based on the interactions and interest characteristics between users in the social network, and identifies the influential nodes in the interest social network by measuring the local characteristics, global characteristics, and position characteristics between users.

[0039] As a further improvement of the present invention, the specific content of Step 2 is as follows:

[0040] For the input interest social network G=(V, E, I), the adjacency matrix A and the interest characteristic matrix H of the network can be obtained. H is used to represent the interest-based interaction relationship between nodes, and its formula is as follows:

[0041]

[0042]

[0043] Among them, x and y represent the indexes of the positions in matrix H. The range of x is (1, 2, 3... n), the range of y is (1, 2, 3... n), and h x,y is the value of the i-th row and j-th column of matrix H, and the value of n is the number of all nodes;

[0044] IN uDenote the set of interest neighbors of node u. After obtaining the adjacency matrix A and the interest feature matrix H of the network, the propagation matrix P = A + H can be calculated. The propagation matrix P represents the propagation relationship in the interest social network, and the reconstructed graph G' can be obtained according to the propagation matrix P.

[0045] As a further improvement of the present invention, the specific content of step 3 is as follows.

[0046] Node quality is a key indicator for measuring the local influence of a node, and its calculation formula is:

[0047]

[0048] Where, is the out-degree of node u, and φ(u) is an adjustment factor used to stabilize the evaluation of node quality and avoid overestimation or underestimation due to small changes in the out-degree. The calculation formula of the adjustment factor is:

[0049]

[0050] As a further improvement of the present invention, the specific content of step 4 is as follows.

[0051] Gravitational acceleration is a key indicator for measuring the global influence of a node, and the calculation formula is:

[0052]

[0053] Where, denotes the set of out-neighbors of node u, w u is the weight of node u, which is expressed as the product of the out-degree of node u and the k-shell value. α u,v is the number of triangles formed by node u and node v, cf u,v is the connection factor between node u and node v, and the calculation is as follows:

[0054] cf u,v =(k u -α u,v )×(k v -α u,v )#(8)

[0055]

[0056] Gravitational acceleration g u By considering the connection relationship between node u and node v, it reflects the global influence of node u in the network.

[0057] As a further improvement of the present invention, the specific content of step 5 is as follows.

[0058] First, by calculating the mass m of node uu The product with the acceleration of gravity g u gives the gravitational centrality G of the node u to initially evaluate the propagation ability of the node, and its calculation formula is as follows:

[0059] G u = m u ·g u #(10)

[0060] To alleviate the influence overlap problem, the relative height is introduced to "avoid the rich club" effect; for any node u in the network, its relative height is defined as shown in formula (11):

[0061]

[0062] where λ is an adjustable parameter between (0, 1), and δ(u) represents the minimum value of the shortest path from node u to a node z more influential than it. The calculation formula of δ(u) is as follows

[0063] δ(u) = min x∈Φ(u) (dist u,z )#(12)

[0064] where Φ(u) is the set of nodes z more influential than u

[0065] As a further improvement of the present invention, the specific content of step 6 is as follows

[0066] For node u in the network, its GPE value is defined as shown in formula (13):

[0067] GPE u = G u ·h u #(13)

[0068] To facilitate the comparison and analysis of GPE values of different nodes, the min-max normalization technique is used to scale the GPE values to [0, 1]; this standardization process is crucial for eliminating the influence of different scales and units, so as to enable a more consistent and interpretable evaluation of node influence. The standardized GPE value is calculated using formula (14)

[0069]

[0070] Here, GPE min and GPE maxRepresent the minimum and maximum GPE values in the network respectively. By applying this normalization, it is ensured that the GPE values are scaled proportionally to the range of [0, 1], where 0 represents the minimum influence and 1 represents the maximum influence; the normalized GPE values provide a clear and consistent metric for evaluating node influence and enhance the interpretability of the results. Description of the Drawings

[0071] Figure 1 This is the state transition process of the SBSIR model in the present invention.

[0072] Figure 2 This is the propagation process of the SBSIR model in the present invention.

[0073] Figure 3 This is the flowchart of the IM_GPE algorithm in the present invention.

[0074] Figure 4 This is the ablation experiment of the IM_GPE algorithm in the present invention.

[0075] Figure 5 This is the influence of IM_GPE and 9 algorithms in the present invention under different numbers of seed nodes.

[0076] Figure 6 This is the influence of IM_GPE and 9 algorithms in the present invention under different infection coefficients.

