A general higher-order supracentrality framework based on motifs of temporal networks and multiplex networks

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As the dynamics and complexity of networks evolve, identifying the important nodes in temporal networks (i.e., the relationships change over time) and multiplex networks (i.e., the layers can encode different types of relationships) becomes a core topic in network analysis and data science. However, the existing researches merely focus on the first-order relationships (i.e., the interactions only lie in two nodes) regardless of the higher-order relationships (i.e., the interactions exist among multiple nodes) especially for intralayer node interactions, which has been proved to be significant to affect centralities of nodes in the temporal networks and multiplex networks. Motivated by this, by observing and analyzing the interaction patterns of nodes in the temporal networks and multiplex networks, and considering the importance of triadic closure, first we adopt triangular motifs, and reconstruct the real-world system as temporal networks or multiplex networks fused with higher-order motifs information to encode the interactions among multiple nodes. Then we design a higher-order supracentrality framework to mine critical nodes with higher-order features in temporal networks and multiplex networks. The framework we proposed can characterize how the importance of nodes changes over time or different relationships, and also illustrate a complicated dependency of the higher-order supracentrality on the network topology, tunable weights of interlayer coupling and layer teleportation probability. To demonstrate the effectiveness and superiority of higher-order supracentrality framework based on motifs, we provide theoretical analysis and sufficient experiments on two empirical datasets including temporal networks and multiplex networks, the experimental results show that the higher-order supracentrality framework can identify much more abundant important nodes accurately. More significantly, our framework can provide a unifying foundation for centrality analysis in the temporal networks and multiplex networks, and also serve as a guidance for practical applications.