Hypergraph-based anti-telepathic propagation model

Abstract

The present application relates to the technical field of anti-remote language transmission, in particular to an anti-remote language transmission model based on hypergraph, comprising the following steps: constructing an OSN anti-rumor high-order system transmission model based on hypergraph; analyzing the principle and composition of hypergraph OSN high-order network; constructing a heterogeneous differential equation group of the hypergraph OSN anti-rumor high-order system transmission model and verifying the positivity and boundedness of the model solution; calculating the basic reproductive number of the model or judging the threshold R0 of whether the rumor automatically dies out; and carrying out numerical simulation verification on the model. The anti-remote language transmission model based on hypergraph microscopically analyzes the rumor transmission of OSN from the perspective of hypergraph and complex network theory, establishes a high-order information transmission model of OSN, focuses on the multi-layer network based on hypergraph modeling and the heterogeneity of the model, emphasizes the combination of network structure, and focuses on the characteristics of multi-level, multi-stage and multi-dimensional network of online social network.

Description

Technical Field

[0001] This invention relates to the field of anti-remote speech propagation technology, specifically to an anti-remote speech propagation model based on hypergraphs. Background Technology

[0002] With the rapid development of mobile internet and mobile devices, various types of online social networks (OSNs) have quickly become widespread. The emergence of social networks has greatly enriched users' social needs. Unlike traditional information media, in social networks, people are not only viewers of information but can also publish and disseminate information. In the internet age, online social networks have become an important medium for people to obtain information, disseminate information, and communicate feelings.

[0003] With the widespread adoption of online social networks, the number of social users has exploded, generating a wealth of social activity data. This data contains important information, and in-depth research into this type of data can effectively uncover users' social influence, thereby promoting research into social applications such as information dissemination, online marketing, community discovery, behavior prediction, social recommendation, and social advertising. These applications will undoubtedly greatly benefit social network platforms and users. Online social networks have become important and efficient platforms for various information disseminations, but the popularity and openness of OSN platforms have also bred rumors, gossip, and other forms of misinformation. The spread of rumors on OSNs can cause widespread panic or huge economic losses in a short period of time. Therefore, this invention proposes a high-order anti-rumor system propagation model based on hypergraphs. Summary of the Invention

[0004] The purpose of this invention is to provide a hypergraph-based anti-remote propagation model to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a hypergraph-based anti-remote propagation model, comprising the following steps:

[0006] S1: Construct a high-order OSN anti-rumor system propagation model based on hypergraphs.

[0007] S2: Analysis of the principles and composition of high-order hypergraph OSNs.

[0008] S3: Constructing a heterogeneous set of differential equations for a high-order hypergraph OSNs anti-rumor propagation model and verifying the positivity and boundedness of the model solution.

[0009] S4: Calculate the basic reproduction number of the model or the threshold R0 for determining whether a rumor will automatically disappear.

[0010] S5: Perform numerical simulation verification on the model.

