An information dissemination control method based on the high-order structure of the network

Abstract

The present invention belongs to the field of Internet technologies, and in particular relates to a method for controlling information dissemination based on the high-order structure of a network. The present invention fills the gap in the relationship between the high-order structure and network functions, and innovatively proposes to regulate the number of high-order structures of a network by means of reconnection, which can generate or disassemble 2-simplices of a real network while keeping the degree sequence unchanged. In addition, another advantage of the present invention is that through experimental verification, the change of the network dissemination ability with the number of high-order structures is calculated, and the significant influence of the number of high-order structures on the network dissemination dynamics is found, and it can be used to design strategies for controlling network dissemination behavior. For example, when the dissemination probability is low, the edges of the 2-simplex structure can be disassembled to inhibit the spread of an epidemic. In terms of information dissemination, increasing the 2-simplex structure in a social network can effectively promote the dissemination and popularization of new products, providing effective tools and strategies for dissemination control.

Description

Technical Field

[0001] The present invention belongs to the field of Internet technologies, and in particular, relates to an information dissemination control method based on a network high-order structure. Background Art

[0002] Complex networks are network-based descriptions of complex systems, consisting of nodes and edges, and widely exist in many real-world systems, such as social networks, biological networks, and brain neural networks. In recent years, complex networks have been widely applied in aspects such as information dissemination, disease spread, and product promotion. In social networks, by analyzing the topological structure of the network and the connection methods between nodes, information dissemination strategies can be optimized, and the efficiency and influence of information dissemination can be improved. In the field of epidemiology, it can help predict and control the spread of diseases, thereby guiding the formulation of disease prevention and control measures, and providing powerful tools and methods for solving practical problems in the social, economic, and scientific fields.

[0003] Previous studies only considered the structure and dynamic behavior of pairwise networks (i.e., networks consisting of nodes and edges). However, in many practical cases, the dissemination behavior of networks is not a simple pairwise relationship, but a complex dissemination involving multiple individuals. For example, in a community, some people adopt a new product, and a person will be persuaded by the people who have already adopted the product to adopt the product. To better describe such interactions involving multiple individuals, a more complex high-order network (i.e., a network with interactions among multiple individuals) structure needs to be introduced.

[0004] The high-order structures widely existing in real networks mainly include simplices, that is, fully connected subgraph structures. For example, a node is a 0-simplex, an edge is a 1-simplex, a triangle is a 2-simplex, a tetrahedron is a 3-simplex, and so on. Modeling complex networks using high-order structures can discover non-trivial characteristics ignored in traditional pairwise interaction networks and better understand the dissemination dynamics of networks. In existing technologies, the research on dissemination control still remains at a low level, and the research on high-order network models does not consider real networks either. There is a lack of research combining high-order structures with network dissemination capabilities, especially in terms of dissemination control, and there is no corresponding technology on how to use high-order network structures to control phenomena such as information dissemination and disease spread. Therefore, developing a method that can quantify how high-order structures systematically affect the dissemination dynamics of real networks has become the research focus in the current field of dissemination control. Summary of the Invention

[0005] Based on the above background, the present invention provides an information propagation control method based on the high-order structure of a network, which can effectively capture the high-order structure and complex propagation behavior in the network, and provides a new solution idea for the field of propagation control. The method of the present invention mainly includes: first, find all cliques from the traditional pairwise interaction network to obtain the clique complex of the network, and regard each clique as a simplex in the simplicial network to obtain a simplicial complex network with high-order interactions. Iterate each network by the method of edge breaking and reconnecting to generate and disassemble the high-order structure (2-simplex), and satisfy the following three restrictive conditions: (1) ensure that there are no multiple edges and self-loops in the network; (2) maintain the network connectivity; (3) maintain the degree distribution unchanged. When the algorithm reaches the given number of re-selections R, stop the iteration, represent the number of successful reconnections as n, indicating that the generated simplex model has generated or disassembled 100% of the 2-simplices. During the iteration, the simplex models generated every 0.1n successful reconnections will be saved, and all results will be statistically analyzed by the average value of 10 realizations.

