Social Network Influence Maximization Method Based on Hop Count and Local Relationship Intimacy

Abstract

A method for maximizing the influence in a social network based on the number of hops and the intimacy of local relationships, which relates to the field of social network technology. The influence propagation range of seed nodes is restricted within 2 hops, fully considering the finiteness of the propagation range of the social network. Moreover, this method introduces the intimacy of local relationships to measure the influence intensity of nodes. Compared with some classic greedy and heuristic methods, this method has a higher accuracy in evaluating the influence of nodes. Not only that, when selecting seed nodes, this method uses the influence coverage gain of nodes as the influence coverage, which can effectively avoid the rich club effect.

Description

Technical Field

[0001] The present invention relates to the technical field of social networks, and in particular to a method for maximizing social network influence based on hop count and local relationship intimacy. Background Art

[0002] In recent years, with the maturation of 4G network technology, the rapid development of 5G networks, and the rise of social apps like WeChat and Weibo, as well as information dissemination apps like TikTok and Toutiao, the internet and its infrastructure have transformed our lifestyles. Disseminating information through social networks has become a part of daily life, storing vast amounts of interactive information data. The study of social networks has garnered widespread attention. Maximizing social network influence has become a research hotspot, as researchers aim to understand the process of information dissemination and diffusion within social networks and identify the most influential nodes.

[0003] The influence maximization method is a fundamental approach to word-of-mouth marketing on social networks. Its goal is to identify opinion leaders within these networks and, through them, spread the word of a product through a one-to-ten, ten-to-a-hundred-to-one spread, ultimately leading to awareness and purchase of the product among users within the social network. Specifically, the influence maximization method involves finding a specific number of influential users (i.e., seed nodes) within a given social network. This group of users serves as the starting point for marketing information, maximizing its spread within the network. Compared to other marketing methods, word-of-mouth marketing offers advantages such as low cost, rapid dissemination, and wide reach, making it a popular choice for many businesses.

[0004] Maximizing influence in social networks has been proven to be an NP-hard problem. Therefore, there are currently two main approaches: greedy algorithms with a better reach, and heuristic algorithms with higher efficiency. However, greedy algorithms take a long time to run, while heuristic algorithms can produce unstable results. Furthermore, when maximizing influence, special attention should be paid to the "rich club" effect. This refers to the fact that, although nodes with high degree values (i.e., rich nodes) in a social network only account for a small proportion, they tend to connect to each other, resulting in a high degree of overlap in the set of nodes they can activate within the network. This results in a smaller final influence spread. Summary of the Invention

[0005] In order to overcome the shortcomings of the above technologies, the present invention provides a social network influence maximization method that uses local relationship intimacy to reflect the relationship intimacy of a node within its influence coverage area.

[0006] The technical solution adopted by the present invention to overcome the technical problems is:

[0007] A method for maximizing influence in a social network based on hop count and local relationship intimacy, comprising the following steps:

[0008] a) Construct a social network to obtain a weighted social network G;

[0009] b) Delete the edges with low propagation probability in the weighted social network G to obtain a new social network G new ;

[0010] c) Calculate the set σ(i) of all user nodes within two hops of each user node in the new social network G new , and store the number |σ(i)| of nodes within the influence coverage of all user nodes in the new social network G new into an array and sort it in descending order, and delete the nodes with |σ(i)| = 0 in the array;

[0011] d) Calculate the local relationship intimacy α(i)1 and α(i)2 of all user nodes;

[0012] e) Add the user node with the largest number of nodes within the current influence coverage to the seed set S, and update the number of nodes within the influence coverage of all user nodes within four hops of the user nodes in the seed set S;

[0013] f) Repeat step e) until the number of user nodes in the seed set S is equal to k, where k is the number of user nodes that the user hopes to select from the social network.

[0014] Further, step a) includes the following steps:

[0015] a-1) Obtain the information of n users from the Twitter dataset, and construct a set V of user nodes in the social network, V = {v1, v2,..., v i ,..., v n}, where v i is the i-th user node, i ∈ {1,..., n};

[0016] a-2) If the i-th user node v i and the j-th user node v j have a follow relationship or interaction data, then an edge e i is formed between the i-th user node v j and the j-th user node v p , i ∈ {1,..., n}, j ∈ {1,..., n}, each node in the set V of user nodes in the social network has m edges, and the edge set of the weighted social network is E, E = {e1, e2,..., e p ,..., e m}, p ∈ {1,..., m};

[0017] a - 3) Normalize the edge e p to obtain the weight p p of the edge e p . The weights of all the normalized edges form the set P of the weights of the edges in the weighted social network, P = {p1, p2,..., p p ,..., p m};

[0018] a - 4) The weighted social network G = (V, E, P).