[0011] Preferably, S2 assumes that in a hypergraph-based online social network (OSN), for a hypergraph, any number of vertices can be connected by an edge, called a hyperedge; formally, a hypergraph G can be represented as G = (V, E), where V is called the set of nodes or vertices, and E is called a hyperedge, which is the set of non-empty subsets of V. The number of hyperedges containing node j is called the degree of node j; each individual is equivalent to a node in the hypergraph, and certain connections between individuals can constitute hyperedges of the hypergraph; nodes within each hyperedge can propagate freely, where E1 = {V1, V2, V3, V4, V5}, E2 = {V1, V2, V3}, E3 = {V2, V3, V6, V7}, E4 = {V3, V8}, and E5 = {V7, V9}, while propagation between hyperedges occurs through intersection nodes; and the degree of a node reflects the complexity of the hypergraph network in which the node is located; Figure 1 We know that the maximum hyperedge contains 5 nodes, therefore M = 5, meaning the maximum superdegree order is 5; the superdegree of a node is k. i =[k i (2) k i (3) , ..., k i (m) , ..., k i (M) (i∈[1, z]), k i (m) The m-order of a node, i.e., the number of m-sized superedges containing the node; superdegree. The degree of V1 is [0, 1, 0, 1], the degree of V2 is [0, 1, 1, 1], the degree of V3 is [1, 1, 1, 1], the degree of V4 and V5 is [0, 0, 0, 1], the degree of V6 is [0, 0, 1, 0], the degree of V7 is [1, 0, 1, 0], and the degree of V8 and V9 is [1, 0, 0, 0]. Arrange the degree numbers in ascending order: k1 = [0, 0, 0, 1], k2 = [0, 0, 1, 0], k3 = [0, 1, 0, 1], k4 = [0, 1, 1, 1], k5 = [1, 0, 0, 0], k6 = [1, 0, 0, 0], k7 = [1, 0, 1, 0], k8 = [1, 0, 0, 0], k9 = [1, 0, 0, 0], k1 = [0, 0, 0, 1], k2 = [0, 0, 1, 0], k3 = [0, 1, 0, 1], k4 = [0, 1, 1, 1], k5 = [1, 0, 0, 0], k6 ... [0, 1, 0], k7 = [1, 1, 1, 1]; In this patent, the participating group is divided into S(t) (unknown), I(t) (infected), D(t) (anti-rumor), and T(t) (silent); the unknown do not know the truth of the rumor, but after accepting the spread of the rumor, they will choose to believe the rumor and become infected or spread the truth and become anti-rumor. Under the mutual influence of infected and anti-rumor, the two will transform into each other; in order to suppress the spread of the rumor, a part of the infected are isolated to prevent the spread of the rumor. This part is called silent. After isolation, some of them will also be transformed into infected or anti-rumor.

[0012] Preferably, S3 is further subdivided into:

[0013] S3.1 Construct the heterogeneous differential equation system of the SIDT model.

[0014] S3.2 Verify the positivity and boundedness of the model solution.

[0015] Preferably, S4 is further subdivided into:

[0016] S4.1 No Rumor Balance Point E0.

[0017] S4.2 Edge equilibrium point E1 (no rumors, but there are debunkers).

[0018] S4.3 Boundary equilibrium point E2 (rumors and counter-rumors).

[0019] S4.4 Rumors continue to balance at E3.

[0020] The threshold R0 of the S4.5 model.

[0021] Preferably, in S5, the degree k i The probability P(k) of the distribution i P(k) follows a generalized power-law distribution: i )∝(b+1)! ||k i || -2-b Here, b is ||k i || takes the minimum value, while ||k i The value of || ranges from 1 to 150.

[0022] Compared with the prior art, the beneficial effects of the present invention are:

[0023] 1. This hypergraph-based anti-rumor propagation model conducts a micro-analysis of rumor propagation in OSNs from the perspective of hypergraph and complex network theory, and establishes a high-order information propagation model for OSNs. Its focus is on the multi-layer network based on hypergraph modeling and the heterogeneity of the model, emphasizing the combination of network structures, and focusing on the characteristics of multi-layer, multi-level and multi-dimensional networks in online social networks. By constructing the state transition diagram of the model, dynamic equations are established, and the existence of rumor-free and rumor equilibrium points in the model is analyzed, which further improves the predictive reliability of high-order rumor propagation.

[0024] 2. The supergraph-based anti-rumor propagation model differs from current research on rumor propagation, which typically uses a one-dimensional simplex or a simplex with two or more dimensions, as the network structure consists of chain-like links within a large region and surfaces formed by chain-like links between nodes. In contrast, the complex network structure of a supergraph is a complex network formed by superimposing and combining multiple regional networks through network intersections. Each sub-network of the supergraph has a different order and more diverse participating groups, which is more in line with the general model of rumor propagation. Attached Figure Description

[0025] Figure 1 This is the overall flowchart;

[0026] Figure 2 For hypergraph networks;

[0027] Figure 3 This is a SIDT state transition diagram;

[0028] Figure 4 The diagram shows the equilibrium point E0 without rumors.