[0006] The technical solution of the present invention is as follows:

[0007] An information propagation control method based on the high-order structure of a network, comprising the following steps:

[0008] Sl. Obtain a pairwise interaction network for information propagation. The pairwise interaction network consists of nodes and edges, and use the pairwise interaction network to generate a simplicial complex network;

[0009] S2. Generate and disassemble the high-order structures in the simplicial complex network respectively to obtain simplex models with different numbers of high-order structures. The specific method is as follows:

[0010] Generating the high-order structure of the network includes setting the maximum number of iterations R for re-selecting the 2-simplices to be generated g , and initialize r = 1:

[0011] a1. Randomly select a node v1 with uniform probability, and satisfy that the degree d1 of the node v1 ≥ 2;

[0012] a2. Randomly select nodes v2 and v3 from the neighbors of the node v1 with uniform probability, and judge whether the degrees d2 and d3 of the nodes v2 and v3 satisfy d2, d3 ≥ 2 and there is no edge between v2 and v3. If so, enter step a3; otherwise, let r = r + 1 and return to step a1;

[0013] a3. Randomly select a node v4 from the neighbors of the node v2, and judge whether it satisfies that the node v4 is different from the node v1 and the node v4 has no common neighbors with the node v2. If so, enter step a4; otherwise, return to step a2; at the same time, use the same method to randomly select a node v5 from the neighbors of the node v3;

[0014] a4. Remove edge e 24 and e 35 , connect edge e 23 and e 45 , judge the network connectivity. If it is connected, at least one 2 - simplex is generated and defined as a successful reconnect. Edge e ij refers to the connecting edge between node v i and node v j . Let r = 1. If it is not connected, restore the connecting edge, let r = r + 1, and go back to step a1;

[0015] a5. Judge whether r = R g holds. If so, end and obtain the generated multiple 2 - simplex models. Otherwise, go back to step a1;

[0016] Decomposing the network high - order structure includes setting the maximum iteration number R for re - selecting the 2 - simplex to be decomposed d , and initializing r = 1:

[0017] b1. Randomly select a 2 - simplex (v1, v2, v3) with uniform probability;

[0018] b2. Randomly select an edge e from all connecting edges 45 such that nodes v4 and v5 are not connected to any node of the 2 - simplex selected in step b1. Otherwise, let r = r + 1 and go back to step b1;

[0019] b3. Remove edge e 23 and e 45 , connect edge e 24 and e 35 , judge the network connectivity. If it is connected, at least one 2 - simplex is decomposed and defined as a successful reconnect. Let r = 1. If it is not connected, restore the connecting edge, let r = r + 1, and go back to step b1;

[0020] b4. Judge whether r = R d holds. If so, end and obtain the decomposed multiple 2 - simplex models. Otherwise, go back to step b1;

[0021] S3. Use the SIR model to calculate the propagation ability of the original pairwise interaction network and the simplex models after generating 2 - simplex and decomposing 2 - simplex in step S2; Select the nodes with the top 1% in the number of node - associated 2 - simplexes as the initial infected, and the remaining nodes as the susceptible. The proportion of immune nodes after the end of the propagation is the propagation ability. Set the recovery rate γ = 1, and the infection rate β = λ c , 2λ c , 3λ c , 5λ c , 8λ c, where λ c is the transmission threshold of the SIR model, <k>is the average degree of the network, <k 2 > is the second moment of the network degree distribution, and the calculation formula is

[0022]

[0023] S4. Calculate the change rate of the network propagation ability with the change in the number of higher-order structures under different propagation probabilities; specifically, repeat 500 random experiments on the empirical network and the model network. Under different propagation probabilities, calculate the change rate of the propagation ability between the original network and the simplex model after generating (disassembling) 2-simplices, and quantify the impact of higher-order structures on the propagation dynamics;

[0024] S5. Control the information propagation according to the relationship between the number of higher-order structures in the network and the propagation ability. Specifically, according to the obtained relationship, weaken or enhance the information propagation ability by disassembling 2-simplices or adding 2-simplices.