[0019] Furthermore, in step b), if the weight p p is less than the constant a, then delete the edge e p . The set of remaining edges is E new . The set of weights of the edges corresponding to the set of edges E new is P new . The new social network G new = (V, E new , P new ).

[0020] Furthermore, step c) includes the following steps:

[0021] c - 1) Calculate the set σ(i) of all nodes within two - hops of the i - th user node v using the formula, where N i is the set of neighbor nodes of the i - th user node v i , i and is the set of neighbor nodes of the neighbor nodes of the i - th user node v i . The set σ(i) is the influence coverage range of the i - th user node v i ;

[0022] c - 2) The number of nodes within the influence coverage range of the i - th user node v i is |σ(i)|. Store the number of nodes within the influence coverage ranges of all user nodes in the social network user node set V into an array and sort it in descending order. Delete the nodes with |σ(i)| = 0 in the array.

[0023] Furthermore, step d) includes the following steps:

[0024] d - 1) Calculate the intimacy α(i)1 between the i - th user node v i 1 and its one - hop neighbors using the formula α(i)1 = (∑P i ) / |N i | and store it in an array, where P i 1 ​​For the i-th user node v i The set of weights of the edges with its one-hop neighbors;

[0025] d-2) By the formula α(i)2=(∑P i 2 ) / |σ(i)| calculates the i-th user node v i The closeness of the relationship with its two-hop neighbor is α(i)2 and stored in an array, where P i 2 For the i-th user node v i The set of weights of the edges with its one-hop neighbors;

[0026] d-3) Delete the nodes in the array where α(i)1<b or α(i)2<c, where b and c are both constants, b>c≥0.2, and b≥0.4. Further, step e) includes the following steps:

[0027] e-1) selecting the user node q with the largest number of user nodes within the influence coverage range according to the descending sorted array of the number of nodes within the influence coverage range of all user nodes in the social network user node set V, q∈{1,...,n};

[0028] e-2) Add the user node q to the seed set S and delete the user node from the array;

[0029] e-3) Traverse the qth user node v q All neighbor nodes within four hops are obtained as set V q , For user node v q The xth user node within four hops, x∈{1,...,l}, l is the user node v q The number of neighbor nodes within four hops is calculated by the formula Calculate the updated qth user node v q The number of nodes within the influence coverage range is The qth user node v q The number of nodes within the updated influence coverage of all neighboring nodes within four hops is stored in an array and sorted in descending order, where For the xth user node The set of all nodes within two hops, For the xth user node The set of neighbor nodes of For the xth user node The set of neighbor nodes of the neighbor nodes, the seed set is the y-th user node in the seed set S, where y ∈ {1,..., j}, j is the number of user nodes in the seed set S, and σ(S) is the influence coverage of the seed set S, σ(S) = σ(S 1 ) ∪ σ(S 2 ) ∪... ∪ σ(S y ) ∪... ∪ σ(S j ), σ(S y ) is the y-th user node in the seed set S the set of all nodes within two hops, is the y-th user node the set of neighbor nodes of, is the y-th user node the set of neighbor nodes of neighbor nodes of.

[0030] The beneficial effects of the present invention are: restricting the influence propagation range of seed nodes within two hops, fully considering the finiteness of the propagation range of the social network. And this method introduces local relationship intimacy to measure the influence intensity of nodes. Compared with some classical greedy and heuristic methods, this method has higher accuracy in evaluating the influence of nodes. Moreover, when selecting seed nodes, this method uses the influence coverage gain of nodes as the influence coverage, which can effectively avoid the rich club effect. Description of the Drawings

[0031] Figure 1 is the flowchart of the method of the present invention. Detailed Embodiments

[0032] The following will further describe the present invention in conjunction with the attached Figure 1 drawings.

