Modeling and Implementation of Echo Chamber Formation in Dynamic Social Networks

Abstract

The present invention belongs to the field of communication. The present invention provides a method for modeling the formation of echo chambers in dynamic social networks. First, the social network G(V, E(t-1)) and the opinion vector X(t) of all people are initialized; where V is a node set, V = {v1, v2, ..., v n}, n is the network size; E is a directed edge set, E={e ij},e ij Refers to node v i Points to node v j Directed edges; X(t)=(x1(t),x2(t),…,x n (t)) T , x i (t) represents the node v i The opinion value at time t (t = 0, 1, 2, ...); secondly, find the outgoing neighbor set of each node, identify the current temporary trust set of each node, and confirm the untrust set of each node; then, update the network based on the temporary trust set and the untrust set to obtain the new network G(V, E(t)), and determine the outgoing neighbor set of each node in the new network; then, confirm the current trust set of each node in the new network based on the outgoing neighbor set of each node in the new network, and calculate the trust matrix W(t); until the preset termination condition is reached, output the updated opinion X(t+1) = W(t)·X(t). The present invention emphasizes the influence of the echo chamber in the opinion evolution modeling process, while fitting the changes in the network.

Description

Technical Field

[0001] The present invention belongs to the field of communication science, and in particular relates to a method for implementing modeling of echo chamber formation in a dynamic social network. Background Art

[0002] In the context of big data and the "Internet Plus" era, data from various fields is now connected through social networks. Therefore, exploring group decision-making within social network environments has significant practical value. Social opinion analysis is a key application scenario for group decision-making within these environments. Current public opinion dynamics often requires integrating theories from social sciences such as psychology and management to avoid being disconnected from social reality. The primary purpose of public opinion dynamics is to establish appropriate models for specific social phenomena, reveal their internal and external drivers, and provide recommendations for public opinion management. In seemingly "free" online social networks, facilitated by internet technologies such as personalized recommendation algorithms, individual opinions are undergoing subtle "transformations." During the evolution of public opinion, selective and repeated interactions between individuals create the conditions for the formation of echo chambers. In communication studies, an echo chamber refers to a lack of information diversity, where individuals are repeatedly exposed to the same ideas within social networks. Bounded belief models, such as the Hegselmann-Krause model, broadly describe the sociological mechanisms that create echo chambers.

[0003] Existing research on echo chambers lacks a mathematical modeling approach to their formation and outcomes. While bounded confidence models in public opinion dynamics focus on understanding consensus and polarization, in real life, managers do not necessarily pursue unanimous consensus. Furthermore, because individuals are embedded in social networks and constantly influence each other, the structure of social networks significantly influences the spread and evolution of ideas and attitudes. Most related research simulates static networks and fails to consider the dynamic impact of individuals within echo chambers on the network. Summary of the Invention

[0004] The technical problem to be solved by the present invention is that the existing technology does not discuss the formation process and results of opinion echo chambers from the perspective of mathematical modeling, and does not take into account the dynamic impact of individuals in the echo chamber on the network.

[0005] The technical solution to the technical problem of the present invention is to provide a method for modeling the formation of echo chambers in dynamic social networks, comprising the following steps:

[0006] Step 1: Initialize the social network G(V, E(t-1)) and the opinion vector X(t) of each person;

[0007] Where V is a node set, V={v1,v2,…,vn}, n is the network size; E is a directed edge set, E={e ij},e ij Refers to node v i Points to node v j Directed edges; X(t)=(x1(t),x2(t),…,x n (t)) T , x i (t) represents the node v i Opinion value at time t, (t = 0, 1, 2, ...);

[0008] Step 2: Find the outgoing neighbor set of each node in the current network, identify the current temporary trust set of each node, and confirm the untrust set of each node;

[0009] Step 3: Update the network based on the temporary trust set and the distrust set to obtain the new network G(V, E(t)), and determine the outgoing neighbor set of each node in the new network;

[0010] Step 4: Confirm the current trust set of each node in the new network based on the outgoing neighbor set of each node in the new network, and calculate the trust matrix W(t);

[0011] Step 5: Repeat steps 2-4 above for each time step until the preset termination condition is reached, and output the updated opinion X(t+1)=W(t)·X(t).

