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 under a limited hop‐measures, whereas a multiplicative ‐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.