[0025] Furthermore, when generating and disassembling the higher-order structures in the simplicial complex network in S2, the following restrictive conditions need to be met:

[0026] (1) Ensure that there are no multiple edges and self-loops in the network;

[0027] (2) Maintain the network connectivity;

[0028] (3) Keep the degree distribution unchanged..

[0029] The beneficial effects of the present invention are as follows: It fills the gap in the relationship between higher-order structures and network functions, and innovatively proposes to regulate the number of higher-order structures in the network by means of rewiring, enabling the generation or disassembly of 2-simplices of real networks while keeping the degree sequence unchanged. In addition, another advantage of the present invention is that through experimental verification, the change of the network propagation ability with the number of higher-order structures is calculated, and it is found that the number of higher-order structures has a significant impact on the network propagation dynamics, and it can be used to design strategies for controlling network propagation behavior. For example, when the propagation probability is low, the edges of the 2-simplex structure can be disassembled to inhibit the spread of the epidemic. In terms of information propagation, increasing the 2-simplex structure in the social network can effectively promote the spread and promotion of new products, providing effective tools and strategies for propagation control. Description of the Drawings

[0030] Figure 1 is the flowchart of the method of the present invention.

[0031] Figure 2 is the schematic diagram of the process of generating and disassembling higher-order structures in the present invention.

[0032] Figure 3 This shows the change of the network propagation ability with the number of higher-order structures under different propagation probabilities in the present invention. Among them, (a) represents the propagation ability of 4 real networks, (b) represents the degree distribution of the Metabolic network, and (c) represents the propagation ability of the modified Metabolic network. Detailed implementation mode

[0033] The present invention will be described in detail below with reference to the accompanying drawings.

[0034] As shown in the attached Figure 1 drawing, the specific steps for information propagation control in the present invention are as follows:

[0035] Sl. Generate a simplicial complex network from the original network data;

[0036] S2. Generate and disassemble the higher-order structures (2-simplices) in the network respectively to obtain simplicial models with different numbers of higher-order structures;

[0037] S3. Use the SIR model to calculate the propagation ability of different networks;

[0038] S4. Calculate the change rate of the network propagation ability with the change of the number of higher-order structures under different propagation probabilities;

[0039] S5. Control information, disease transmission, etc. according to the relationship between the number of network higher-order structures and the propagation ability.

[0040] First, find all the cliques from the traditional pairwise interaction network to obtain the clique complex of the network, and regard each clique as a simplex in the simplicial complex network to obtain a simplicial complex network with higher-order interactions. Iterate each network by the method of edge breaking and reconnecting to generate and disassemble the higher-order structures (2-simplices), and satisfy the following three restrictive conditions: (1) Ensure that there are no multiple edges and self-loops in the network; (2) Maintain the network connectivity; (3) Maintain the degree distribution unchanged. When the algorithm reaches the given re-selection times R g or R d , stop the iteration, and represent the successful reconnection times as n, indicating that the generated simplicial model has generated or disassembled 100% of the 2-simplices. During the iteration, the simplicial models generated every 0.1n successful reconnections will be saved, and all results will be statistically analyzed by the average value of 10 realizations.

