Method for determining a threshold of information propagation burst in a social network and applications thereof

Abstract

The application discloses a method for determining a social network information propagation burst threshold and application thereof, and the method comprises the following steps: according to the fact that the behavior propagation of each individual is affected by the limited contact ability of the individual due to the limitation of personal time, wealth and influence in the real society, a multi-layer limited contact network model is constructed; according to the fact that an individual usually receives or propagates information on multiple social networks in a social crowd, and then shows a gradually decreasing interest degree in information acquisition, showing a marginal diminishing effect of the individual, a behavior threshold probability function is proposed to represent the marginal diminishing effect behavior of the individual; according to the constructed multi-layer limited contact network model and the constructed behavior probability function, a method for determining a social network information propagation burst threshold is proposed. Through the method, the critical point of information burst and the behavior propagation trend are calculated. The application provides more accurate, diverse and specific behavior propagation modes and influence factors.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of complex network information propagation, and in particular to a method for determining a social network information propagation outbreak threshold and application thereof. BACKGROUND

[0002] Researchers have paid a high degree of attention to the behavior propagation, and found that people tend to confirm information when taking behavior, which embodies a reinforcement effect. When people accept information from neighbors, social reinforcement makes them have a complete or incomplete memory effect on accumulated information, showing a non-Markovian characteristic. In addition, individual memory effect contains non-redundant accumulated behavior information in the process of behavior propagation. When people hear enough non-redundant information from neighbors, people are more inclined to accept information. Based on this, scientists have studied a large number of potential information propagation elements, such as memory effect, group heterogeneity, heterogeneous adoption threshold, truncated Gaussian distribution threshold, special adoption threshold, etc.

[0003] In information propagation, due to the reasons of time, wealth and influence, individuals can only contact with limited neighbors in a short time. For example, users of social networks may find it difficult to communicate with all friends in a period of time. In the circle of academic collaborators, a scientist will only cooperate with a few scholars in a short time. In previous studies, some researchers have constructed a heterogeneous adoption model to study the influence of heterogeneous contact ability on social propagation. However, the model does not consider the influence of limited interaction of individuals in reality.

[0004] Based on this, the social acceptance of individuals should be represented by the contact ability of individuals. In addition, many people like to use a variety of social networks, including commonly used social software such as WhatsApp, Instagram, Tinder and Twitter. People are connected to each other in various social networks through different numbers of neighbors and limited contacts. Therefore, when analyzing information propagation, the present application considers a multi-layer limited contact network reflecting the contact ability of individuals, and further proposes a method for determining a social network information propagation outbreak threshold. SUMMARY

[0005] The present application aims at the fact that the existing information propagation model does not consider the influence of limited interaction of individuals in reality, and proposes a method for determining a social network information propagation outbreak threshold and application thereof, which provides more accurate, diverse and specific behavior propagation patterns and influencing factors.

[0006] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0007] In one aspect, the present application provides a method for determining a social network information propagation outbreak threshold, comprising the following steps:

[0008] S101, construct a multi-layer limited contact network model as follows: the contact capacity of the adoptive individual is set as C, the maximum number of neighbors of the adoptive individual under the adoptive state is denoted by C, if C i where k i is the degree of individual i, then the adopted individual can only contact part of the neighbors; if C≥k i , the adopted individual can contact all neighbors;

[0009] S102, a behavior threshold probability function is proposed to represent the marginal decreasing effect behavior of individuals, the behavior threshold probability function is a trapezoidal probability function, which is divided into two regions, in the first region, the adoption probability of individuals slowly rises to 1 in a nonlinear manner; in the second region, the adoption probability of individuals remains at 1;

[0010] S103, according to the multi-layer limited contact network model constructed in S101 and the behavior threshold probability function constructed in S102, a method for determining the outbreak threshold of social network information propagation is proposed;

[0011] S104, according to the method proposed in S103, the critical point of information outbreak and the behavior propagation trend are calculated.

[0012] Further, in step S101, the probability of an individual in the non-susceptible state accepting information is λ, and the probability of an individual i's non-susceptible neighbor j receiving information is denoted as

[0013] Further, in step S102, the behavior threshold probability function h X (x,α,β) is represented as:

[0014]

[0015] Where x is the percentage between the information received by an individual and the number of its limited contact individuals; the variable α represents the IDME parameter of the individual, when 0≤x<α, the adoption probability of the individual slowly rises to 1 in a nonlinear manner; when α≤x≤1, the adoption probability of the individual remains at 1.