[0077] Figure 7 This is the average shortest path length between the seed nodes of IM_GPE and 9 algorithms in the present invention. Detailed Implementation Manner

[0078] The present invention will be further described below with reference to the accompanying drawings:

[0079] As Figure 1-2 shown, a method for constructing an SBSIR model includes the following steps:

[0080] Step 1, input the interest social network;

[0081] For an interest social network, it can be modeled as G = (V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes.

[0082] Step 2, calculate the node potential influence and the interest similarity between nodes based on the node interest characteristics and interaction relationships;

[0083] Based on the node interest characteristics and interaction relationships, calculate the node potential influence and the interest similarity between nodes. The potential influence of a node is calculated by the following formula:

[0084]

[0085] Among them, PI u represents the potential influence of node u, and Γ u is the set of neighbor nodes of node u, and d u is the degree of node u, and d v is the degree of node v, where node v is other nodes except node u.

[0086] Step 3: Construct server nodes according to the potential influence of nodes and the interest similarity between nodes. The server node set is composed of the interest neighbors of each node;

[0087] Step 3.1: For each node u, calculate its interest similarity with node v and sort it in descending order. The interest similarity between nodes is calculated by cosine similarity, and the formula is as follows:

[0088]

[0089] Among them, i is the interest limit, and there are c dimensions in total. represents the q - dimensional interest vector of node u. represents the q - dimensional interest vector of node v. By calculating the interest similarity between nodes, node pairs with similar interests can be identified;

[0090] Step 3.2: Select the top PI u non - direct neighbor nodes from the sorting result as the interest neighbor set IN u of node u;

[0091] Step 3.3: Record the interest neighbor sets of all nodes and construct server nodes.

[0092] Step 4: Information propagation process;

[0093] Step 4.1: Initial state setting: The initial state of all nodes is susceptible;

[0094] Step 4.2: Infection process: The infected nodes spread information through direct connections and server recommendations, and the infection probability is jointly determined by the connection strength and interest similarity of the nodes;

[0095] Step 4.3: Recovery process: The infected nodes recover to the immune state with a certain probability;

[0096] Step 4.4: Termination condition: When there are no new infected nodes, the propagation process ends.

[0097] As Figure 3 shown, an IM_GPE algorithm for identifying the influence of network nodes includes the following steps.

[0098] Step 1, input an interest social network;

[0099] An interest social network can be modeled as G=(V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes;

[0100] Step 2, construct a propagation matrix;

[0101] For the input interest social network G=(V, E, I), the adjacency matrix a and the interest characteristic matrix H of the network can be obtained. H is used to represent the interest-based interaction relationship between nodes, and its formula is as follows:

[0102]

[0103] where x and y represent the indices of positions in matrix H, the range of x is (1, 2, 3... n), the range of y is (1, 2, 3... n), and h x,y is the value of the i-th row and j-th column of matrix H, and the value of n is the number of all nodes;

[0104] IN u represents the set of interest neighbors of node u. After obtaining the adjacency matrix A and the interest characteristic matrix H of the network, the propagation matrix P = A + H can be calculated. The propagation matrix P represents the propagation relationship in the interest social network, and the reconstructed graph G' can be obtained according to the propagation matrix P.

[0105] Step 3, calculate the quality of nodes;

[0106] The node quality is a key indicator to measure the local influence of nodes, and its calculation formula is:

[0107]

[0108] where, is the out-degree of node u, and φ(u) is an adjustment factor used to stabilize the evaluation of node quality and avoid overestimation or underestimation caused by small changes in the out-degree. The calculation formula of the adjustment factor is:

[0109]

[0110] Step 4, calculate the gravitational acceleration of nodes;

[0111] The gravitational acceleration is a key indicator to measure the global influence of nodes, and the calculation formula is:

[0112]

[0113] where, represents the set of out-neighbors of node u, and w uis the weight of node u, expressed as the product of the out-degree of node u and the k-shell value, α u,v is the number of triangles formed by node u and node v, cf u,v is the connection factor between node u and node v, calculated as follows:

[0114] cf u,v =(k u -α u,v )×(k v -α u,v )#(8)

[0115]

[0116] Gravitational acceleration g u By considering the connection relationship between node u and node v, it reflects the global influence of node u in the network.

