Quantizing netwoifying the significance of ties in preserving network connectivity is crucial for identifying weak ties, which often serve as bridges between communities, and for detecting community structures. However, accurately characterrk connectivity and formalizing the relationship between weak ties and communities remain challenging. In this study, we introduce hierarchy-based link centrality (HLC), a novel metric based on the dissimilarity between the original network and its contracted version, where the terminal nodes of links merge and connect to all their neighbors. This dissimilarity is quantified by variations in the network hierarchy, specifically the nodal distance distributions. In addition to the experiments on weak tie identification and link-based network disintegration, we develop a link-based community detection (LCD) approach that focuses on optimal link ranking to elucidate community structures. Experiments across various networks demonstrate that HLC excels in identifying weak ties, achieving a 2.9% higher accuracy than the second-best metric. It also outperforms others in detecting critical link combinations for network disintegration, reducing the average size of the giant connected component by 7.2% compared to the suboptimal counterpart. Furthermore, HLC enhances community detection, achieving optimal partitioning with an average 5.7% improvement in modularity over five other indices. These results highlight the effectiveness of HLC in quantifying weak ties and suggest broad applications for this innovative approach in network analysis.