[0016] Further, the edge partition theory of the method in step S103 is as follows:

[0017] Firstly, some nodes are randomly selected as initial proportion of seeds and set as adopter state, and other nodes are set as non-infected state, and edges between nodes are randomly generated according to the degree distribution; for the non-infected state nodes in the network, the initial cumulative amount of information received by the nodes is 0; each adopter node transmits information to the non-infected neighbor nodes with a certain probability, and when a non-infected node accepts an information, the cumulative information amount of the node is added by 1; when the information amount received by each individual in the group exceeds the adoption threshold of the individual, the non-infected state of the individual is changed to h X (x,α,β) is changed to the adopter state; next, when the adopter individual successfully transmits information to the non-infected neighbor node, the adopter individual loses interest in the information and becomes the recovered state, and is changed to the recovered state with a probability of γ; finally, when there is no adopter node on the network, the information propagation process is ended.

[0018] Further, the method for calculating the critical point of information outbreak and the behavior propagation trend in step S104 is as follows:

[0019] The probability θ A (t) or θ B (t) that the neighbor j does not successfully transmit information to the A-layer or B-layer node i at time t is expressed as:

[0020]

[0021]

[0022] wherein, denotes the probability that the node i and the node j with the degree of k are neighbors in the X layer; denotes the probability that the edge in the X (X ∈ {A, B}) layer does not see the behavior propagation of the non-infected state neighbor j before time t;

[0023] At time t, a non-infected state node i with k i = (k i A ,k i B ) receives m A or m B amount of information in the A layer or the B layer, and the probability is expressed as:

[0024]

[0025]

[0026] If the node i receives m X amount of information in the X layer, the non-infected state node i is expressed as The non-infected state node i accepts m XThe probability that the number information is still in the uninfected state is defined as:

[0027]

[0028] The probability that the node i is still in the uninfected state after receiving m A and m B pieces of information at time t is represented as:

[0029]

[0030] The probability that the node in the subnetwork accepts information and remains in the uninfected state at time t is represented as:

[0031]

[0032] The probability that the node remains in the uninfected state is represented by η X ; then the proportion of uninfected nodes in the multilayer network at time t is represented as:

[0033]

[0034] Convert to:

[0035]

[0036] where, represents the probability that the node i in the uninfected state is connected to the neighbor j in the adopted state through an edge, and has not successfully received the information of j at time t, or represents the probability that the node i in the uninfected state is connected to the neighbor j in the uninfected or recovered state through an edge of X layers;

[0037] The probability that the neighbor j accepts n X pieces of information in the X (X ∈ {A, B}) layer is:

[0038]

[0039] The probability that the neighbor j is still in the uninfected state in layer A after receiving n A and n A pieces of information is represented as:

[0040]

[0041] The probability that the neighbor j is still in the uninfected state in layer B after receiving n A and n A pieces of information is represented as:

[0042]

[0043] Given the degree distribution p(k), the probability that node i is connected to an uninfected neighbor j through an edge is given by:

[0044]

[0045] where denotes the probability that node i is connected to a neighbor with degree or k j B ;

[0046] An uninfected node i successfully acquires information from an adjacent adopter node j with probability λ, The evolution of

[0047]

[0048] Meanwhile, a node in the adopter state loses interest in the information with probability γ, reverting to the recovered state, The evolution of

[0049]

[0050] Given the initial condition Combining equations (15) and (16), The evolution of

[0051]

[0052] By combining equations (10), (14), and (17), we obtain

[0053]

[0054] Substituting equation (18) into equation (15), The evolution of

[0055]

[0056] The time evolution of the blocks of nodes in the adopter and recovered states throughout the network is given by

[0057]

[0058]

[0059] By jointly and iteratively calculating equations (9), (20), and (21), we obtain S(t), A(t), and R(t), which allow us to calculate the proportion of each state at any given time step. When t→∞, only the uninfected and recovered nodes remain in the entire network, and R(∞) represents the final adoption size. To determine R(∞), we have :

[0060]