[0029] Figure 5 Diagram of boundary equilibrium point E1;

[0030] Figure 6 Figure E2 shows the boundary equilibrium point.

[0031] Figure 7 The E3 diagram represents the ongoing balance point for rumors. Detailed Implementation

[0032] like Figure 1-7 As shown, this invention provides a technical solution: a hypergraph-based anti-remote propagation model, comprising the following steps:

[0033] S1: Construct a high-order OSN anti-rumor system propagation model based on hypergraphs.

[0034] S2: Analysis of the principles and composition of high-order hypergraph OSNs.

[0035] In a hypergraph-based online social network (OSN), for a hypergraph, any number of vertices can be connected by an edge called a hyperedge. Formally, a hypergraph G can be represented as G = (V, E), where V is called the set of nodes or vertices, and E is called a hyperedge, which is a set of non-empty subsets of V. The number of hyperedges containing node j is called the degree of node j. Each individual is equivalent to a node in the hypergraph, and certain connections between individuals can constitute hyperedges. Nodes within each hyperedge can propagate freely, where E1 = {V1, V2, V3, V4, V5}, E2 = {V1, V2, V3}, E3 = {V2, V3, V6, V7}, E4 = {V3, V8}, and E5 = (V7, V9}. Propagation between hyperedges occurs through intersection nodes. The degree of a node reflects the complexity of the hypergraph network in which that node belongs. Figure 1 We know that the maximum hyperedge contains 5 nodes, therefore M = 5, meaning the maximum hyperdegree order is 5. The hyperdegree of a node is k. i =[k i (2) k i (3) , ..., k i (m) , ..., k i (M) (i∈[1, z]), k i (m) This represents the order m of a node, i.e., the number of hyperedges of size m containing the node. (Superdegree) The degree of V1 is [0, 1, 0, 1], the degree of V2 is [0, 1, 1, 1], the degree of V3 is [1, 1, 1, 1], the degree of V4 and V5 is [0, 0, 0, 1], the degree of V6 is [0, 0, 1, 0], the degree of V7 is [1, 0, 1, 0], and the degree of V8 and V9 is [1, 0, 0, 0]. Arrange the degree numbers in ascending order: k1 = [0, 0, 0, 1], k2 = [0, 0, 1, 0], k3 = [0, 1, 0, 1], k4 = [0, 1, 1, 1], k5 = [1, 0, 0, 0], k6 = [1, 0, 1, 0], k7 = [1, 1, 1, 1].

[0036] In this patent, the participating groups are divided into S(t) (unknown individuals), I(t) (infected individuals), D(t) (anti-rumor participants), and T(t) (silent individuals). Unknown individuals do not know the truth of the rumors, but after being exposed to them, they may choose to believe the rumors and become infected individuals, or spread the truth and become anti-rumor participants. These two groups can transform into each other through mutual influence. To suppress the spread of rumors, a portion of the infected individuals are isolated to prevent them from spreading rumors; this group is called silent individuals. After isolation, some of them will also transform into infected individuals or anti-rumor participants.

[0037] (1) After hearing the rumors spread by the infected, the unknown person will become an infected person with a probability of α; after hearing the truth from the debunkers, the unknown person will become a debunker with a probability of β1.

[0038] (2) Over time, the anti-rumorers will forget the rumors and become unknown with a probability of β2.

[0039] (3) If an infected person chooses to believe the truth again, they will become an anti-rumor person with a probability of δ1. If an anti-rumor person chooses to believe the rumors again, they will become an infected person with a probability of δ2.

[0040] (4) When infected individuals are suppressed from spreading rumors, they are converted into silent individuals with a probability of γσ.

[0041] (5) The silenced person regains freedom of speech with a probability of μ, of which there is a probability of σ to become an infected person and a probability of 1-σ to become an anti-rumor person.

[0042] (6) The immigration rate of unknowns is ω, while the immigration rate of participants is g.