[0041] The process of generating network higher-order structures is as shown in the attached Figure 2 drawing. Set the maximum iteration times R g for re-selecting the 2-simplices to be generated, initialize r = 1, and the specific steps are as follows:

[0042] (1) Randomly select a node v1 with a uniform probability, and satisfy that the degree d1 of the node v1 ≥ 2;

[0043] (2) Randomly select nodes \(v_2\) and \(v_3\) from the neighbors of node \(v_1\) with uniform probability, and satisfy \(d_2, d_3\geq2\) and there is no edge between \(v_2\) and \(v_3\). Otherwise, let \(r = r + 1\) and return to step (1);

[0044] (3) Randomly select node \(v_4\) from the neighbors of node \(v_2\), and satisfy that node \(v_4\) is different from node \(v_1\) and node \(v_4\) has no common neighbors with node \(v_2\). Otherwise, return to step (2). According to the same method, randomly select node \(v_5\) from the neighbors of node \(v_3\);

[0045] (4) Remove edge \(e\) 24 and \(e\) 35 , connect edge \(e\) 23 and \(e\) 45 , judge the network connectivity. If it is connected, at least one 2 - simplex is generated and defined as a successful reconnect. Let \(r = 1\). If it is not connected, restore the connection of the edge, let \(r = r + 1\), and return to step (1);

[0046] (5) Judge whether \(r = R\) g holds. If so, end and obtain the generated multiple 2 - simplex models. Otherwise, return to step (1).

[0047] The process of disassembling the high - order structure of the network is as shown in the appendix Figure 2 , set the maximum number of iterations \(R\) d for re - selecting the 2 - simplex to be disassembled, initialize \(r = 1\), and the specific steps are as follows:

[0048] (1) Randomly select a 2 - simplex \((v_1, v_2, v_3)\) with uniform probability;

[0049] (2) Randomly select an edge \(e\) 45 from all the edges, and satisfy that nodes \(v_4\) and \(v_5\) are not connected to any node of the 2 - simplex selected in step (1). Otherwise, let \(r = r + 1\) and return to step (1);

[0050] (3) Remove edge \(e\) 23 and \(e\) 45 , connect edge \(e\) 24 and \(e\) 35 , judge the network connectivity. If it is connected, at least one 2 - simplex is disassembled and defined as a successful reconnect. Let \(r = 1\). If it is not connected, restore the connection of the edge, let \(r = r + 1\), and return to step (1);

[0051] (4) Judge whether \(r = R\) d holds. If so, end and obtain the disassembled multiple 2 - simplex models. Otherwise, return to step (1).

[0052] Secondly, the SIR model is used to calculate the propagation ability of different networks. Nodes with the top 1% in the number of node-associated 2-simplices are selected as the initial infected individuals, and the remaining nodes are used as susceptible individuals. The proportion of immune individuals after the end of the propagation is the propagation ability. The recovery rate γ is set to 1, and the infection rate β is set to λ c , 2λ c , 3λ c , 5λ c , 8λ c , where λ c is the propagation threshold of the SIR model, <k>is the average degree of the network, <k 2 >> is the second moment of the network degree distribution, and the calculation formula is

[0053]

[0054] Finally, repeat 500 random experiments on the empirical network and the model network. At different propagation probabilities, calculate the change rate of the propagation ability between the original network and the simplex model after generating (disassembling) 2-simplices, and quantify the impact of the high-order structure on the propagation dynamics.

[0055] Figure 3 are the results of the impact of the number of 2-simplices on the propagation dynamics. The x-axis represents the proportion of generated or disassembled 2-simplices in the generated simplex model. The y-axis represents the change rate of the propagation ability of each simplex model compared to the simplex model with the least number of 2-simplices. For the change in the propagation ability, first, as the number of 2-simplices increases, when the infection probability is equal to the propagation threshold, i.e., β = λ c , the propagation ability of the network is greatly improved. Compared with the network with the least number of 2-simplices, on the three datasets, the propagation ability of the network increases from 30% to more than 100%. Second, when the infection rate increases from 2λ c to 8λ c , the propagation ability of the network even decreases slightly, indicating that increasing the number of 2-simplices will inhibit its propagation. For the Metabolic network, after deleting the nodes with extremely large degrees, the corrected network is consistent with the results of other networks.

