TSCR value for all nodes in the network of Fig 1.

Nodes that play strategic roles in networks are called critical or influential nodes. For example, in an epidemic, we can control the infection spread by isolating critical nodes; in marketing, we can use certain nodes as the initial spreaders aiming to reach the largest part of the network, or they can be selected for removal in targeted attacks to maximise the fragmentation of the network. In this study, we focus on critical node detection in temporal networks. We propose three new measures to identify the critical nodes in temporal networks: the temporal supracycle ratio, temporal semi-local integration, and temporal semi-local centrality. We analyse the performance of these measures based on their effect on the SIR epidemic model in three scenarios: isolating the influential nodes when an epidemic happens, using the influential nodes as seeds of the epidemic, or removing them to analyse the robustness of the network. We compare the results with existing centrality measures, particularly temporal betweenness, temporal centrality, and temporal degree deviation. The results show that the introduced measures help identify influential nodes more accurately. The proposed methods can be used to detect nodes that need to be isolated to reduce the spread of an epidemic or as initial nodes to speedup dissemination of information.