[0033] As shown in the attached Figure 1 drawings, a method for maximizing social network influence based on hop count and local relationship intimacy includes the following steps:

[0034] a) Construct a social network to obtain a weighted social network G.

[0035] b) Delete the edges with low propagation probability in the weighted social network G to obtain a new social network G new .

[0036] c) Calculate the set σ(i) of all user nodes within two hops of each user node in the new social network G new , store the number of nodes |σ(i)| within the influence coverage of all user nodes in the new social network G new in an array and sort it in descending order, and delete the nodes with |σ(i)| = 0 in the array.

[0037] d) Calculate the local relationship intimacy α(i)1 and α(i)2 of all user nodes.

[0038] e) Add the user node with the largest number of nodes within the current influence coverage to the seed set S, and update the number of nodes within the influence coverage of all user nodes within four hops of the user nodes in the seed set S. f) Repeat step e) until the number of user nodes in the seed set S is equal to k, where k is the number of user nodes that the user hopes to select from the social network, and generally, it is determined by the user when using this influence maximization algorithm.

[0039] Generally speaking, there are mainly two metrics for verifying the influence maximization problem, one is the influence range, and the other is the propagation efficiency. However, most current work does not consider the real factors in the social network, such as the propagation range and probability of node influence and the possible "rich club" effect generated by the algorithm results. In social networks and network theory, "hop count" is a concept used to measure the distance between two nodes. It indicates how many connections (or edges) are required to reach one node from another node. Each connection is called a hop. In multiple previous studies, it has been mentioned that when considering each additional propagation hop in influence diffusion, the increase in influence diffusion usually decreases with the increase in the hop count, and most influence diffusion occurs within the first few propagation hops. Goel et al. showed in the paper "The structure of online diffusion networks" that after observing multiple domain datasets, in influence diffusion, less than 10% of the cascades are more than 2 hops away from the seed nodes. Therefore, in order to effectively reflect the propagation of influence, this study focuses on the first two hops in influence propagation, that is, the neighbor nodes within 2 hops of the seed nodes may be activated by the influence of the seed nodes, and specifically which nodes can be activated is related to the propagation probability between nodes. This patent proposes "local relationship intimacy" to reflect the degree of intimacy of the relationship of a node within its influence coverage. To sum up, this patent proposes an influence maximization method in social networks based on hop count and local relationship intimacy.

[0040] In an embodiment of the present invention, step a) includes the following steps:

[0041] a-1) Obtain the information of n users from the Twitter dataset, and construct a set V of social network user nodes, V = {v1, v2,..., v i ,..., v n}, where v i is the i-th user node, and i ∈ {1,..., n}.

[0042] a-2) If the i-th user node vi and the j-th user node v j has a follow relationship or interaction data, then the i-th user node v i and the j-th user node v j form an edge e p , i ∈ {1,..., n}, j ∈ {1,..., n}, each node in the set V of social network user nodes has m edges, and the edge set of the weighted social network is E, E = {e1, e2,..., e p ,..., e m}, p ∈ {1,..., m}.

[0043] a-3) Normalize the edge e p to obtain the weight p p of the edge e p , and the weights of the normalized edges form the weight set P of the edges of the weighted social network, P = {p1, p2,..., p p ,..., p m}.

[0044] a-4) The weighted social network G = (V, E, P).

[0045] In an embodiment of the present invention, in step b), if the weight p p is less than the constant a, then delete the edge e p , 0 ≤ a ≤ 0.2, the set of remaining edges is E new , the set of corresponding edge weights of the edge set E new is P new , and the new social network G new = (V, E new , P new ).

[0046] In an embodiment of the present invention, step c) includes the following steps:

[0047] c-1) Calculate the set σ(i) of all nodes within two hops of the i-th user node v through the formula i , where N i is the set of neighbor nodes of the i-th user node v i , the set of neighbor nodes of the neighbor nodes of the i-th user node v i , and the set σ(i) is the influence coverage range of the i-th user node v i .

[0048] c-2) The i-th user node v iThe number of nodes within the influence range of [|σ(i)|] is stored in an array for all user nodes in the social network user node set V, sorted in descending order, and nodes with |σ(i)| = 0 are deleted from the array.