[0012] In one embodiment, in step 2, the outgoing neighbor of each node is the endpoint node of the outgoing edge of the node, N i (t-1)={v j |e ij ∈E(t-1)}, where N i (t-1) represents the node’s outgoing neighbor set.

[0013] In one embodiment, in step 2, the current temporary trust set formula of each node is as follows:

[0014]

[0015] in, represents the current temporary trust set of the node, and ε is the preset unified opinion confidence.

[0016] In one embodiment, in step 2, the distrust set formula of each node is as follows:

[0017] U i (t)={v j |v j ∈N i (t-1),|xi (t)-x j (t)|>ε};

[0018] or:

[0019]

[0020] Among them, U i (t) represents the distrust set of each node.

[0021] In one embodiment, in step 3, updating the network according to the temporary trust set and the untrust set to obtain a new network G(V, E(t)) includes the following steps:

[0022] Step 3.1: If node v i Trust all its outgoing neighbors, then skip to step 3.5; otherwise, v i In its current distrust set U i In (t), a random outgoing neighbor is selected to disconnect;

[0023] Step 3.2: If node v i Temporary trust set If it is empty, go to step 3.5; otherwise, node v i In its current temporary trust set Randomly select an outgoing neighbor v j ;

[0024] Step 3.3: If node v j Temporary trust set If it is empty, skip to step 3.5; otherwise, calculate Where A\B represents the result of deleting the elements of set A from set B, that is, the elements currently being v j Trusted and not v i The set of trusted nodes;

[0025] Step 3.4: If Then go directly to step 3.5; otherwise, Randomly select v k , add v i to v k The edge of

[0026] Step 3.5: Set i=i+1 and return to step 3.1; proceed to step 4 after traversing all nodes.

[0027] In one embodiment, the trust matrix W(t) is calculated as follows:

[0028] W(t)=(w ij (t)) n×n ;

[0029] Among them, w ij (t) represents v at time t i Point v j The degree of trust is calculated as Where card(A) represents the cardinality of set A.

[0030] In one embodiment, the preset termination condition is ||X(t+1)-X(t)|| ∞ ≤0.0001.

[0031] The beneficial effects of the present invention are: First, the present invention emphasizes the influence of echo chambers in the process of opinion evolution modeling, helps to understand the formation of echo chambers, and grasps the evolution law of opinions in this scenario. Secondly, the present invention designs a new dynamic network algorithm to fit the changes in the network. The present invention also takes into account that when individuals are affected by the echo chamber effect, they will seek to visit individuals with similar opinions as themselves. Based on the trust transfer theory, the present invention assumes that users will trust the objects trusted by the people they trust more. Such a network update algorithm is closer to reality and helps public opinion managers predict the direction of public opinion and make decisions while considering the echo chamber effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 , the overall process of the method for implementing modeling of echo chamber formation in a dynamic social network in Example 1 of the present invention.

[0033] Figure 2 , a specific flow chart of the network update algorithm in Example 1 of the present invention.

[0034] Figure 3 , the initial network G(0) in embodiment 2 of the present invention.

[0035] Figure 4 , the updated network G(1) in embodiment 2 of the present invention. DETAILED DESCRIPTION

[0036] In order to make the technical problems, technical solutions and beneficial effects to be solved by this application more clearly understood, this application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0037] Example 1

[0038] First, let the social network of size n be G(V,E), where V = {v1,v2,…,v n} is a node set, E={e ij} is a directed edge set, e ij Point v iPoint v j The opinion value vector of all nodes is recorded as X(t)=(x1(t),x2(t),…,x n (t)) T , where x i (t) represents point v i Opinion value at time t (t=0,1,2,…).

[0039] The overall process of the implementation method of the echo chamber formation modeling in the dynamic social network in this example is as follows Figure 1 As shown, at time t (t = 1, 2, ...), the implementation method is as follows:

[0040] start

[0041] Input: unified opinion confidence ε, network size n, social network G(V,E(t-1)), and everyone's opinion vector X(t).

[0042] Output: The updated social network G(V,E(t)) and everyone’s opinion vector X(t+1).