[0056] The simplex model generated by the present invention discovers the significant impact of the number of high-order structures on the network propagation dynamics. Based on the experimental results of the above propagation model, strategies for controlling the network propagation behavior can be designed. For example, when the propagation probability is low, the edges of the 2-simplex structure can be disassembled to inhibit the spread of the epidemic. In terms of information dissemination, increasing the 2-simplex structure in the social network can effectively promote the spread and promotion of new products, providing effective tools and strategies for propagation control.< / k> < / k>

Claims

1. An information dissemination control method based on the network high-order structure, characterized in that It includes the following steps: S1. Obtain a pairwise interaction network for information dissemination. The pairwise interaction network consists of nodes and edges, and generate a simplicial complex network using the pairwise interaction network; S2. Generate and disassemble the high-order structures in the simplicial complex network respectively to obtain simplicial models with different numbers of high-order structures. The specific method is as follows: The high-order structure of the generation network includes setting the maximum number of iterations R for reselecting the 2-simplices to be generated g , initialize r = 1: a1. Randomly select a node v1 with a uniform probability, and ensure that the degree d1 of the node v1 ≥ 2; a2. Randomly select nodes v2 and v3 from the neighbors of the node v1 with a uniform probability, and judge whether the degrees d2 and d3 of the nodes v2 and v3 satisfy d2, d3 ≥ 2 and there is no edge between v2 and v3. If so, go to step a3; otherwise, let r = r + 1 and return to step a1; a3. Randomly select a node v4 from the neighbors of the node v2, and judge whether it satisfies that the node v4 is different from the node v1 and the node v4 has no common neighbors with the node v2. If so, go to step a4; otherwise, return to step a2. At the same time, use the same method to randomly select a node v5 from the neighbors of the node v3; a4. Remove edge e 24 and e 35 , connect edge e 23 and e 45 , determine the network connectivity. If it is connected, generate at least one 2 - simplex and define it as a successful reconnection. Edge e ij refers to the connecting edge between node v i and node v j . Let r = 1. If it is not connected, restore the connecting edge, let r = r + 1, and go back to step a1; a5. Determine whether r = R g holds. If so, end and obtain the generated multiple 2-simplex models; otherwise, return to step a1. The disassembled network high-order structure includes setting the maximum number of iterations R for reselecting the 2-simplices to be disassembled d , initialize r = 1: b1. Randomly select a 2-simplex (v1, v2, v3) with a uniform probability; b2. Randomly select an edge e from all the connected edges 45 , such that nodes v4 and v5 are not connected to any node of the 2-simplex selected in step b1. Otherwise, let r = r + 1 and go back to step b1; b3. Remove edge e 23 and e 45 , connect edge e 24 and e 35 , determine the network connectivity. If it is connected, at least one 2-simplex is disassembled and defined as a successful reconnect. Let r = 1. If it is not connected, restore the connected edge, let r = r + 1, and go back to step b1; b4. Determine whether r = R d holds. If so, end and obtain multiple disassembled 2-simplex models; otherwise, return to step b1; S3. Use the SIR model to calculate the propagation capabilities of the original pairwise interaction network and the simplicial model after generating and disassembling 2-simplices in step S2; S4. Calculate the change rate of the network propagation capability with the change of the number of high-order structures under different propagation probabilities; S5. Control information dissemination according to the relationship between the number of high-order structures in the network and the propagation capability. Specifically, according to the obtained relationship, weaken or enhance the information dissemination capability by disassembling 2-simplices or adding 2-simplices.

2. The information dissemination control method based on the network high-order structure according to claim 1, characterized in that When generating and disassembling the high-order structures in the simplicial complex network in S2, the restrictive conditions to be satisfied are: (1) Ensure that there are no multiple edges and self-loops in the network; (2) Maintain the network connectivity; (3) Maintain the degree distribution unchanged.

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