Rumor suppression maximization method based on overlapping communities

Abstract

The invention discloses an overlapping community-based rumor suppression maximization method, which comprises the following steps of: firstly, dividing a social network related to a rumor source into a plurality of communities based on a democratic estimation algorithm of a network modular organization, and identifying overlapping communities and overlapping nodes in the communities; secondly, distributing a positive seed node budget for each community in proportion according to the community scale, screening out the positive seed nodes with the most influence in each community according to the trust center value, selecting the positive seed nodes meeting the community positive seed node budget from the positive seed nodes, forming a candidate positive seed node set, and incorporating the candidate positive seed node set into overlapped nodes; and finally, optimizing the candidate positive seed node set by using a genetic algorithm to generate an optimal positive seed node set. According to the method, the network position attributes of the nodes are comprehensively considered, the precision and effect of the positive sub-nodes are improved, good adaptability and expansibility are achieved in networks of different scales, and the dual targets of rumor suppression and true phase propagation are effectively achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of social network information suppression, and particularly relates to a method for maximizing rumor suppression based on overlapping communities. Background Art

[0002] With the rapid development of network information technology, more and more people spread and share information through social networks. However, the prevalence of social networks has also facilitated the rapid spread of rumors and false information, which not only causes public panic, but may also damage reputations, mislead decisions, and even bring serious social, economic, and political consequences. Timely and effective rumor suppression can reduce the spread of false information, reduce public misunderstanding and panic, and thus maintain social stability and order.

[0003] Regarding rumor suppression, the main strategies proposed by researchers are network interruption strategies and network balance strategies. Among them, the network interruption strategy is to remove or block a group of the most influential nodes or key edges to minimize the spread of rumors; the network balance strategy is to select a group of the most influential positive seed nodes in the network to spread true information. In the network interruption strategy, blocking influential users may prevent them from spreading valuable information on other important topics, which will not only cause dissatisfaction of some users with the network, but may even cause turmoil in the network structure; even if rumors are suppressed by blocking some key edges, users can still continue to spread rumors through other unblocked edges. Therefore, the network interruption strategy has many limitations in practical applications, and the network balance strategy is more helpful for suppressing the spread of rumors.

[0004] In addition, due to the characteristic of the community structure of social networks, that is, the nodes within the community are closely connected, while the connections between different communities are relatively weak. Most existing studies search for positive seed nodes that maximize local influence within the community, but do not fully consider the propagation potential of overlapping nodes. However, in real life, overlapping nodes, as the hubs of multiple communities, play a crucial role in information dissemination. Reasonably using the overlapping nodes in the overlapping community structure can not only effectively connect each community, break through the barriers between communities, but also spread true information to different communities, expand the coverage of information, and thus significantly slow down the spread of rumors. Therefore, using the key role of overlapping nodes in suppressing the spread of rumors is an effective way to solve the rumor suppression problem. Summary of the Invention

[0005] Aiming at the problems existing in the above background art, the purpose of the present invention is to provide a method for maximizing rumor suppression based on overlapping communities.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A method for maximizing rumor suppression based on overlapping communities, comprising the following steps: S1. Divide the social network involving the rumor source into multiple communities by using the democratic estimation algorithm based on network modular organization, and identify the overlapping communities and overlapping nodes in the communities; S2. Allocate the positive seed node budget for each community according to the community size proportionally, screen out the most influential positive seed nodes in each community according to the trust centrality value, select the positive seed nodes that meet the community positive seed node budget from the most influential positive seed nodes in each community to form a candidate positive seed node set, and at the same time incorporate the overlapping nodes into the candidate positive seed node set; S3. Optimize the candidate positive seed node set by using the genetic algorithm, first generate the initial population of the genetic algorithm, then perform crossover and mutation operations on the initial population, and finally generate the optimal positive seed node set.

[0007] Further, in step S1, when dividing the community by using the democratic estimation algorithm based on network modular organization, first gradually analyze the local neighborhood of each node in the social network, then dynamically adjust the community division by using the voting mechanism, and retain similar or overlapping communities through weighted connection to identify the overlapping communities and overlapping nodes in the social network.

