Hypergraph-Based Influence Maximization in Online Social Networks
Abstract
:1. Introduction
- We take into account adjacent influence and higher-order influence relationships to construct a novel influence diffusion model to improve influence diffusion efficiency, by introducing hypergraph theory.
- We propose a hypergraph sampling greedy algorithm (HSGA) to effectively select the most influential seed nodes, where a random walk-based influence diffusion algorithm and a Monte Carlo-based influence approximation algorithm are devised to achieve fast approximation and calculation of node influences. Influence increments of multiple nodes are calculated and simulation diffusion results are reused.
- We conduct simulations on six real datasets to evaluate the performance of the HSGA. Simulation results demonstrate that compared to benchmark algorithms, the HSGA improves computational efficiency and seed selection accuracy.
2. Related Works
Literature | Optimization Objective | Solution | Method |
---|---|---|---|
[5] | maximize information diffusion spread | network motifs-based influence maximization algorithm | Bayesian machine learning |
[6] | maximize influence spread while guaranteeing seed budget constraints | parallel greedy influence maximization algorithm | multiple influence maximization |
[7] | maximize multi-attribute-based influence spread | sandwich algorithm and supermodular algorithm | – |
[8] | minimize computational overheads of seed selection | progressive evolutionary influence maximization framework | search space reduction strategy |
[9] | accurately determine seed nodes | adaptive agent-based evolutionary influence maximization algorithm | capture real-time user and diffusion features |
[10] | maximize influence spread | multi-transformation evolutionary influence maximization framework | overlap degree |
[11] | maximize targeted influence | reverse reachable set-based greedy algorithm | novel independent cascade model |
[12] | minimize computational cost | two-stage iterative influence maximization framework | exclude less influential nodes |
[13] | minimize computational cost | three-stage iterative influence maximization framework | — |
[16] | maximize influence spread | DRL-based influence maximization framework | graph neural networks |
[17] | maximize balanced influence of seed set | DRL-based balanced influence maximization framework | balance influence of multiple different entities |
[18] | maximize competitive opinion diffusion spread | multistage competitive opinion maximization framework | dynamic opinion propagation model |
[19] | maximize influence spread | graph embedding and graph neural network-based algorithm | pseudo-regression model |
[20] | identify user’s activation level | fuzzy influence maximization algorithm | fuzzy graph |
[21] | maximize influence spread | link prediction-based influence maximization algorithm | DRL model |
[22] | maximize influence spread | activation probability aware influence maximization framework | dynamically update node influence |
[23] | improve propagation efficiency | group trust and local topology structure-based influence maximization algorithm | local topology structure extraction and credibility ranking of groups |
[24] | reduce noise in metadata and uncertainties in connectivity inference | topology-aware ranking strategy for influence maximization with unknown topology | — |
[25] | maximize influence spread | adapted greedy-based compatible influence maximization algorithm | — |
[26] | improve the quality of seed nodes | group-based effective influence maximization algorithm | enhanced independent cascade model |
[27] | minimize rumors’ influences | truth campaign rumor influence maximization strategy | — |
[28] | maximize community opinion | memetic-based community opinion maximization algorithm | multi-faceted opinion evolution model |
[29] | reduce runtime | community-aware influence maximization framework | progressive budgeting method |
[30] | maximize influence spread | overlapping community-based particle swarm optimization algorithm | obtain overlapping community structures |
[31] | maximize influence spread | heuristic general weighted social influence maximization algorithm | crowd influence model |
[32] | maximize information diffusion spread | hypergraph-based sequential interactive framework | dual-channel hypergraph neural networks |
[33] | reduce influence overlap | adaptive degree-based heuristic influence maximization algorithm | — |
[34] | maximize influence spread | advanced greedy-based influence maximization algorithm | novel influence evaluation function |
3. System Model and Problem Formulation
3.1. System Model
3.1.1. Social Network Model
3.1.2. Influence Diffusion Model
3.2. Problem Formulation
4. HSGA Solution
4.1. RWID Algorithm
- (1)
- At the initial stage, all nodes in the social network are first initialized to be in inactive state. Then, the nodes in the seed set are initialized to be in active state. The diffusion probabilities under two different influence modes are initialized as follows.
- (2)
- At each time step , for each active node u, we find its each hyperedge , and set the influence factor . The probability of randomly selecting one hyperedge is set as .