[0043] Step 1: Find the outgoing neighbor set of each node in the current network. i For example, its outgoing neighbor is v i The endpoint node of the outgoing edge is represented by N i (t-1)={v j |e ij ∈E(t-1)}. At the beginning, the current network represents the initial social network. As time steps go by, the current network represents the updated new social network corresponding to each time step.

[0044] Step 2: Identify the current temporary trust set of each node. During the evolution of opinions, due to the influence of the echo chamber caused by bounded trust, individuals will repeatedly come into contact with the same or similar ideas in the social network, and the people who hold the ideas are v i The trusted individual is represented by That is, if v j V i Trusted, then its opinion value must be at v i within an acceptable range.

[0045] Step 3: Confirm the untrusted set of each point. If v j It is v i outgoing neighbor, but its opinion value exceeds v i The acceptable range is called v j It is v i Untrusted object, and expressed as U i (t)={v j |vj ∈N i (t-1),|x i (t)-x j (t)|>ε} or

[0046] Step 4: Update the network. The specific process of the network update algorithm is as follows: Figure 2 As shown in the figure, a static network is not suitable for today's rapidly changing internet environment. Therefore, new algorithms are needed to adapt to network dynamics. In particular, when individuals are influenced by the echo chamber effect, they will seek to visit individuals with similar opinions. Based on trust transfer theory, this example assumes that users will trust those trusted by those they trust. This network update algorithm is more realistic and helps public opinion managers predict the direction of public opinion and make decisions while considering the echo chamber effect.

[0047] Let i = 1, for node v i , perform steps 4.1 to 4.5:

[0048] Step 4.1: If node v i Trust all its outgoing neighbors, then jump to step 4.5, otherwise, v i In its current distrust set U i In (t), a random outgoing neighbor is selected to disconnect.

[0049] Step 4.2: If point v i Temporary trust set If it is empty, skip to step 4.5. Otherwise, click v i In its current temporary trust set Randomly select an outgoing neighbor v j .

[0050] Step 4.3: If point v j Temporary trust set If it is empty, skip to step 4.5, otherwise calculate Where A\B represents the result of deleting the elements of set A from set B, that is, the elements currently being v j Trusted and not v i The set of trusted nodes.

[0051] Step 4.4: If Then go directly to step 4.5, otherwise, Randomly select v k , add v i to v k The edge.

[0052] Step 4.5: Let i = i + 1. If i ≤ n, return to step 4.1; otherwise, go to step 5.

[0053] Step 5: Based on the new network G(V, E(t)) obtained in step 4, re-determine the outgoing neighbor set of each node in the new network, that is, N i (t)={v j |e ij ∈E(t)}.

[0054] Step 6: Confirm the current trust set of each node. For individuals affected by the echo chamber, their trust set is T i (t)={v j |v j ∈N i (t),|x i (t)-x j (t)|≤ε}∪{v i}.

[0055] Step 7: Calculate the trust matrix W(t) = (w ij (t)) n×n , where w ij (t) represents v at time t i Point v j The degree of trust is calculated as Where card(A) represents the cardinality of set A.

[0056] Step 8: Calculate the updated opinion. According to the opinion vector and the trust matrix, X(t+1)=W(t)·X(t).

[0057] Finish.

[0058] The above algorithm is repeated at each time step until everyone's opinions no longer change and a stable state is reached. The termination condition is set to ||X(t+1)-X(t)|| ∞ ≤0.0001.

[0059] In summary, this example uses a dynamic network design algorithm based on the echo chamber effect. This algorithm leverages the psychology of the echo chamber effect and the trust transmission mechanism, empowering individuals with autonomy and making the network more realistic during the opinion evolution process.

[0060] Example 2

[0061] In this example, a directed network of size 5 is given, and the confidence level of the unified opinion is set to ε=0.2, and the technical solution of the present invention is explained in detail.

[0062] t=0:The initial network G(0) is as follows Figure 3As shown. The outgoing neighbor sets of each point are N1(0) = {v3, v4}, N2(0) = {v1, v5}, N3(0) = {v1, v2}, N4(0) = {v3, v5} and N5(0) = {v3, v4}. Assume that the initial opinions of each individual are X(0) = (0.29, 0.71, 0.32, 0.11, 0.51) T , combined with the initial opinions, the trust sets of each point are T1(0) = {v1, v3, v4}, T2(0) = {v2, v5}, T3(0) = {v1, v3}, T4(0) = {v4} and T5(0) = {v3, v5}.