[0008] Further, in step S2, the number of candidate positive seed nodes for allocating the positive seed node budget for each community is calculated according to the following formula: (1) In the formula, represents the number of nodes in the th overlapping community, is the number of selected overlapping communities, represents the number of nodes in the th overlapping community selected from , is the positive seed node budget.

[0009] Further, in step S2, the trust centrality value is obtained by calculating the comprehensive centrality value of the degree centrality, betweenness centrality, closeness centrality and PageRank value of the node, and calculating the distance between each node in the community and the rumor source node through the breadth-first algorithm. Sort the trust centrality values of each node in the community, and evaluate the influence of the node in the community according to the sorting.

[0010] Further, the trust centrality value of each node in the community is calculated by the following formula: (2) (3) In the formula, is the trust center value of the node ; is the comprehensive centrality value of the node ; is the shortest path length from any rumor seed to the node ; Set the rumor seed node at level 0, the direct neighbors of the rumor at level 1, and so on is the path length from the highest-level rumor seed to the node ; , , , respectively represent the centrality values of the degree centrality, betweenness centrality, closeness centrality and PageRank value of the node ; , , , are all weight coefficients.

[0011] Furthermore, the method for optimizing and processing the candidate positive seed node set by the genetic algorithm includes the following steps: S301. Initialize the population: Normalize the candidate positive seed node set according to the trust center value, calculate the cumulative probability of the candidate positive seed nodes, and randomly select vertices from the candidate positive seed node set as candidate solutions, and insert the candidate solutions into the population to generate an initial population; S302. Crossover: Perform single-point crossover operation, randomly select two parent solutions from the initial population and perform crossover at a random position to ensure that there are no duplicate nodes in the offspring; If the number of nodes in the child solution is less than , then randomly fill in from the unselected nodes according to the cumulative probability; S303. Mutation: Mutate the offspring after crossover, randomly select a node and replace it with another node according to the cumulative probability of the trust center value to increase the diversity of the population and avoid local optimum; Use the linear threshold model based on one-way state transition to perform diffusion simulation on the selected node, and select the optimal positive seed node set by comparing the diffusion range of the selected node, thereby generating the optimal positive seed node set.

[0012] Compared with the disadvantages and deficiencies of the prior art, the present invention has the following beneficial effects: (1) The method for maximizing rumor suppression based on overlapping communities proposed by the present invention is not limited to the local influence within a single community, but comprehensively considers the network position attributes of nodes, further improving the accuracy and effect of positive seed nodes, making it have good adaptability and scalability in different scale networks, and effectively achieving the dual goals of rumor suppression and truth dissemination; (2) The present invention allocates the positive seed node budget of the community proportionally according to the community scale, ensuring the rationality of the seed node allocation. (3) Using the genetic algorithm to generate the initial population for the candidate positive seed node set based on the overlapping community structure and the trust center value can ensure a more comprehensive coverage of high-influence nodes, laying a good foundation for the further search for the optimal positive seed set. Description of the Drawings

[0013] Figure 1 is a flowchart of the method for maximizing rumor suppression based on overlapping communities provided by an embodiment of the present invention; Figure 2 is a schematic structural diagram of obtaining node information by combining the TSSO module and the TRCE module provided by an embodiment of the present invention; Figure 3 is a schematic diagram of the competitive diffusion of truth and rumor under the TRCE module provided by an embodiment of the present invention. (a) is the given rumor and truth seed sets, (b) is the preliminary diffusion effect formed by the two seed node sets respectively influencing their directly adjacent nodes, (c) is the result of the competitive diffusion of rumor and truth affected by the influence threshold under a certain number of iterations, and (d) is the result of the competitive diffusion of rumor and truth affected by the decision threshold under a certain number of iterations; Figure 4 is a comparison chart of the truth diffusion ranges of different algorithms on four datasets under fixed threshold conditions; (a) represents the congress_network dataset, (b) represents the netscience dataset, (c) represents the email-Eu-core dataset, and (d) represents the Facebook dataset; Figure 5 is a comparison chart of the truth diffusion ranges of different algorithms on four datasets under random threshold conditions; (a) represents the congress_network dataset, (b) represents the netscience dataset, (c) represents the email-Eu-core dataset, and (d) represents the Facebook dataset. Detailed Embodiments

[0014] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0015] The flowchart of the method for maximizing rumor suppression based on overlapping communities of the present invention is as Figure 1As shown in the figure, fully considering the characteristics of node position and community overlap in rumor suppression, the rumor suppression effect and the spread range of the truth are improved. The following is a detailed description.