[0117] Step 5, calculate the relative height of the node;

[0118] First, by calculating the product of the mass m u of node u and the gravitational acceleration g u , the gravitational centrality G u of the node is obtained to initially evaluate the propagation ability of the node. The calculation formula is as follows:

[0119] G u =m u ·g u #(10)

[0120] To alleviate the problem of influence overlap, relative height is introduced to "avoid the rich club" effect; for any node u in the network, its relative height is defined as shown in formula (11):

[0121]

[0122] where λ is an adjustable parameter between (0, 1), and δ(u) represents the minimum value of the shortest path from node u to a more influential node z. The calculation formula of δ(u) is as follows,

[0123] δ(u)=min x∈Φ(u) (dist u,z )#(12)

[0124] where Φ(u) is the set of nodes z that are more influential than u.

[0125] Step 6, calculate the gravitational potential energy.

[0126] For node u in the network, the value of its GPE is defined as shown in formula (13):

[0127] GPE u =G u ·h u #(13)

[0128] In order to facilitate the comparison and analysis of GPE values of different nodes, the minimum-maximum normalization technique is used to scale the GPE values to [0, 1]. This normalization process is crucial to eliminate the effects of different scales and units, thereby enabling a more consistent and interpretable assessment of node impact. The standardized GPE value is calculated using formula (14),

[0129]

[0130] Here, GPE min and GPE max Represent the minimum and maximum GPE values in the network, respectively. By applying this normalization, we ensure that the GPE value is scaled proportionally to the range of [0, 1], where 0 represents the smallest impact and 1 represents the largest impact. The normalized GPE value provides a clear and consistent indicator for evaluating node influence and enhances the interpretability of the results.

[0131] In the present invention, Figure 1 As shown in Figure 1, based on the traditional infectious disease model SIR, combined with the characteristics of interest social networks, the traditional SIR model is expanded into the SBSIR model. According to the actual process of infectious disease transmission, the population within the epidemic range is divided into three categories:

[0132] S (Susceptible) status: A person in this status has not yet been infected and cannot infect others. I (Infectious) status: A person in this status has been infected and can infect others. R (Recovered) status: A person in this status has recovered and has antibodies in their body, so they cannot infect others.

[0133] This paper uses the SBSIR model to describe the process of information dissemination in interest-based social networks. The status of these three types of people in the information dissemination process is as follows:

[0134] S state: People in this state have not yet been exposed to the information and will not spread it to others. N and β I The probability of receiving information from their friends' interactions and the platform's recommendations of users with similar interests, and believing in the information and becoming an information diffuser (transitioning to state I).

[0135] State I: A person in this state has received the information, believes it, and will spread it to others. However, due to factors such as a decrease in enthusiasm for forwarding, he or she may stop spreading the information (transitioning to state R) with a probability of γ.

[0136] R state: People in this state have once received and believed the information, but due to factors such as a decline in the enthusiasm for forwarding, they no longer spread the information to others.

[0137] Figure 2 It is an interest social network composed of 9 nodes and 7 edges.

[0138] An IM_GPE algorithm for identifying the influence of network nodes, where the IM_GPE algorithm is a method for maximizing the influence of an interest social network based on the gravitational potential energy model (An Influence Maximization Algorithm Based on Gravitational Potential Energy).

[0139] To evaluate the effectiveness of the IM_GPE algorithm, in six real-world social networks (Email, Simmons, Elec, UChicago, Bitcoinalpha, and RfA), the IM_GPE algorithm proposed in the present invention is compared with nine existing algorithms (OutDegree, Betweenness Centrality, K-Shell, VoteRank, CGG, LSS, LGC, NPIC, EPC). All methods are evaluated under the SBSIR model, and the infection rate is where <d 2 > is the average value of the degrees of the nodes in the graph, <d> 2 is the mean square of the node degrees in the graph, and α is the infection coefficient.

[0140] Figure 4 Compares the influence propagation effects of the IM_GPE algorithm before and after introducing the graph reconstruction mechanism. Removing the graph reconstruction part of IM_GPE and its previous part results in IM_GPEN (the ablation experiment of the IM_GPE algorithm). In all datasets, the propagation values of both IM_GPE and IM_GPEN increase monotonically with the increase of the parameter k (the number of seed nodes), but the growth slope of IM_GPE is larger, indicating that the performance of the IM_GPE algorithm has been significantly improved after introducing the graph reconstruction mechanism. This advantage is particularly obvious in the Elec, UChicago, Bitcoinalpha, and RfA datasets. In the Email and Simmons datasets, IM_GPE is slightly better than IM_GPEN. This is because the network scales of Email and Simmons are small, restricting the scope of influence propagation.