[0061] Then, by combining and iterating equations (9) and (22), we obtain S(∞) and R(∞);

[0062] Will Substituting into equations (2) and (3), θ X The evolution of (∞) into θ A (∞) and θ B (∞) functions:

[0063]

[0064] In θ A (∞) < 1 and θ B Under the condition (∞) < 1, when θ A (∞)=F A (θ A (∞),θ B (∞)) and θ B (∞)=F B (θ A (∞),θ B When (∞) is tangent, the basic case of the critical point is expressed as:

[0065]

[0066] On the other hand, the present invention also provides the application of the above-described method for determining the information propagation burst threshold of social networks in multilayer limited contact ER networks or SF networks.

[0067] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0068] This invention proposes a method for determining the information dissemination outbreak threshold on social networks. Based on the critical point of information outbreak and the trend of behavioral dissemination, it provides more accurate, diverse, and specific behavioral dissemination patterns and influencing factors of information dissemination mechanisms. This method is used to analyze multi-layered finite-contact network models and a behavioral function, expanding the research on the social dissemination dynamics of computer viruses. The proposed dissemination model can be applied to research on issues such as virus epidemics, innovation dissemination, commercialization, and computer virus propagation. Furthermore, this invention can further explore the application of the proposed method in social dissemination on reusable networks, providing valuable reference for people regarding the spread of information, public opinion, and rumors. Attached Figure Description

[0069] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed in the embodiments will be briefly introduced as follows. Obviously, the accompanying drawings in the following description only represent some embodiments of the present application, and all other drawings obtained by those of ordinary skill in the art based on these accompanying drawings without creative effort should fall within the protection scope of the present application.

[0070] Figure 1 A flowchart of a method for determining a social network information propagation burst threshold according to an embodiment of the present application.

[0071] Figure 2 An information propagation schematic diagram of a multi-layer limited contact network and an individual marginal decreasing effect probability function in an embodiment of the present application.

[0072] Figure 3 Influence of transmission probability and IDME parameter a on final propagation scale in a multi-layer limited contact ER network in an embodiment of the present application.

[0073] Figure 4 Comprehensive influence of transmission probability and IDME parameter a on final propagation scale in a multi-layer limited contact ER network in an embodiment of the present application.

[0074] Figure 5 Comprehensive influence of transmission probability and IDME parameter β on final propagation scale in a multi-layer limited contact ER network in an embodiment of the present application.

[0075] Figure 6 Influence of transmission probability and IDME parameter a on final propagation scale in a multi-layer limited contact SF network in an embodiment of the present application.

[0076] Figure 7 Comprehensive influence of transmission probability and IDME parameter β on final propagation scale in a multi-layer limited contact SF network in an embodiment of the present application. DETAILED DESCRIPTION

[0077] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments only represent some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the protection scope of the present application.

[0078] A method for determining a social network information propagation burst threshold according to an embodiment of the present application is provided, as shown in Figure 1 The method comprises the following steps:

[0079] S101, according to the fact that in real society, individual behavior propagation is affected by the limited contact ability of individuals due to the limitations of personal time, wealth and influence, a multi-layer limited contact network model is constructed.

[0080] The multi-layer limited contact network model is represented as follows:

[0081] The independent g A (w) and g B (w) are used to represent the weight distribution on the complex network, and when the node i in the adoption state has a neighbor j in the non-susceptible state, the probability that they become an adoption state node is: The contact ability of the adoption state individual can be set as C to explain the influence of limited contact on behavior propagation. The maximum number of neighbors of the individual in the adoption state is denoted by the symbol C. If C < k i , where k i is the degree of individual i, then the adopted individual can only contact part of the neighbors. However, if C ≥ k i , it can contact all neighbors. The probability that the individual in the non-susceptible state receives information is λ. The probability that the non-susceptible neighbor j of individual i receives information is denoted as The greater the limited contact ability C, the greater the maximum number of nodes that a unit node can contact, and the more active the network will be.

[0082] S102, according to the fact that in a social crowd, individuals usually receive or propagate information on multiple social networks, and then show a gradually decreasing interest in information acquisition, showing individual diminishing marginal effect (IDME), a behavior threshold probability function is proposed to represent the individual diminishing marginal effect behavior.