[0043] Table 1 Symbols

[0044]

[0045]

[0046]

[0047] S3: Constructing a heterogeneous set of differential equations for a high-order hypergraph OSNs anti-rumor propagation model and verifying the positivity and boundedness of the model solution.

[0048] S3.1 Constructing the heterogeneous differential equation system of the SIDT model;

[0049]

[0050]

[0051]

[0052]

[0053] in:

[0054]

[0055]

[0056] This indicates the average excess.

[0057] S3.2 Verify the positivity and boundedness of the model solution;

[0058] Assumption initial conditions are met Then for Θ D When (0)>0 and t>0, Θ I (t)>0,Θ D Proof that (t) > 0:

[0059]

[0060]

[0061]

[0062]

[0063] so

[0064]

[0065]

[0066] For <Θ′ I Integrating from 0 to t, we get:

[0067]

[0068] Because Θ I (0), and Therefore <Θ I (t) > 0 when t > 0

[0069] Therefore Θ I (t) is greater than 0 when t > 0.

[0070] Similarly

[0071] It can be known that Θ D (t) is greater than 0 when t > 0.

[0072] Assumption Suppose there exists a sufficiently small τ such that h(τ) = 0, h′(τ) ≤ 0, h(t) > 0, and τ ∈ (0, t), satisfying the initial conditions.

[0073] if hour, and Contradictory, for t > 0, Where i = 1, 2, ... z.

[0074] Similarly, it can be proved that for Where i = 1, 2, ... z.

[0075] S4: Calculate the basic reproduction number of the model or the threshold R0 for determining whether a rumor will automatically disappear.

[0076] To find the equilibrium point of the model, we assume that all model equations are equal to zero, and thus obtain...

[0077]

[0078] S4.1 No Rumor Equilibrium Point E0

[0079] make The solution is:

[0080] The resulting rumor-free equilibrium point

[0081] S4.2 Edge equilibrium point E1 (no rumors, but there are debunkers).

[0082] make After rearranging the equation, we get the following equation:

[0083]

[0084] Solving for:

[0085]

[0086] The edge equilibrium point obtained from this

[0087] S4.3 Boundary equilibrium point E2 (rumors and counter-rumors).

[0088] make After rearranging the equation, we get the following equation:

[0089]

[0090] Solving for:

[0091]

[0092] The edge equilibrium point obtained from this

[0093] S4.4 Rumors continue to balance at E3.

[0094] Solving the system of equations yields

[0095]

[0096]

[0097]

[0098]

[0099] The resulting equilibrium point for the persistence of rumors

[0100] The threshold R0 of the S4.5 model

[0101] From 4.4, let Θ I * =Θ I Θ D * =Θ D

[0102]

[0103]

[0104] Let the above formula Therefore, f(0) = 0

[0105]

[0106]

[0107] so

[0108] threshold

[0109]

[0110] When R0 > 1, the rumor propagation model has a persistent rumor equilibrium point.

[0111] S5: Perform numerical simulation verification on the model.

[0112] Deliverance to K i The probability P(k) of the distribution i P(k) follows a generalized power-law distribution: i )∝(b+1)! ||k i || -2-b Here, b is ||k i || takes the minimum value, while ||k i The value of || ranges from 1 to 150.

[0113] Table 2 Numerical Simulation Parameters

[0114]

[0115]

