# Influence Maximization in Social Network Considering Memory Effect and Social Reinforcement Effect
## 4 Algorithms
### General Greedy Algorithm
It should be noted that, considering the characteristics of the real network, the nodes selection did not select the node with the minimum degree of 1, but the node with a small degree of connection. The basic popularity of information \(\lambda\) was calculated as \(0.05,0.1,\cdots,0.45,0.5\), and 100 times for each experiment, then the average value was calculated. ### Evaluation Index

Maximum infection rate (MIR), which is the ratio of the number of infected nodes to the total number of network nodes after the completion of the infection process. Since all infected nodes in the model will eventually become immune nodes, we can consider the proportion of the final immune nodes as the final infection rate. MIR is used to characterize the final influence range of propagation nodes on the entire network. ### Results and Analysis of Experiment

From the experimental results, which are showed in Figure 4, we could see that the value of MIR increases with the increase of \(\lambda\). Except the MIR of Epinions, Twitter and sina weibo in RWSIR model were between 0.4-0.6, the other MIRs were all close to 1, and the information basically covered the whole network. Compared with the two models, when \(\lambda\) is small, the MIR of RWSIR is lower than DCM4 VM, meanwhile, when \(\lambda\) is large, it is the opposite. In other words, with the increase of the importance of the propagation object, the algorithm proposed in this paper could achieve a greater range of influence. Figure 4: _Cont._

## 7 Conclusions

This paper proposes a new propagation model to capture the dynamic changes of memory effect and social reinforcement effect, and improves this model. Experimental results show that the improved model can capture some important features of viral marketing in social networks and explain some phenomena that cannot be explained by the existing definition of impact maximization problem. What's more, the improved model also has lower time complexity. Finally, in order to illustrate the effectiveness of the algorithm proposed in this paper in the propagation process, this paper compares the DCM4 VM method proposed in this paper with a method called RWSIR; the result also shows that the method in this paper has a much greater effect. Although this paper could achieve good results in terms of performance and time complexity, further research and improvements are needed in the following aspects:

1. In the degree discount algorithm, a method is adopted to compute and update the expectations of accepted nodes (which is influenced nodes in the original algorithm) in each round of selection considering only one-step neighbor nodes. This calculation method has a certain randomness. In the next step, empirical value and experimental value can be considered to replace the existing method and reduce the complexity of calculation. 2. This paper adopts a combination of greedy and heuristic algorithms to improve the problem of impact maximization, and divides the whole process into two parts. In future research, these two parts could be iterated to further improve the effect. This method also has a hidden danger of falling into local optimization. The next step is to consider the most effective method to prevent local entanglement, such as some bionic algorithms. 3. The propagation problem studied in this paper does not take into account the time delay. In fact, time delay has a very important impact on this study, which will also be the focus of future research. Writing--original draft, F.W. ; Writing--review & editing, Z.Z. and P.L. ; Data curation, P.W. ; Methodology, P.L. ; Software, P.W. ; Funding acquisition, P.L. ; Project administration, Z.Z. ; Supervision, P.L. This work was supported National Natural Science Foundation (61373148), National Social Science Fund (12 BXW040); Science Foundation of Ministry of Education of China(14Y)C860042), Shandong Provincial Social Science Planning Project (18 CXWJ01, 18 BJYJ04, 19 BJC51). The authors declare no conflict of interest. ## References

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