[0016] S1. The democratic estimation algorithm based on network modular organization divides the social network involving the rumor source into multiple communities, and identifies the overlapping communities and overlapping nodes in the communities.

[0017] In a social network, due to certain relationships, tight small groups will be formed, and this phenomenon is called community structure. The community structure has the following characteristics: the connections within the community are usually relatively dense, while the connections between communities are relatively sparse; this characteristic provides a theoretical basis for community division. However, in real social networks, there are often a large number of overlapping communities, many nodes belong to multiple communities at the same time, and the overlapping nodes connecting different communities usually have higher influence. Therefore, finding seed nodes within each community and among the overlapping nodes can improve the propagation efficiency.

[0018] In order to identify these key nodes across communities, the present invention uses the democratic estimation algorithm of network modular organization to divide communities. This algorithm is a bottom-up method that simulates the mode of preferential interaction between nodes and their neighbors during the information propagation process. By gradually analyzing the local neighborhoods of each node in the social network, using a voting mechanism to dynamically adjust the community division, and retaining similar or overlapping communities through weighted connections, the overlapping communities and overlapping nodes in the social network are identified. The democratic estimation algorithm of network modular organization is shown in Table 1: Table 1 Democratic Estimation Algorithm of Network Modular Organization In Table 1, represents the social network, represents a directed graph, is the node set, is the edge set, represents the overlapping community, represents the community similarity threshold, represents the node, represents the node The subgraph formed by the set of all neighbors of, represents applying the label propagation algorithm to calculate the local community structure, and the community obtained after dynamically updating the community to which the node belongs through labels.

[0019] S2. After completing the division of overlapping communities, allocate the positive seed node budget for spreading the truth to each community, and select a certain number of nodes with greater influence inside and outside the community as candidate seed nodes to spread the truth. To ensure the reasonable allocation of seed nodes, allocate the positive seed node budget to each community according to the proportion of the community size. Assume the social network is divided into communities, and the defined set of overlapping communities is , where the number of candidate positive seed nodes in each community is calculated according to the following formula: (1) In the formula, represents the number of nodes in the th overlapping community, is the number of selected overlapping communities, represents the number of nodes in the th overlapping community selected from , is the positive seed node budget.

[0020] For optimizing community selection, only communities with larger scales are considered in the experiment. The communities are screened through the community filtering parameter , and communities with fewer nodes are ignored. Finally, the top communities are selected according to the scale, where the value is determined according to Equation (2): (2).

[0021] After determining the budget allocation for each community, the most influential positive seed nodes in each community are screened. In a social network, the evaluation of node influence usually depends on various centrality metrics, including degree centrality, betweenness centrality, closeness centrality, and PageRank value. Although these centrality metrics have their own advantages, a single metric cannot comprehensively reflect the potential influence of a node in rumor propagation suppression. For example, degree centrality only focuses on direct connections and ignores the global position of the node; betweenness centrality overly relies on the global network structure and ignores local connections. Therefore, the present invention proposes a method based on the trust central value to comprehensively evaluate the influence of users in the community by combining multiple centrality metrics. This method not only combines the advantages of different metrics but also particularly considers the dynamic process of rumor propagation, effectively improving the intervention potential of positive seed nodes by combining the distance from the rumor source node.

