Critical Node Detection in Temporal Social Networks, Based on Global and Semi-local Centrality Measures

TL;DR

Three new measures to identify the critical nodes in temporal networks are proposed: the temporal supracycle ratio, temporal semi-local integration, and temporal semi-local centrality and the results show that the introduced measures help identify influential nodes more accurately.

Abstract

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.

Figures (7)

• Figure 1: A simple temporal network with edge labeled with time steps.
• Figure 2: Illustration of the temporal supracycle ratio (TSCR). The most important nodes have lighter colour.
• Figure 3: Illustration of important nodes using Temporal Semi-Local Integration (TSLI). The most important nodes have lighter colour.
• Figure 4: Illustration of important nodes using Temporal Semi-Local Centrality (TSLC). The most important nodes have lighter colour.
• Figure 5: (a-d) Epidemic spread after removing the top $1\%$ critical nodes for isolation and then comparing the six measures in different networks. (e-h) Epidemic spread in the network when the top $1\%$ nodes are selected as initial spreaders or seeds in the different networks.