[0083] The individual in step S102 shows individual diminishing marginal effect, which is mathematically represented as a trapezoidal probability function, which is divided into two regions. In the first region, the adoption probability of the individual slowly rises to 1 in a nonlinear manner; in the second region, the adoption probability of the individual remains at 1.

[0084] Further, the trapezoidal probability function h X (x,α,β) is represented as:

[0085]

[0086] where x is the percentage of information received by an individual and the number of limited contact individuals; the variable α represents the IDME parameter of the individual, when 0 ≤ x ≤ α, the adoption possibility slowly rises to 1 with x. When α < x ≤ 1, the adoption possibility remains unchanged at 1. A smaller α value promotes the adoption ability of the individual, and a larger α value indicates that the individual shows weaker adoption behavior.

[0087] S103, according to S101 constructed multi-layer limited contact network model and S102 constructed a behavior probability function, put forward a method to determine the social network information propagation outbreak threshold.

[0088] The edge partition theory of this method is as follows: first, randomly select some nodes as initial proportion of seeds, and set them as adopter nodes, and set other nodes as uninfected nodes, and generate edges between nodes according to degree distribution at random; for the uninfected nodes in the network, the initial cumulative number of information received by them is 0; each adopter node transmits information to uninfected neighbor nodes with a certain probability, when an uninfected node accepts an information, the cumulative number of information received by it is increased by 1; when the number of information received by each individual in the group exceeds its adoption threshold, the uninfected state of the individual changes to h X The probability of (x, α, β) changes to adopter state; next, when the adopter individual successfully transmits information to the uninfected neighbor node, the adopter individual may also lose interest in the information and change to the recovered state, and change to the recovered state with a probability of γ; finally, when there is no adopter node on the network, the information propagation process ends.

[0089] S104, according to the edge generalized partition theory constructed in S103, the critical point of information outbreak and the behavior propagation trend are calculated.

[0090] There is a null state node in the network, which means that the node only accepts messages from adopter neighbors and cannot send messages to uninfected neighbors. Since the node edges are random, θ A (t) and θ B (t) are expressed as:

[0091]

[0092]

[0093] Where, θ A (t) and θ B (t) represent the probability that neighbor j does not successfully transmit information to A layer or B layer node i at time t; represents the probability that node i and node j with degree are neighbors in X layer; represents the probability that the edge in X (X ∈ {A, B}) layer has not seen the behavior propagation of its uninfected neighbor j before time t.

[0094] At time t, a k i = (k i A ,k i BThe unsensing node i receives m cumulatively at layer A or layer B. A or m B The probability of a message is expressed as:

[0095]

[0096]

[0097] If node i receives m in layer X X Based on the IDME features and the adoption threshold function, the node i in the unsensible state is represented as: Unsensory node i receives m at time t X The probability that the quantity information is still in an unsensible state is expressed as:

[0098]

[0099] Node i receives m at time t A and m B The probability of remaining in an unresponsive state after receiving one message is expressed as:

[0100]

[0101] The probability that a node at time t receives information and remains in an unperceived state is expressed as:

[0102]

[0103] The probability that a node remains in an insensitive state is denoted by η. X The proportion of nodes in an unperceived state in a multilayer network at time t is expressed as:

[0104]

[0105] To analyze S(t), and since all individuals in the model can only alternate between three states, therefore It can be converted to:

[0106]

[0107] in, Let $\mathbf{i}$ represent the probability that node $i$, which is in an unresponsive state, is connected to neighbor $j$, which is in an responsive state, and fails to receive information from $j$ at time $t$. or This represents the probability that a node i in an unsensible state is connected to its neighbor j in an unsensible or recovered state through an edge at layer X.