[0022] The method for screening the most influential positive seed nodes in each community is as follows: a method based on the trust central value, which combines the centrality values of the degree centrality, betweenness centrality, closeness centrality, and PageRank value of the node. The trust central value is calculated by the following formula: (3) (4) In the formula, is the trust central value of node , is the node The comprehensive centrality value, is the shortest path length from any rumor seed to the node ; Set the rumor seed node at level 0, the direct neighbors of the rumor at level 1, and so on. is the path length from the rumor seed at the highest level to the node ; , , , respectively represent the centrality values of the degree centrality, betweenness centrality, closeness centrality, and PageRank value of the node ; , , , are all weight coefficients; Sort the trust centrality values of each node in the community, and evaluate the influence of the node in the community according to the sorting. Select the high-trust seed set that meets the positive seed budget of each community according to the number of candidate positive seed nodes calculated by formula (1) as the candidate positive seed node set. At the same time, since the connection between communities depends on overlapping nodes, when selecting candidate positive seed nodes, it is necessary to include overlapping nodes in the candidate positive seed node set to enhance the effect of real information dissemination between communities.

[0023] S3. Process the candidate positive seed node set based on the overlapping community structure and trust centrality value using the genetic algorithm. First, generate the initial population of the genetic algorithm, then perform crossover and mutation operations on the initial population, and finally generate the optimal positive seed node set, which has stronger propagation ability in the information diffusion process.

[0024] The genetic algorithm is an optimization technique inspired by natural selection and the evolution process. By performing crossover and mutation operations on the initial population, new candidate solutions are generated, and the quality of the solutions is evaluated according to the fitness function, gradually approaching the optimal solution. The method of the present invention generates the initial population of the genetic algorithm based on the overlapping community structure and trust centrality value to ensure a more comprehensive coverage of high-influence nodes, laying a good foundation for the further search for the optimal positive seed set.

[0025] Optimize the candidate positive seed node set using the genetic algorithm. The method includes the following steps: S301. Initialize the population: Normalize the candidate positive seed node set according to the trust centrality value, calculate the cumulative probability of the candidate positive seed nodes, and randomly select vertices from the candidate positive seed node set as candidate solutions, and insert the candidate solutions into the population to generate the initial population; S302. Crossover: Perform single-point crossover operation. Randomly select two parent solutions from the initial population and perform crossover at a random position, ensuring no duplicate nodes in the offspring; if the number of nodes in the sub-solution is insufficient , then randomly fill in from the unselected nodes according to the cumulative probability; S303. Mutation: Mutate the offspring after crossover. Randomly select a node and replace it with another node according to the cumulative probability of the trust center value to increase the diversity of the population and avoid local optimum; Use the linear threshold model based on one-way state transfer (LT1DT) to perform diffusion simulation on the selected node, and select the optimal positive seed node set by comparing the diffusion ranges of the selected nodes, so as to generate the optimal positive seed node set.

[0026] The positive seed node set optimized by the genetic algorithm can cover a wider network area, improve the information dissemination effect, and effectively inhibit the spread of rumors.

[0027] The generation algorithm of the optimal positive seed node set proposed by the present invention is implemented through the positive seed node selection optimization (TSSO) module, as shown in Table 2: Table 2 Generation algorithm of the optimal positive seed node set In the table, represents the set of all current candidate solutions, represents the number of iterations, represents the set of new candidate solutions generated by the crossover operation, represents the set of new candidate solutions generated by the mutation operation, represents the th candidate solution in which is a specific positive seed node set, represents the th new candidate solution in

[0028] To verify the technical effect of the rumor suppression maximization method based on overlapping communities of the present invention, a real-world dataset is selected for verification. In the experiment, the truth and rumor diffusion competition evaluation (TRCE) module based on the linear threshold model with one-way state transfer (LT1DT) simulates the competitive diffusion process of truth and rumor in the social network. This module analyzes the interaction and competition between positive seed nodes and rumor nodes in information dissemination, and analyzes the final rumor suppression effect and the scope of truth dissemination. The structural schematic diagram of node information obtained by combining the TSSO module and the TRCE module is as shown in Figure 2 . In the LT1DT model, the network N is represented by the quadruple ( ), where represents a directed graph, is the set of nodes, is the set of edges, is the set of edge weights, representing the intensity of influence propagation between nodes, is the set of influence thresholds of nodes, is the set of decision thresholds of nodes, is the number of rumor nodes. For a target node there are two associated thresholds: the influence threshold and the decision threshold , the influence threshold is used to measure the tendency of a node to participate in an activity or adopt information after being influenced by its neighbors, and the decision threshold represents the tendency of a node to take action after being influenced by a cascade . This model assumes that there are both rumors and the truth in the network. If there are two cascades, then a node can have three possible states: inactive state, rumor-activated state, and truth-activated state. In addition, there is an intermediate state, the influenced state. The propagation process of nodes starts from their respective seed sets, namely the negative seed set of rumors and the positive seed set of the truth , and the propagation process is divided into two stages: the influence stage and the decision stage.

