  Closeness Centrality (CC) and Betweenness Centrality (BC) are crucial metrics
in network analysis, providing essential reference for discerning the
significance of nodes within complex networks. These measures find wide
applications in critical tasks, such as community detection and network
dismantling. However, their practical implementation on extensive networks
remains computationally demanding due to their high time complexity. To
mitigate these computational challenges, numerous approximation algorithms have
been developed to expedite the computation of CC and BC. Nevertheless, even
these approximations still necessitate substantial processing time when applied
to large-scale networks. Furthermore, their output proves sensitive to even
minor perturbations within the network structure.
  In this work, We redefine the CC and BC node ranking problem as a machine
learning problem and propose the CNCA-IGE model, which is an encoder-decoder
model based on inductive graph neural networks designed to rank nodes based on
specified CC or BC metrics. We incorporate the MLP-Mixer model as the decoder
in the BC ranking prediction task to enhance the model's robustness and
capacity. Our approach is evaluated on diverse synthetic and real-world
networks of varying scales, and the experimental results demonstrate that the
CNCA-IGE model outperforms state-of-the-art baseline models, significantly
reducing execution time while improving performance.
