Assessing edge importance in social networks: an importance indicator based on the \(k\)-sup structure

Within the realm of social networks, most research efforts have concentrated on identifying crucial nodes in networks, with little attention paid to identifying critical edges. Nevertheless, edges, serving as conduits for information dissemination, hold significant importance. Mining critical edges in networks can serve as a valuable target for both network disassembly as an attack strategy and network preservation as a defensive measure. This paper introduces the \(k\) $k$ -sup structure by taking into account the strength of relationships between nodes and investigates the critical subgraph based on the \(k\) $k$ -sup structure. Furthermore, this paper distinguishes between the significance of inter-community edges and intra-community edges, proposing an importance indicator based on the \(k\) $k$ -sup structure. To validate the effectiveness of the proposed indicator, comparative experiments are conducted with seven classic edge importance indicators on eight real-world network datasets and three synthetic network datasets. The experimental results demonstrate that the proposed indicator assesses their importance, exhibiting superiority over alternative methods in terms of network connectivity.