[0029] In the influence stage, if the total influence exerted on an inactive target node by its active neighbors reaches or exceeds the influence threshold of the target node , then the target node will be activated and participate in the propagation activity, and this condition can be expressed as: (5) In the formula, represents the set of in-neighbors of the target node , that is, all neighbor nodes pointing to the target node .

[0030] In the decision stage, the behavior selection of a node is determined by the decision threshold . If the influence exerted on a target node by its rumor-activated neighbors, relative to the influence of all active neighbors, reaches or exceeds its decision threshold , then the target node will choose to accept the rumor, and this condition can be expressed as: (6) The propagation process terminates when no new nodes are activated and the states of the nodes remain unchanged. The spread of rumors and truths starts from the seed nodes and goes through multiple iterations until the propagation tends to be stable. The schematic diagram of the competitive spread of truth and rumors under the TRCE module is as shown in Figure 3 shown. According to Figure 3 the schematic diagrams of the competitive spread of rumors and truths shown in (a)-(d) in

[0031] The selected real-world datasets are as follows: (1) congress_network: Based on the interaction network of a certain member on Twitter, the nodes represent members, and the edges represent the relationship of forwarding, quoting, replying or mentioning between members to quantify the information propagation probability; (2) netscience: Derived from the scientific cooperation network, the nodes represent scientists, and the edges represent the cooperation relationship between scientists, which is used to simulate the spread and influence of information in the scientific research field; (3) email-Eu-core: Based on the email interaction of a large European research institution, the nodes represent the members of the research institution, and the edges represent at least one email exchange between members; (4) Facebook: It is composed of a "friend list" from Facebook. The nodes represent users, and the edges represent the social connections between users, reflecting the social relationships between users; The basic information of the four datasets is shown in Table 3: Table 3 Basic Information of Four Datasets Set the community similarity threshold in the democratic estimation algorithm for network modular organization to 0.8, and set the community filtering parameter to 10. In the weight setting of the comprehensive centrality value, the weights of degree centrality and betweenness centrality are both set to 0.4, while the weights of closeness centrality and Pagerank value are both set to 0.1. The LT1DT model is used for the competitive spread of rumors and truths, and the influence threshold and decision threshold are set to be random or fixed. The fixed threshold is selected as 。The number of rumor seeds is set to 1% of the number of dataset nodes, and seed nodes are selected based on the maximum degree or randomly. The size of the positive seed node set is set to 10 to 50 (step size of 10) in the netscience, email-Eu-core, and Facebook datasets, generating a total of 10 instances. Since the congress_network dataset is relatively small, when the number of positive seeds reaches 20, most nodes in the network have been covered, and continuing to increase the number of seeds has little effect on reducing the number of nodes affected by the rumor. Therefore, only the cases where the number of positive seeds is 5 to 20 (step size of 5) are considered in the congress_network dataset, generating a total of 8 instances.