[0108] Due to the cavity theory, it has The unsensory neighbor j can only be obtained from other or The probability that neighbor j accepts n X pieces of information in layer X (X ∈ {A, B}) is:

[0109]

[0110] The probability that neighbor j accepts n A and n A pieces of information in layer A and remains in the unresponsive state is:

[0111]

[0112] The probability that neighbor j accepts n A and n A pieces of information in layer B and remains in the unresponsive state is:

[0113]

[0114] Given the degree distribution p(k), the probability that node i is connected to an unresponsive neighbor j through an edge is:

[0115]

[0116] where denotes the probability that node i is connected to a neighbor with degree or in layer X;

[0117] The probability that unresponsive node i successfully acquires information from adjacent responsive node j with λ is: The evolution of

[0118]

[0119] At the same time, the node in the responsive state loses interest in the information with a probability of γ and returns to the recovery state, The evolution of

[0120]

[0121] Since the initial condition Combining formulas (15) and (16), The evolution of

[0122]

[0123] By combining formulas (10), (14), and (17), we get:

[0124]

[0125] Substituting formula (18) into formula (15), The evolution of θ

[0126]

[0127] The time evolution of the fraction of nodes in the susceptible and recovered states in the whole network is given by:

[0128]

[0129]

[0130] By combining and iterating equations (9), (20), and (21), we can obtain S(t), A(t), and R(t), which are the fractions of each state at any given time step. When t→∞, only the susceptible and recovered states exist in the whole network, and R(∞) represents the final spreading size. To determine R(∞), we have:

[0131]

[0132] Then, by combining and iterating equations (9) and (22), we can obtain S(∞) and R(∞).

[0133] The critical spreading probability is the next issue of concern. Substituting into equations (2) and (3), the evolution of θ X (∞) can be transformed into a function of θ A (∞) and θ B (∞):

[0134]

[0135] Under the conditions of θ A (∞) < 1 and θ B (∞) < 1, when θ A (∞) = F A (θ A (∞), θ B (∞)) is tangent to θ B (∞) = F B (θ A (∞), θ B (∞)), a discontinuous rising spreading mode occurs.

[0136] Therefore, the basic condition of the critical point can be expressed as:

[0137]

[0138] ​Firstly, the person who simultaneously utilizes multiple social networks has different contact abilities, which has an important influence on the behavior propagation. In addition, individuals show individual marginal diminishing effect on behavior propagation, which shows IDME behavior. Therefore, we construct a non-regular trapezoidal probability function on the multi-layer contact network. Then, in order to study the behavior propagation process on the multi-layer contact network, we propose a new edge division theory. Finally, through simulation results and theoretical analysis, the phase transition cross phenomenon of multi-layer contact ER network and SF network is revealed. With the change of IDME, the distribution mode of the final propagation scale first increases continuously in the second-order phase transition, and then increases discontinuously in the first-order phase transition. At the same time, we determine an explicit IDME value that produces the maximum final propagation scale under a given propagation probability. In addition, the increase of limited contact heterogeneity makes information more easily spread, and the first-order discontinuous phase transition is more likely to be replaced by the second-order continuous phase transition. In addition, in the SF network, the degree heterogeneity distribution also has an impact on information diffusion, but it cannot change the phase transition mode.

[0139] S105, according to the critical point of information burst and the behavior propagation trend, an information propagation mechanism is provided.

[0140] In summary, the present application expands the research on the social propagation dynamics of computer viruses, and the proposed propagation model can be applied to the research on virus epidemic, innovation propagation, commercialization and computer virus propagation. In addition, the social propagation problem on the reuse network can be further discussed.

[0141] In the method embodiment of the present application for determining the social network information propagation burst threshold based on the information propagation model factor on the multi-layer limited contact network, the multi-layer limited contact network information propagation schematic diagram and the individual marginal diminishing effect behavior adoption function are determined, as shown in Figure 2 . Figure 2For the multiple finite contact network information propagation schematic diagram in the embodiments of the present application, in the figure: (a) is a propagation schematic diagram based on a multi-layer finite contact network. Individual 1 in the adopting state at time t will propagate information to neighbors in the uninfected state. The probability of propagation in layer A or layer B is denoted by the symbol λ. The links between individual 1 and neighbors 4, 7 in layer A and neighbors 5, 8 in layer B are denoted by dashed lines, and the information cannot be propagated. The reason is that, before time t, the information has been successfully transmitted from individual 1 to its neighbors 4, 7 (or neighbors 5, 8) through the dashed line in layer X (X ∈ {A, B}). The solid line indicates that the edge is not used to propagate information. (b) is a graph of a non-regular trapezoidal behavior probability model. The symbol h represents the proportion of the information obtained by the individual in the uninfected state to its degree. The symbol α represents the IDME behavior parameter of the individual. In region I, 0 < x ≤ α, the adoption probability slowly rises to 1 as x increases. In region II, α < x ≤ 1, the adoption probability remains unchanged at 1. A smaller α value promotes the adoption ability of the individual, and when the α value is larger, the individual exhibits weaker adoption behavior.