Claims

1. A hypergraph-based anti-remote speech propagation model, characterized in that, Includes the following steps: S1: Construct a high-order OSN anti-rumor system propagation model based on hypergraph; S2: Analysis of the principles and composition of high-order hypergraph OSN networks; S3: Constructing a heterogeneous set of differential equations for a high-order hypergraph OSN anti-rumor system propagation model and verifying the positivity and boundedness of the model solution; S4: The basic reproduction number of the calculation model or the threshold for determining whether a rumor automatically disappears. ; S5: Perform numerical simulation verification on the model; The S2 assumption states that in a hypergraph-based social network (OSN), for a hypergraph, any number of vertices can be connected by an edge, which is called a hyperedge. In terms of form, HyperGraph Represented as ,in A node or vertex is a set of elements. It is called a hyperedge. A set of non-empty subsets containing nodes The number of hyperedges is called the number of nodes. The hypergraph represents the graph's hierarchy; each individual is equivalent to a node in the hypergraph, and certain connections between individuals constitute the hyperedges of the hypergraph; nodes within each hyperedge can propagate freely. , , , , Propagation between hyperedges occurs through intersection nodes; the degree of a node reflects the complexity of the hypergraph network to which it belongs; the maximum number of nodes in a hyperedge is 5, therefore... That is, the maximum degree of transcendence is 5; the degree of transcendence of a node is ( ), The m-order of a node, i.e., the number of m-sized superedges containing the node; superdegree. ; The salvation is , The salvation is , The salvation is , The salvation is , The salvation is , The salvation is , The salvation is Sort the above degrees in ascending order. , , , , , , ; Divide the participating groups into (Unknown) (Infected person) (Anti-rumorers) (Silent Ones); The unknown do not know the truth of the rumors, but after being exposed to the spread of the rumors, they will choose to believe the rumors and become infected or spread the truth and become anti-rumorers. Under the mutual influence of infected and anti-rumorers, the two can transform into each other. In order to suppress the spread of rumors, some infected people are isolated to prevent them from spreading rumors. This part is called silent ones. After isolation, some of them will also be transformed into infected or anti-rumorers. S3: The heterogeneous differential equation system for constructing a high-order system propagation model of hypergraph OSNs for anti-rumor systems and the verification of the positivity and boundedness of the model solution include; S3.1 Constructing the heterogeneous differential equation system of the SIDT model; in: Indicates average excess; S3.2 Verify the positivity and boundedness of the model solution; Assumption initial conditions are met For hour, prove: = = so right Integrating from 0 to t yields: because ,and ,so exist When greater than 0 so exist When greater than 0; Similarly = It can be known exist When greater than 0; Assumption Assuming there is a sufficiently small Make , , , The initial conditions are met. ; if , , , hour, ,and Contradictory, for , ,in ; Similarly, it can be proved that for , , , ,in ; S4: The basic reproduction number of the calculation model or the threshold for determining whether a rumor automatically disappears. ; To find the equilibrium point of the model, we assume that all model equations are equal to zero, and thus obtain... S4.1 No Rumor Balance Point make The solution is: = The resulting equilibrium point free of rumors S4.2 Edge Balance Point (No rumors, but there are people who debunk them); make After rearranging the equation, we get the following equation: Solving for: The edge equilibrium point obtained from this S4.3 Boundary Equilibrium Point (Rumor-mongers and those who refute rumors); make After rearranging the equation, we get the following equation: Solving for: The edge equilibrium point obtained from this S4.4 The Equilibrium Point of Rumor Continuation ; Solving the system of equations yields The resulting equilibrium point for the persistence of rumors Threshold of S4.5 model From 4.4, let , Let the above formula therefore so threshold when At that time, the rumor propagation model has a persistent equilibrium point for rumors.

2. The anti-telepathic propagation model based on a hypergraph according to claim 1, characterized in that: S3 is further subdivided into: S3.1 Constructing the heterogeneous differential equation system of the SIDT model; S3.2 Verify the positivity and boundedness of the model solution.

3. The anti-telepathic propagation model based on a hypergraph according to claim 1, characterized in that: S4 is further subdivided into: S4.1 No Rumor Balance Point ; S4.2 Edge Balance Point (No rumors, but there are people who debunk them); S4.3 Boundary Equilibrium Point (Rumor-mongers and those who refute rumors); S4.4 The Equilibrium Point of Rumor Continuation ; Threshold of S4.5 model .

4. The anti-telepathic propagation model based on a hypergraph according to claim 1, characterized in that: The super-degree in S5 probability of distribution Follows a generalized power-law distribution: , here yes The minimum value, and The range of values ​​is .

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