[0032] To verify the effectiveness of the present invention, several currently popular and high-performance algorithms are selected as benchmark algorithms for comparative experiments. The experimental results of the following algorithms are all cited from the original papers: MinGreedy (MG): Select a node that minimizes the spread of the rumor to the greatest extent in each iteration until the specified number of nodes is selected or the spread of the rumor cannot be further reduced; ProxMinGreedy (PMG): Iteratively select the node with the smallest gain in rumor spread from the neighbors of the rumor seed nodes; PageRank (PR): By calculating the PageRank value of the nodes, select the node with the highest PageRank value as the positive seed node to contain the spread of the rumor; ProxPageRank (PPR): Select the node with the highest PageRank value from the neighbors of the rumor seed nodes; ContrId (CI): Based on the dynamic rumor spread, identify the nodes that contribute the most to the spread of the rumor, calculate the contribution of each node to the activation of external neighbors during the spread process, and interrupt the critical path of the rumor spread; ProxContrId (PCI): Select the node that contributes the most to the spread of the rumor from the neighbors of the rumor seed nodes as the positive seed node; GA: This genetic algorithm only depends on betweenness centrality when generating the initial population, selects positive seed nodes randomly from the entire network, and gradually optimizes the node set through crossover and mutation operations to suppress the spread of the rumor.

[0033] For each dataset, under the conditions of two fixed thresholds and rumor seeds selected based on the maximum degree, the effects of the present invention and different baseline algorithms in suppressing rumors are evaluated by comparing the diffusion values of rumors. The generation algorithm of the optimal positive seed node set of the present invention is denoted as RSM-OC. In different instances of four datasets, the average number of nodes affected by rumors and the truth for each algorithm are shown in Tables 4 - 7: Table 4 Average number of nodes affected by rumors and the truth in 8 instances generated from the congress_network dataset Table 5 Average number of nodes affected by rumors and the truth in 10 instances generated from the netscience dataset Table 6 Average number of nodes affected by rumors and the truth in 10 instances generated from the email-Eu-core dataset Table 7 Average number of nodes affected by rumors and the truth in 10 instances generated from the Facebook dataset As shown in the table, RSM-OC performs significantly better than other algorithms on the four datasets, demonstrating strong rumor suppression and truth dissemination capabilities, especially in complex networks such as Facebook and email-Eu-core. For example, in the email-Eu-core dataset, RSM-OC reduces an average of 9.3 rumor nodes compared to GA; in Facebook, it reduces an average of 21 nodes and far outperforms traditional heuristic algorithms. Although the MG and PMG algorithms perform slightly better in the netscience dataset, overall, RSM-OC still has a significant advantage, with the average rumor suppression rate increasing by 23.3% compared to the baseline algorithms, achieving more efficient rumor control. In addition, the truth dissemination range of RSM-OC on the four datasets is on average twice as large as that of the baseline algorithms. Especially in netscience and email-Eu-core, the average number of nodes affected by the truth is 24.7 and 22.3 more than that of GA respectively, showing the significant two-way optimization effect of RSM-OC in suppressing rumors and spreading the truth.

[0034] On the basis of evaluating the rumor suppression effect, the performance of each algorithm in the truth dissemination range is further analyzed. To more comprehensively demonstrate the ability to spread positive information, all algorithms adopt two settings: deterministic and random, namely: (1) fixed threshold and rumor seeds based on the maximum degree, (2) randomly select the threshold and rumor seeds. Figure 4 andFigure 5 They respectively show the performance differences of RSM-OC and other baseline algorithms in terms of the truth diffusion range under fixed threshold conditions and random threshold conditions.

[0035] As Figure 4 shown in (a)-(d), as the positive seed budget increases, the truth diffusion ranges of all algorithms generally show an upward trend, and RSM-OC always performs the best. Among them, for the PR algorithm, its truth diffusion effect is only good on the netscience dataset ( Figure 4 (b)), indicating that the algorithm has limited ability to identify key nodes in different networks. For the GA algorithm, although it is superior to traditional heuristic algorithms in most cases, its truth diffusion range is still inferior to that of RSM-OC. For example, on the email-Eu-core ( Figure 4 (c)) and Facebook ( Figure 4 (d)) datasets, the advantage of RSM-OC over GA is more significant. In addition, for other traditional heuristic algorithms (such as CI, PCI, PPR, etc.), when the budget increases, the increase in the diffusion range is relatively small, especially their performance gradually lags behind at larger seed numbers, while RSM-OC shows stronger scalability at medium and high budgets.

