## 1 Introduction
The authors of [16] considered the number of connections as link weights and redefined the centrality metrics to consider both the number of links and their weights in the graphs. On the other hand, the authors of [17] proposed time-based measures that leverage the temporal patterns of changing topologies. Furthermore, individuals have inherent social tendencies, and their behavioral patterns, which are substantially influenced by the patterns of interaction among individuals, are not random [18; 19]. Thus, when identifying hub nodes in the network, mobility patterns, spatiotemporal connections, and social behavior must also be considered. In examining the current landscape of detecting influential nodes, several notable works have delved into incorporating both non-social and social attributes associated with network nodes. The research conducted by the authors of [20] focuses on centrality metrics, which help identify important nodes in a network, crucial for understanding network structures and behaviors. Static and dynamic centrality metrics are discussed, including their relevance in weighted networks. The study highlights challenges, proposes new centrality metrics, and emphasizes the importance of considering temporal aspects in network analysis. It also explores network resilience and the impact of centrality on fault tolerance. However, the authors do not explore a broader range of centrality measures or compare this measure with other existing centrality measures comprehensively. The research conducted by the authors of [21] delves into online information propagation within complex networks, emphasizing the critical role of influential nodes in network structure and operation. The paper classifies centrality measures into global, local, and semi-local types, exploring their effectiveness in identifying influential nodes. It introduces a novel centrality measure, 'centripetal centrality,' and presents an algorithm,'seeds exclusion,' to enhance information propagation. The work demonstrates the effectiveness of 'centripetal centrality' in identifying key nodes and improving propagation effects. The authors assume that identifying influential spreaders is essential for maximizing information coverage. However, this assumption might not always hold true, especially in scenarios where the objective differs from maximizing information spread. For instance, in communication networks, it is crucial to minimize overhead rather than increase it. The authors of [22] address the prediction of social network dynamics and evolution, distinguishing between short-term dynamics and long-term changes. The proposed methodology, MONDE, utilizes hidden Markov models and a genetic algorithm to predict individual, group, and network dynamics. The approach aims to provide a comprehensive view of network evolution and dynamics, benefiting fields such as marketing and public security by aiding decision-making and strategy planning. However, the accuracy and effectiveness of MONDE heavily depend on the quality and availability of data, especially the posting activities and comments used for feature extraction. Incomplete or inaccurate data could lead to less reliable predictions, particularly in the case of low-density networks where empty or discontinuous samples may exist in the data. The study carried out by the author of [23] explores critical node detection and introduces a novel centrality measure, known as isolating centrality, to identify nodes that significantly impact network connectedness. The paper emphasizes the importance of accurately identifying critical nodes for ensuring network reliability and provides a comparative analysis of centrality measures' performance. It also investigates the correlation between leverage centrality and critical nodes, showcasing the effectiveness of the proposed centrality measure.