Generalized hop-based approaches for identifying influential nodes in social networks

Abstract

Locating a set of influential users within a social network, known as the Influence Maximization (IM) problem, can have significant implications for boosting the spread of positive information/news and curbing the spread of negative elements such as misinformation and disease. However, the traditional simulation-based spread computations under conventional diffusion models render existing algorithms inefficient in finding optimal solutions. In recent years, hop and path-based approaches have gained popularity, particularly under the cascade models to address the scalability issue. Nevertheless, these existing functions vary based on the considered hop-distance and provide no guidance on capturing spread sizes beyond two-hops. In this paper, we introduce Hop-based Expected Influence Maximization (HEIM), an approach utilizing generalized functions to compute influence spread across varying hop-distances in conventional diffusion models. We extend our investigation to the Linear Threshold (LT) model, in addition to the Independent Cascade (IC) and Weighted Cascade (WC) models, filling a gap in current literature. Our theoretical analysis shows that the proposed functions preserve both monotonicity and submodularity, and the proposed HEIM algorithm can achieve an approximation ratio of $\left(1-\frac{1}{e}\right)$ under a limited hop-measures, whereas a multiplicative $\left(\frac{1}{k_{{\sigma }_h}}\left(1-e^{-k_{{\sigma }_h}}\right)\alpha \right)$-approximation under global measures. Furthermore, we show that expected spread methods can serve as a better benchmark approach than existing simulation-based methods. The performance of the HEIM algorithm is evaluated through experiments on three real-world networks, and is compared to six other existing algorithms. Results demonstrate that the three-hop based HEIM algorithm achieves superior solution quality, ranking first in statistical tests, and is notably faster than existing benchmark approaches. Conversely, the one-hop-based HEIM offers faster computation while still delivering competitive solutions, providing decision-makers with flexibility based on application needs.