[0063] The trust matrix is

[0064] Therefore, the new opinion set is X(1)=W(0)·X(0)=(0.24, 0.61, 0.305, 0.11, 0.415) T .

[0065] t=1:Combined with X(1), the temporary trust sets of each point are and

[0066] The distrust sets of each point are and Vertices v2, v3, v4, and v5 currently have untrusted outbound neighbors and will implement network transformation before continuing opinion evolution.

[0067] For point v2, randomly select an outgoing neighbor in its current untrusted set U2(1) to disconnect. Since v2 has only one untrusted outgoing neighbor v1, it can only disconnect edge e 21 , then in its current temporary trust set Randomly select an outgoing neighbor who is not your own, then you can only choose v5, and then in the temporary trust set of v5 Randomly select an outgoing neighbor that is not currently trusted by v2 (avoiding self-connected edges and duplicate edges) and add v2 to the edge of the outgoing neighbor. So add edge e 23 .

[0068] For point v3, randomly select an outgoing neighbor in its current untrusted set U3(1) to disconnect. Since v3 has only one untrusted outgoing neighbor v2, we can only disconnect edge e. 32 , then in its current temporary trust set Randomly select an outgoing neighbor who is not your own, at this time you can only choose v1, and then in the temporary trust set of v1 Randomly select an outgoing neighbor that is not currently trusted by v3 (avoiding self-connected edges and duplicate edges) and add v3 to the edge of the outgoing neighbor. So add edge e 34 .

[0069] For point v4, randomly select an outgoing neighbor in its current untrusted set U4(1) to disconnect. Since v4 has only one untrusted outgoing neighbor v5, we can only disconnect edge e 45 , then in its current temporary trust set Randomly select an outgoing neighbor who is not your own, at this time you can only choose v3, and then in the current temporary trust set of v3 Randomly select an outgoing neighbor that is not currently trusted by v4 (avoiding self-connected edges and duplicate edges) and add v4 to the edge of the outgoing neighbor. So add edge e 41 .

[0070] For point v5, randomly select an outgoing neighbor from its current untrusted set U5(1) to disconnect. Since v5 has only one untrusted outgoing neighbor v4, we can only disconnect edge e. 54 , then in its current temporary trust set Randomly select an outgoing neighbor who is not your own, at this time you can only choose v3, and then in the current temporary trust set of v3 Randomly select an outgoing neighbor that is not currently trusted by v5 (avoiding self-connected edges and duplicate edges) and add v5 to the edge of the outgoing neighbor. So add edge e 51 .

[0071] Therefore, we get Figure 4 The network G(1) is shown. The outgoing neighbor sets of each node are N1(1) = {v3, v4}, N2(1) = {v3, v5}, N3(1) = {v1, v4}, N4(1) = {v1, v3} and N5(1) = {v1, v3}. Combined with X(1), the trust sets of each node are T1(1) = {v1, v3, v4}, T2(1) = {v2, v5}, T3(1) = {v1, v3, v4}, T4(1) = {v1, v3, v4} and T5(1) = {v1, v3, v5}.

[0072] The trust matrix is

[0073] Therefore, the new opinion set is X(2)=W(1)·X(1)=(0.22,0.51,0.22,0.22,0.32) T .

[0074] t=2:Combined with X(2), the temporary trust sets of each point are and The distrust sets of each point are and At this point, only point v2 still has untrusted outbound neighbors, and network transformation is implemented before continuing opinion evolution.