[0049] In an embodiment of the present invention, to avoid extreme cases in influence propagation simulation, the present invention introduces local relationship intimacy to evaluate the strength of node influence. Local relationship intimacy is the degree of closeness of a node to its neighbor nodes within a certain number of hops. Specifically, step d) includes the following steps:

[0050] d-1) Calculate the relationship intimacy α(i)1 between the i-th user node v i 1 and its one-hop neighbors through the formula α(i)1 = (∑P i ) / |N i | and store it in an array. In the formula, P i 1 is the set of weights of the edges between the i-th user node v i and its one-hop neighbors.

[0051] d-2) Calculate the relationship intimacy α(i)2 between the i-th user node v i 2 and its two-hop neighbors through the formula α(i)2 = (∑P i ) / |σ(i)| and store it in an array. In the formula, P i 2 is the set of weights of the edges between the i-th user node v i and its one-hop neighbors.

[0052] d-3) Delete the nodes in the array where α(i)1 < b or α(i)2 < c. Both b and c are constants. The constants b and c are two constants set according to the specific social network to determine whether a certain user node can be selected as a seed node. For example, a user node has many neighbors and a large degree value, but it is not close enough to its neighbors (low propagation probability), and we consider it cannot be used as a seed node. The constant b is used to determine whether the node is close enough to its one-hop neighbor nodes. When [condition for b], it is close enough to its one-hop neighbor nodes. The constant c is used to determine whether it is close enough to the nodes within the influence range. When [condition for c], it is close enough to the nodes within its influence range. Since the influence propagation of the seed node to its two-hop neighbors depends on the influence propagation to its one-hop neighbors, b > c ≥ 0.2 and b ≥ 0.4 are set.

[0053] In an embodiment of the present invention, step e) includes the following steps:

[0054] e-1) Select the user node q with the largest number of nodes within the influence coverage range from the array sorted in descending order of the number of nodes within the influence coverage range of all user nodes in the social network user node set V, where q ∈ {1,..., n}.

[0055] e-2) Add the user node q to the seed set S and delete this user node from the array.

[0056] e-3) Traverse all neighbor nodes within four hops of the q-th user node v q to obtain the set V q , for the x-th user node v q within four hops, where x ∈ {1,..., l}, and l is the number of neighbor nodes of the user node v q within four hops. Calculate the updated number of nodes within the influence coverage range of the q-th user node v using the formula q to be Store the updated number of nodes within the influence coverage range of all neighbor nodes within four hops of the q-th user node v q in the array and sort it in descending order. In the formula, is the set of all nodes within two hops of the x-th user node , is the set of neighbor nodes of the x-th user node , is the set of neighbor nodes of neighbor nodes of the x-th user node , and the seed set is the y-th user node in the seed set S, where y ∈ {1,..., j}, j is the number of user nodes in the seed set S, and σ(S) is the influence coverage range of the seed set S. σ(S) = σ(S 1 ) ∪ σ(S 2 ) ∪... ∪ σ(S y ) ∪... ∪ σ(S j ), and σ(S y ) is the set of all nodes within two hops of the y-th user node in the seed set S , is the set of neighbor nodes of the y-th user node , is the set of neighbor nodes of neighbor nodes of the y-th user node v Sy .