[0142] In the method embodiment of the present application for determining the social network information propagation outbreak threshold based on the information propagation model factor on a multi-layer finite contact network, the change of the unit transmission probability to the final propagation scale under different IDME parameters α on the multi-layer ER finite contact network is determined, as shown in Figure 3 From Figure 3 (a) (β = 0.5) and (b) (β = 0.9), it can be seen that as the propagation probability λ increases, the final propagation scale R(∞) increases to global propagation. In addition, Figure 3 (a) and (b) also show the influence of IMDE behavior on the phase transition. In subgraph (a), regardless of any IDME behavior (α A = α B = 0.1, 0.5, 0.9), the mode of R(∞) always shows a second-order growth in continuous phase transition. In subgraph (b), when the individual exhibits strong IMDE behavior, for example, α A = α B = 0.1, the propagation mode of R(∞) shows a second-order growth in continuous phase transition, which indicates that even if λ is small, strong IDME will lead to extensive behavior propagation. When α A = α B = 0.5, R(∞) also shows the same propagation phenomenon. When α A = α B = 0.9, R(∞) shows a first-order growth in discontinuous phase transition, at which time the individual exhibits weak IDME behavior. This indicates that individuals with weak IDME behavior will slow down the propagation of information. Figure 3 The relative deviation and the key behavior propagation probability of (a) and (b) are respectivelyFigure 3 The bias of the behavior propagation, described by the maximum of the relative difference χ, is where the global adoption will occur. In addition, the theoretical analysis values (lines) match the simulation results values (symbols).

[0143] In an embodiment of the method for determining the information propagation burst threshold of a social network based on the factors of the information propagation model on a multi-layer limited contact network, the comprehensive influence of the transmission probability and the IDME parameter α on the final propagation scale on the multi-layer limited contact ER network in the embodiment of the application is determined, as shown in Figure 4 . Figure 4 The comprehensive influence of the parameter plane (λ, α) on the final propagation scale R(∞) on the multi-layer limited contact ER network is shown. The influence of (λ, α) on the information propagation is as shown in Figure 4 (a) (β A = β B = 0.5) and Figure 4 (b) (β A = β B = 0.9). In subgraph (a), the phase transition is in a continuous mode throughout the region. Then, in subgraph (b), the graph can be divided into two parts. In region I, the R(∞) growth mode exhibits a second-order discontinuous phase transition. The critical value between region I and region II is α * = 0.61. In region II, the R(∞) growth mode exhibits a first-order discontinuous phase transition. In addition, the node limited contact capability parameter is set to C = 5.

[0144] In an embodiment of the method for determining the factors of the information propagation model based on a multi-layer limited contact network, the comprehensive influence of the transmission probability and the IMDE parameter β on the final propagation scale on the multi-layer limited contact ER network in the embodiment of the application is determined, as shown in Figure 5 . Figure 5 The comprehensive influence of the parameter plane (λ, β) on the final propagation scale R(∞) on the multi-layer limited contact ER network is shown. The influence of (λ, β) on the information propagation is as shown in subgraph (a) (α A = α B = 0.5) and subgraph (b) (α A = α B = 0.9). In subgraph (a), the graph can be divided into two regions. In region I, the R(∞) growth mode exhibits a second-order continuous phase transition. The critical value between region I and region II is β * = 0.95. In region II, the R(∞) growth mode exhibits a first-order discontinuous phase transition. Then, in subgraph (b), the graph can also be divided into two regions. In region I, the R(∞) growth mode exhibits a second-order continuous phase transition. The critical value between region I and region II is β *=0.78. In region II, the R(∞) growth pattern exhibits a first-order discontinuous phase transition. Furthermore, the nodal finite contact capability parameter is set to C=5.