[0075] For point v2, randomly select an outgoing neighbor in its current untrusted set U2(2) to disconnect. Since v2 has only one untrusted outgoing neighbor v3, we can only disconnect edge e 23 , then in its current temporary trust set Randomly select an outgoing neighbor who is not your own, then you can only choose v5, and then in the temporary trust set of v5 Randomly select an outgoing neighbor that is not currently trusted by v2 (avoiding self-connected edges and duplicate edges) and add v2 to the edge of the outgoing neighbor. So add edge e 23 The network has not changed at this time, so we still get the following Figure 4 The network G(2) is shown. The outgoing neighbor sets of each node are N1(2) = {v3, v4}, N2(2) = {v3, v5}, N3(2) = {v1, v4}, N4(2) = {v1, v3} and N5(2) = {v1, v3}. Combined with X(2), the trust sets of each node are T1(2) = {v1, v3, v4}, T2(2) = {v2, v5}, T3(2) = {v1, v3, v4}, T4(2) = {v1, v3, v4} and T5(2) = {v1, v3, v5}.

[0076] The trust matrix is

[0077] Therefore, the new opinion set is X(3)=W(2)·X(2)=(0.22, 0.42, 0.22, 0.22, 0.25) T .

[0078] Repeat the above steps and stop when the difference between the two opinions is no more than 0.0001. Finally, the evolution reaches stability at t = 11, and the stable opinion is X(12) = (0.22, 0.22, 0.22, 0.22) T , and the corresponding final network is still Figure 2 shown.

Claims

1. A method for modeling echo chamber formation in dynamic social networks, characterized in that: The following steps are involved: Step 1: Initialize the social network G(V,E(t-1)) and the opinion vector X(t) of each person; Where V is a node set, V={v1,v2,…,v n }, n is the network size; E is a directed edge set, E={e ij },e ij Refers to node v i Points to node v j Directed edges; X(t)=(x1(t),x2(t),…,x n (t)) T , x i (t) represents the node v i Opinion value at time t, (t = 0, 1, 2, ...); Step 2: Find the outgoing neighbor set of each node in the current network, identify the current temporary trust set of each node, and confirm the untrust set of each node; Step 3: Update the network based on the temporary trust set and the distrust set to obtain the new network G(V, E(t)), and determine the outgoing neighbor set of each node in the new network; Step 4: Confirm the current trust set of each node in the new network based on the outgoing neighbor set of each node in the new network, and calculate the trust matrix W(t); Step 5: Repeat steps 2-4 above for each time step until the preset termination condition is reached, and output the updated opinion X(t+1)=W(t)·X(t); In step 2, the outgoing neighbor of each node is the endpoint node of the outgoing edge of the node, N i (t-1)={v j |e ij ∈E(t-1)}, where N i (t-1) represents the node’s outgoing neighbor set; In step 2, the current temporary trust set formula of each node is as follows: in, represents the node’s current temporary trust set, x j (t) represents the node v j The opinion value at time t, (t = 0, 1, 2, ...); ε is the preset unified opinion confidence; In step 2, the distrust set formula of each node is as follows: U i (t)={v j |v j ∈N i (t-1),|x i (t)-x j (t)|>ε}; or: Among them, U i (t) represents the distrust set of each node; In step 3, the network is updated according to the temporary trust set and the distrust set to obtain a new network G(V, E(t)), which includes the following steps: Step 3.1: If node v i Trust all its outgoing neighbors, then skip to step 3.5; otherwise, v i In its current distrust set U i In (t), a random outgoing neighbor is selected to disconnect; Step 3.2: If node v i Temporary trust set If it is empty, go to step 3.5; otherwise, node v i In its current temporary trust set Randomly select an outgoing neighbor v j ; Step 3.3: If node v j Temporary trust set If it is empty, skip to step 3.5; otherwise, calculate Where A\B represents the result of deleting the elements of set A from set B, that is, the elements currently being v j Trusted and not v i The set of trusted nodes; Step 3.4: If Then go directly to step 3.5; otherwise, Randomly select v k , add v i to v k The edge of Step 3.5: Set i=i+1 and return to step 3.1; proceed to step 4 after traversing all nodes.

2. The method for modeling echo chamber formation in a dynamic social network according to claim 1, characterized in that: The trust matrix W(t) is calculated as follows: W(t)=(w ij (t)) n×n ; Among them, w ij (t) represents v at time t i Point v j The degree of trust is calculated as Where card(A) represents the cardinality of set A.

3. The method for modeling echo chamber formation in a dynamic social network according to claim 2, characterized in that: The preset termination condition is ||X(t+1)-X(t)|| ∞ ≤0.0001.

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