[0141] Figure 5 and Figure 6 Respectively compare the influence propagation capabilities of the IM_GPE algorithm proposed in the present invention and nine comparison algorithms under different numbers of seed nodes and different propagation coefficients. In all six datasets, the propagation ability of the IM_GPE algorithm proposed in the present invention is better than that of the other nine comparison algorithms, and its advantage gradually expands with the increase of the number of seed nodes and the propagation coefficient. Especially in the Bitcoinalpha dataset, this advantage is most significant, which is because the average degree of the Bitcoinalpha dataset is large, resulting in a higher infection rate of the model.

[0142] Figure 7 Shows the average distance between seed nodes of the IM_GPE algorithm proposed in the present invention and the comparison algorithms in six different datasets. The more dispersed the distribution of seed nodes, the less the overlap of their propagation effects, and thus the better the propagation effect. In the Simmons, Elec, UChicago, Bitcoinalpha, and RfA datasets, the average distance of the seed nodes selected by the IM_GPE algorithm proposed in the present invention is significantly higher than that of the other comparison algorithms, and the average distance generally shows a downward trend with the increase of the number of nodes. However, in the Elec, Bitcoinalpha, and RfA datasets, the average distance of the seed nodes selected by the IM_GPE algorithm proposed in the present invention remains at a large value and shows no obvious downward trend, which is because there is no direct path between some of the seed nodes in these datasets. In the Email dataset, the average path length of the EPC algorithm is shorter than that of the GGC, LSS, LGC, and NPIC algorithms, mainly because the scale of the Email dataset is small and the distribution of more influential nodes is relatively concentrated.

[0143] The present invention proposes the SBSIR model to solve the problem of modeling information dissemination in the interest social network by traditional IM methods. Meanwhile, an influence maximization algorithm for the interest social network (IM_GPE algorithm) is proposed to identify influential nodes in the interest social network. Experiments on 6 real-world datasets verify its superiority and practicability, providing a new solution to the IM problem in complex networks.

[0144] The present invention is not limited to the above embodiments. Based on the technical solutions disclosed in the present disclosure, those skilled in the art can make some substitutions and deformations to some technical features without creative labor according to the disclosed technical content, and these substitutions and deformations are all within the protection scope of the present invention.< / d>

Claims

1. A method for constructing an SBSIR model, characterized in that: It includes the following steps: Step 1, input the interest social network; Step 2, calculate the potential influence of nodes and the interest similarity between nodes based on node interest characteristics and interaction relationships; Step 3, construct server nodes according to the potential influence of nodes and the interest similarity between nodes. The server node set is composed of the interest neighbors of each node; Step 4, the information dissemination process; Step 4.1, initial state setting: all nodes are in the susceptible state initially; Step 4.2, infection process: the infected nodes spread information through direct connections and server recommendations, and the infection probability is jointly determined by the connection strength and interest similarity of the nodes; Step 4.3, recovery process: the infected nodes recover to the immune state with a certain probability; Step 4.4, termination condition: when there are no new infected nodes, the dissemination process ends.

2. A method for constructing an SBSIR model according to claim 1, characterized in that: The specific content of Step 1 is as follows: For an interest social network, it can be modeled as G=(V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes.

3. A method for constructing an SBSIR model according to claim 2, characterized in that: The specific content of Step 2 is as follows: Based on node interest characteristics and interaction relationships, calculate the potential influence of nodes and the interest similarity between nodes. The potential influence of a node is calculated by the following formula: Among them, PI u represents the potential influence of node u, and Γ u is the set of neighbor nodes of node u, d u is the degree of node u, and d v is the degree of node v, where node v is other nodes except node u.

4. A method for constructing an SBSIR model according to claim 3, characterized in that: The specific content of Step 3 is as follows: Step 3.1, for each node u, calculate its interest similarity with node v and sort it in descending order. The interest similarity between nodes is calculated by cosine similarity, and the formula is as follows: Among them, \(i\) is the interest limit, and it has a total of \(c\) dimensions. represents the \(q\)-th dimensional interest vector of node \(u\). represents the \(q\)-th dimensional interest vector of node \(v\). By calculating the interest similarity between nodes, node pairs with similar interests can be identified. Step 3.2, select the top PI u non-direct neighbor nodes from the sorting result as the interest neighbor set IN u ; Step 3.3, record the interest neighbor sets of all nodes and construct server nodes.