[0145] In an embodiment of the present invention, a propagation mechanism for the behavioral adoption preferences of heterogeneous groups on a multi-layer finite-touch network is proposed, which determines the impact of transmission probability and IDME parameter α on the final propagation scale in a two-layer finite-touch SF network, such as... Figure 6 As shown. For each subgraph, there is the same node finite contact capability parameter C = 5 and IDME parameter β(β). A =β B =0.9). Subgraphs (a) and (b) show that as λ increases, the final propagation scale R(∞) increases until global adoption is reached. In subgraph (a) (v=2), when α A =α B =0.1 and α A =α B When α = 0.5, the growth pattern of the final propagation scale is a second-order continuous phase transition. However, when α... A =α B When = 0.9, the growth of R(∞) exhibits a first-order discontinuous phase transition. Subplot (b) (v = 4) also shows the same growth pattern. Furthermore, compared to subplot (b) (v = 4), subplot (a) (v = 2) shows less complete global adoption due to its stronger heterogeneity distribution. In addition, the theoretical analysis values ​​(lines) match the simulation results (symbols).

[0146] In an embodiment of the method for determining information propagation model factors based on multilayer finite contact networks of the present invention, the combined influence of transmission probability and IDME parameter β on the final propagation scale in multilayer finite contact SF networks is determined, such as... Figure 7 As shown. Subgraphs (a), (b), (c), and (d) are set to the same node finite contact capabilities C=5 and C=10, respectively. Subgraphs (a), (b), (c), and (d) also represent the growth trends of the final propagation scale R(∞) for parameters v=2 and v=4, respectively. In subgraph (a) with v=2 and C=5, the graph can be divided into three regions. In region I, the growth pattern of the final propagation scale R(∞) exhibits a second-order continuous phase transition. The critical value between region I and region II is β. * =0.85. In region II, the growth pattern of R(∞) exhibits a first-order discontinuous phase transition. The critical value between region II and region III is β. * =0.99. In region III, R(∞) does not exhibit an information burst. In subgraph (b) with v=2 and C=10, the graph can be divided into two regions. In region I, the growth pattern of the final propagation scale R(∞) exhibits a second-order continuous phase transition. The critical value between region I and region II is β.* = 0.75. In region II, the growth pattern of the final spreading size R(∞) exhibits a first-order discontinuous phase transition. In the subgraph (c) of v = 4 and C = 5, the graph can be divided into two regions. In region I, the growth pattern of the final spreading size R(∞) exhibits a second-order continuous phase transition. The critical value between region I and region II is β * = 0.8. In region II, the growth pattern of the final spreading size R(∞) exhibits a first-order discontinuous phase transition. In the subgraph (d) of v = 4 and C = 10, the graph can be divided into two regions. In region I, the growth pattern of the final spreading size R(∞) exhibits a second-order continuous phase transition. The critical value between region I and region II is β * = 0.85. In region II, the growth pattern of the final spreading size R(∞) exhibits a first-order discontinuous phase transition. In addition, the non-uniformity distribution changes the behavioral propagation, but cannot change the phase transition pattern. When the multi-layer finite contact SF network exhibits a strong heterogeneity distribution (v = 2), due to the existence of some hub individuals in the multi-layer finite contact SF network, there is an information suppression pattern in the phase transition. Therefore, the non-uniformity distribution will affect the growth of R(∞) and the behavioral propagation.

[0147] The above examples are only used to illustrate the technical solutions of the present application, but not limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features, but these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for determining the information dissemination burst threshold on a social network, characterized in that, The method comprises the following steps: S101, construct a multi-layer finite contact network model as follows: the contact capacity of the adoptive individual is set as C, the maximum number of neighbors of the adoptive individual under the symbol C is represented, if C i , wherein k i is the degree of individual i, then the adopted individual can only contact part of the neighbors; If C ≥ k i Adopted individuals can contact all neighbors; the probability that an uninfected individual in state S101 receives information is λ, and the probability that an uninfected neighbor j of individual i receives information is denoted by S102, a behavior threshold probability function is proposed to represent the individual's diminishing marginal effect behavior, the behavior threshold probability function is a trapezoidal probability function, which is divided into two regions, in the first region, the individual's adoption probability slowly rises to 1 in a nonlinear manner; in the second region, the individual's adoption probability remains at 1; the behavior threshold probability function h X (x,α,β) is expressed as: Where x is the percentage between the information received by the individual and the number of individuals with which the individual has limited contact; the variable a represents the IDME parameter of the individual, when 0≤x S103, according to S101 constructed multilayer finite contact network model and S102 constructed behavior threshold probability function, put forward a kind of method for determining the threshold of social network information propagation burst;The edge partition theory of step S103 method is as follows: first, randomly select some nodes as initial proportion of seed, and set to adopt state node, other nodes are set to uninfected state, the nodes are connected according to the degree distribution randomly generated edge;For the uninfected state nodes in the network, the initial cumulative number of information received by them is 0;Each adopt state node transmits information to uninfected neighbor nodes with a certain probability, when uninfected node accepts a piece of information, the cumulative information number is added by 1;When the number of information received by each individual in the group exceeds the individual adoption threshold, the uninfected state of the individual changes to h X The probability of (x, α, β) changes to the adoption state;Next, when the adopt state individual successfully transmits information to the uninfected neighbor node, the adopt state individual loses interest in information and becomes the recovery state, and changes to the recovery state with a probability of γ;Finally, when there is no adopt state node on the network, the information propagation process ends; S104. According to the method proposed in S103, the critical point of information explosion and the behavior propagation trend are calculated.