- (3)
- We select a node that belongs to hyperedge as the next activation object.
- (4)
- We repeat the above steps (2) and (3) until there are no new active nodes added during information propagation process. That is, the information propagation process is completed, and accordingly, the final set of seed nodes can be obtained.
Algorithm 1 RWID |
Input: Social network H; Initial seed set S; Output: Set of activated nodes
|
4.2. MCA Algorithm
Algorithm 2 MCA |
Input: Social network H; Initial seed set S; Node u; Monte Carlo simulation times M; Walk step number t; Output: Expected influence
|
4.3. HSGA
- (1)
- We set current node , and set an empty set to store the sampling nodes.
- (2)
- We add current node v to the set , and update node v as its next walk node. We repeat this sampling operation t times iteratively.
- (3)
- After completing t times iterations, we record next node of node v and store it into .
- (4)
- If node v is not in the set , we update the score of node v and to record the real-time visit times of node v, illustrated in Lines 10–13.
Algorithm 3 HSGA |
Input: Social network H; Walk step number t; Size of seed set k; Output: Seed set S
|
Algorithm 4 RWS |
Input: Social network H; Random walk record ; Record array r; Increment ; Transition probability P; Output: Updated transition probability ; Updated increment
|
5. Performance Evaluation
5.1. Simulation Setups
- Algebra [37]: It contains mathematical websites on the relationships among users who comment on problems. Each node represents a user, and users who comment, ask, or answer the same question (in algebra or geometry) are included in the same hyperedge.
- Restaurant-Rev [38]: It represents restaurant reviews. Each node is a Yelp user, and each hyperedge represents specific category reviews of different types of restaurants in Madison, Wisconsin established by connected users within one month.
- Norwegian Interlocking Directorate (NID) [31]: It is a network of interlocking boards in Norway, which describes the relationships among company directors. Each hyperedge represents the complex impact relationship among the resignations of directors.
- DBLP [39]: It is a collection of co-authors who co-authored DBLP papers. Each node is an author, and each hyperedge is a publication.
- Email Enron [40]: It is a dataset of email addresses for Enron employees. Each node is Enron’s email address, and each hyperedge includes the sender and all recipients of the email.
- Email-W3C [41]: It is a set of email addresses on the W3C mailing list. Each hyperedge consists of a set of email addresses that appear in the same email.
5.2. Simulation Results
5.3. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Notation | Description |
---|---|
A social network with a set V of nodes and a set E of hyperedges | |
Set of neighbor nodes of node u | |
Set of in-degree neighbor nodes of node u | |
Set of out-degree neighbor nodes of node u | |
Set of hyperedges that node u belongs to | |
Set of hyperedge neighbor nodes of node u | |
Influence proportion of hyperedge neighbor nodes on node u | |
Influence weight between node u and its in-degree neighbor node v | |
Influence weight between node u and its hyperedge neighbor node v | |
Overall influence probability node u on node v | |
S | Set of seed nodes |
k | Size of seed set |
M | Times of Monte Carlo simulation |
t | Number of Walk steps |
Influence evaluation function | |
Approximation influence at t |
Dataset | Node Number | Hyperedge Number | Edge Number |
---|---|---|---|
Algebra | 423 | 1268 | 50,209 |
Restaurant-Rev | 565 | 601 | 31,241 |
NID | 2045 | 4977 | 7710 |
DBLP | 2727 | 874 | 4298 |
Email-Enron | 2807 | 5000 | 88,926 |
Email-W3C | 5601 | 6000 | 11,130 |
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Zhang, C.; Cheng, W.; Li, F.; Wang, X. Hypergraph-Based Influence Maximization in Online Social Networks. Mathematics 2024, 12, 2769. https://doi.org/10.3390/math12172769
Zhang C, Cheng W, Li F, Wang X. Hypergraph-Based Influence Maximization in Online Social Networks. Mathematics. 2024; 12(17):2769. https://doi.org/10.3390/math12172769
Chicago/Turabian StyleZhang, Chuangchuang, Wenlin Cheng, Fuliang Li, and Xingwei Wang. 2024. "Hypergraph-Based Influence Maximization in Online Social Networks" Mathematics 12, no. 17: 2769. https://doi.org/10.3390/math12172769