5. An IM_GPE algorithm for identifying the influence of network nodes, characterized in that: It includes the following steps: Step 1, input the interest social network; For an interest social network, it can be modeled as G=(V, E, I), where V represents the set of all nodes, E represents the set of interaction relationships between nodes, and I represents the set of interest characteristics of all nodes; Step 2, construct the propagation matrix; Step 3, calculate the mass of nodes; Step 4, calculate the gravitational acceleration of nodes; Step 5, calculate the relative height of nodes; Step 6, calculate the gravitational potential energy.

6. The IM_GPE algorithm for identifying the influence of network nodes according to claim 5, characterized in that: The specific content of Step 2 is as follows: For the input interest social network G=(V, E, I), the adjacency matrix A and the interest characteristic matrix H of the network can be obtained. H is used to represent the interest-based interaction relationships between nodes, and the formula is as follows: Among them, x and y represent the indices of positions in matrix H, where the range of x is (1, 2, 3... n), the range of y is (1, 2, 3... n), and h x,y is the value at the i-th row and j-th column of matrix H, and the value of n is the number of all nodes; IN u Denote the set of the interest neighbors of node u. After obtaining the adjacency matrix A and the interest feature matrix H of the network, the propagation matrix P = A + H can be calculated. The propagation matrix P represents the propagation relationship in the interest social network, and the reconstructed graph G' can be obtained according to the propagation matrix P.

7. The IM_GPE algorithm for identifying the influence of network nodes according to claim 6, characterized in that: The specific content of Step 3 is as follows: The node mass is a key indicator to measure the local influence of nodes, and its calculation formula is: where \(e\) is the natural constant, is the out-degree of node \(u\), and \(\varphi(u)\) is an adjustment factor used to stabilize the evaluation of node quality and avoid overestimation or underestimation caused by small changes in the out-degree. The calculation formula for the adjustment factor is as follows:

8. The IM_GPE algorithm for identifying the influence of network nodes according to claim 7, characterized in that: The specific content of Step 4 is as follows: The gravitational acceleration is a key indicator to measure the global influence of nodes, and the calculation formula is: Among them, represents the set of out-neighbors of node u, and w u is the weight of node u, which is expressed as the product of the out-degree of node u and the k-shell value. α u,v is the number of triangles formed by node u and node v. cf u,v is the connection factor between node u and node v, which is calculated as follows: cf u,v =(k u -α u,v )×(k v -α u,v )#(8) Acceleration due to gravity g u By considering the connection relationship between node u and node v, it reflects the global influence of node u in the network.

9. The IM_GPE algorithm for identifying the influence of network nodes according to claim 8, characterized in that: The specific content of Step 5 is as follows: First, calculate the product of the mass m of node u u and the acceleration of gravity g u to obtain the gravitational centrality G of the node u , for a preliminary assessment of the propagation ability of the node. The calculation formula is as follows: G u = m u · g u #(10) To alleviate the influence overlap problem, the relative height is introduced to "avoid the rich club" effect; for any node u in the network, its relative height is defined as shown in formula (11): where λ is an adjustable parameter between (0, 1), and δ(u) represents the minimum value of the shortest path from node u to a more influential node z. The calculation formula of δ(u) is as follows, δ(u) = min x∈Φ(u) (dist u,z )#(12) where Φ(u) is the set of nodes z that are more influential than u.

10. The IM_GPE algorithm for identifying the influence of network nodes according to claim 9, characterized in that: The specific content of Step 6 is as follows: For node u in the network, the value of its GPE is defined as shown in formula (13): GPE u = G u ·h u #(13) To facilitate the comparison and analysis of GPE values at different nodes, the min-max normalization technique is used to scale the GPE values to the range [0, 1]; This standardization process is crucial for eliminating the influence of different scales and units, enabling a more consistent and interpretable assessment of node impacts. The standardized GPE values are calculated using Equation (14). Here, GPE min and GPE max represent the minimum and maximum GPE values in the network, respectively. By applying this normalization, it is ensured that the GPE values are scaled proportionally to the range [0, 1], where 0 represents the minimum influence and 1 represents the maximum influence; The normalized GPE values provide a clear and consistent metric for evaluating node impacts and enhance the interpretability of the results. The obtained GPE values are sorted in descending order, and the top k largest values are selected as seed nodes, where k is a natural number and its value is determined manually.

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