2. The method of determining a social network information propagation burst threshold according to claim 1, wherein, The method for calculating the critical point of information explosion and the behavior propagation trend in step S104 is as follows: the probability θ that neighbor j does not successfully transmit information to node i at tier A or tier B at time t A (t) or θ B (t) is expressed as: where, denotes the probability that node i and node j of degree are neighbors at layer X; denotes the probability that an edge in X (X e {A, B}) layer has not seen the behavior propagation of its uninfected state neighbor j before time t. At time t, one The unsensed node i receives m A or m B The probability of the information amount of m If node i receives m X pieces of information at level X, then node i in the uninfected state is denoted as Uninfected node i accepts m X pieces of information at time t and remains in the uninfected state with probability Node i receives m at time t A and m B The probability that node i is still in the uninfected state after receiving m pieces of information is The probability that a node in the subnetwork accepts information and remains in the uninfected state at time t is represented as: The probability that a node remains in the susceptible state is denoted by η X ; then at time t, the proportion of nodes in the susceptible state in the multi-layer network is denoted by Will Convert to: wherein, Pij(t) denotes the probability that a node i in the unaware state is connected to a neighbor j in the accepting state through an edge and has not successfully received j's information at time t, or Pij(t) denotes the probability that a node i in the unaware state is connected to a neighbor j in the unaware or recovering state through an edge of layer X; The neighbor j accepts n in the X (X e {A, B}) layer X The probability of a bar information is: Neighbor j receives n A and n A The probability that a node in layer A is still in the un-aware state after receiving n pieces of information is Neighbor j receives n A and n A The probability that a piece of information is still in the unperceived state in layer B after n pieces of information is given by: Given the degree distribution p(k), the probability that a node i is connected to an uninfected neighbor j through an edge is represented as: wherein represents the probability that node i in X is connected to a neighbor of degree or k. The non-susceptible node i successfully acquires information from the adjacent susceptible node j with a probability of λ, The evolution is represented as: At the same time, the node in the adoption state loses interest in the information through the γ probability and returns to the recovery state, The evolution is expressed as: Due to the initial condition Combining equations (15) and (16), The evolution of is rewritten as: By combining equation (10), equation (14) and equation (17), we have: Substituting equation (18) into equation (15), The evolution of equation (17) is rewritten as: In the entire network, the time evolution of the node blocks in the adoption state and the recovery state is represented as: By the combination and iteration calculation of formula (9), formula (20) and formula (21), S(t), A(t) and R(t) are obtained, the proportion of each state at any given time step is calculated, when t→∞, only the nodes in the uninfected state and the recovered state in the whole network, R(∞) represents the final adoption scale; in order to determine R(∞), it is clear that R(∞) = 1 - S(∞) - A(∞) Then, by combining and iterating equation (9) and equation (22), S(∞) and R(∞) are obtained; Substituting equations (2) and (3) into equation (1), θ (∞) is a function of θ X (∞) and θ A (∞) and θ B (∞) is a function of θ In θ A (∞) < 1 and θ B Under the condition (∞) < 1, when θ A (∞)=F A (θ A (∞),θ B (∞)) and θ B (∞)=F B (θ A (∞),θ B When (∞) is tangent, the basic case of the critical point is expressed as:

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