[0036] Figure 5 Among them, (a) represents the congress_network dataset, (b) represents the netscience dataset, (c) represents the email-Eu-core dataset, and (d) represents the Facebook dataset. It can be intuitively seen from the figure that RSM-OC shows good adaptability and robustness in all datasets. Its truth propagation range is always better than that of other baseline algorithms and steadily expands as the positive seed budget increases. On the contrary, for some baseline algorithms, although their performance is slightly better than that of RSM-OC on individual datasets, they have problems with low robustness in the random propagation environment and cannot well adapt to different types of datasets. Generally speaking, the stable performance and effective propagation ability of RSM-OC highlight its advantages in dealing with uncertain propagation environments in complex networks.

[0037] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A rumor suppression maximization method based on overlapping communities, characterized in that: The following steps are involved: S1. The democratic estimation algorithm based on network modular organization divides the social network involving the rumor source into multiple communities and identifies the overlapping communities and overlapping nodes in the communities; S2. Allocate a positive seed node budget to each community in proportion to the community size, select the most influential positive seed nodes in each community according to the trust center value, select positive seed nodes that meet the community positive seed node budget from the most influential positive seed nodes in each community, form a candidate positive seed node set, and include the overlapping nodes in the candidate positive seed node set; S3. Optimizing the candidate positive seed node set by using a genetic algorithm, first generating an initial population of the genetic algorithm, then performing crossover and mutation operations on the initial population, and finally generating an optimal positive seed node set.

2. The rumor suppression maximization method based on overlapping communities as claimed in claim 1, characterized in that: In step S1, when the democratic estimation algorithm of the network modular organization divides the community, it first gradually analyzes the local neighborhood of each node in the social network, then dynamically adjusts the community division using a voting mechanism, and retains similar or overlapping communities through weighted connections, thereby identifying overlapping communities and overlapping nodes in the social network.

3. The rumor suppression maximization method based on overlapping communities as claimed in claim 1, characterized in that: In step S2, the number of candidate positive seed nodes allocated to each community is Calculated as follows: （1） In the formula, Indicates The number of nodes in overlapping communities, is the number of overlapping communities selected, Indicates from Selected in The number of nodes in overlapping communities, Budget for positive seed nodes.

4. The rumor suppression maximization method based on overlapping communities as claimed in claim 1, characterized in that: In step S2, the trust center value is obtained by calculating the comprehensive centrality value of the node's degree centrality, betweenness centrality, closeness centrality and PageRank value, and calculating the distance between each node in the community and the rumor source node through the breadth-first algorithm. The trust center value of each node in the community is sorted, and the influence of the node in the community is evaluated based on the sorting.

5. The rumor suppression maximization method based on overlapping communities as claimed in claim 4, characterized in that: The trust center value of each node in the community is calculated by the following formula: （2） （3） In the formula, For Node The trust center value of For Node The comprehensive centrality value of is from any rumor seed to the node The shortest path length; The highest level rumor seed to the node The path length; , , , Respectively represent nodes The centrality values ​​of degree centrality, betweenness centrality, closeness centrality and PageRank value, , , , are all weight coefficients.

6. The rumor suppression maximization method based on overlapping communities as claimed in claim 1, characterized in that: In step S3, the method of optimizing the candidate positive seed node set using a genetic algorithm comprises the following steps: S301, initializing the population: normalizing the candidate positive seed node set according to the trust center value, calculating the cumulative probability of the candidate positive seed node, and randomly selecting from the candidate positive seed node set using probability distribution Vertices are taken as candidate solutions, and the candidate solutions are inserted into the population to generate the initial population; S302, crossover: Perform a single-point crossover operation, randomly select two parent solutions from the initial population and crossover at random positions to ensure that there are no duplicate nodes in the offspring; if there are not enough nodes in the child solution , then fill in randomly from the unselected nodes according to the cumulative probability; S303, mutation: mutate the offspring after crossover, randomly select a node and replace it with another node according to the cumulative probability of the trust center value, use the linear threshold model based on unidirectional state transfer to simulate the diffusion of the selected node, and select the optimal positive seed node set by comparing the diffusion range of the selected node.

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