[0057] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for maximizing influence in a social network based on hop count and local relationship intimacy, characterized in that, It includes the following steps: a) Construct a social network to obtain a weighted social network G; b) Delete the edges with small propagation probability in the weighted social network G to obtain a new social network G new ; c) Calculate the new social network G new For each user node i in, collect the set σ(i) of all user nodes within two hops, and store the number of nodes |σ(i)| within the influence coverage of all user nodes in the new social network G new into an array and sort it in descending order. Delete the nodes with |σ(i)| = 0 from the array; d) Calculate the local relationship intimacy α(i)1 and α(i)2 of all user nodes; e) Add the user node with the largest number of nodes in the current influence coverage range to the seed set S, and update the number of nodes within the influence coverage of all user nodes within four hops of the user nodes in the seed set S; f) Repeat step e) until the number of user nodes in the seed set S is equal to k, where k is the number of user nodes that the user hopes to select from the social network; Step a) includes the following steps: a-1) Obtain the information of n users from the Twitter dataset and construct a set V of social network user nodes, where V = {v1, v2,..., v i ,..., v n}, and v i is the i-th user node, where i ∈ {1,..., n}; a-2) If the i-th user node v i and the j-th user node v j have a following relationship or interaction data, then an edge e i is formed between the i-th user node v j and the j-th user node v p , where i ∈ {1,..., n}, j ∈ {1,..., n}, each node in the set V of social network user nodes has m edges, and the edge set of the weighted social network is E, E = {e1, e2,..., e p ,..., e m}, and p ∈ {1,..., m}; a-3) Normalize edge e p to obtain the weight p p of edge e p . The weights of all the normalized edges form the set P of the weights of the edges of the weighted social network, P = {p1, p2,..., p p ,..., p m}; a-4) The weighted social network G = (V, E, P); Step d) includes the following steps: d-1) Calculate the relationship intimacy α(i)1 between the i-th user node v i 1 ) and its one-hop neighbors through the formula α(i)1 = (∑P i and store it in an array. In the formula, P i is the set of weights of the edges between the i-th user node v i 1 and its one-hop neighbors; i ​ d-2) Calculate the relationship intimacy α(i)2 between the i-th user node v i 2 and its two-hop neighbors through the formula α(i)2 = (∑P i ) / |σ(i)| and store it in an array, where P i 2 is the set of weights of the edges between the i-th user node v i and its one-hop neighbors; d-3) Delete the nodes in the array where α(i)1 < b or α(i)2 < c, where b and c are both constants, b > c ≥ 0.2, and b ≥ 0.

4.

2. The method for maximizing the influence in a social network based on the number of hops and the intimacy of local relationships according to claim 1, wherein: If the weight p in step b p is less than the constant a, then the edge e p is deleted, and the set of remaining edges is E new , and the set of edges is E new . The corresponding set of edge weights is P new . The new social network G new =(V, E new , P new ).

3. The method for maximizing social network influence based on hop count and local relationship intimacy according to claim 1, wherein Step c) includes the following steps: c-1) Calculate the set σ(i) of all nodes within two hops of the i-th user node v through the formula where N i is the set of neighbor nodes of the i-th user node v i and i is the set of neighbor nodes of the neighbor nodes of the i-th user node v. The set σ(i) is the influence coverage range of the i-th user node v ; i i ​ c-2) The number of nodes within the influence coverage of the $i$-th user node $v$ i is $|\sigma(i)|$. Store the number of nodes within the influence coverage of all user nodes in the social network user node set $V$ into an array and sort it in descending order. Delete the nodes with $|\sigma(i)| = 0$ from the array.

4. The method for maximizing social network influence based on hop count and local relationship intimacy according to claim 3, characterized in that, Step e) includes the following steps: e-1) Select the user node q with the largest number of nodes within the influence coverage according to the array sorted in descending order of the number of nodes within the influence coverage of all user nodes in the social network user node set V, q ∈ {1,..., n}; e-2) Add the user node q to the seed set S and delete this user node from the array; e-3) Traverse all neighbor nodes within four hops of the q-th user node v q to obtain the set V q , for the user node v q the x-th user node within four hops, x ∈ {1, …, l}, where l is the number of neighbor nodes of the user node v q The number of neighbor nodes within four hops, and calculate the updated number of nodes within the influence coverage of the q-th user node v as q Store the number of nodes within the updated influence coverage of all neighbor nodes within four hops of the q-th user node v into the array and sort them in descending order. In the formula is the x-th user node q is the set of all nodes within two hops, is the set of neighbor nodes of the x-th user node is the set of all nodes within two hops, is the set of neighbor nodes of the x-th user node is the set of neighbor nodes of the neighbor nodes of the x-th user node, and the seed set is the y-th user node in the seed set S, y ∈ {1, …, j}, where j is the number of user nodes in the seed set S, and σ(S) is the influence coverage of the seed set S, σ(S) = σ(S ) ∪ σ(S ) ∪... ∪ σ(S 1 ) ∪... ∪ σ(S 2 ) ∪... ∪ σ(S y ) ∪... ∪ σ(S j ), σ(S y ) is the y-th user node in the seed set S is the set of all nodes within two hops, is the set of neighbor nodes of the y-th user node is the set of neighbor nodes of the neighbor nodes of the y-th user node is the set of neighbor nodes of the neighbor nodes of the y-th user node is the set of neighbor nodes of the neighbor nodes of the y-th user node

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