Estimating the all-terminal signatures for networks by using deep neural network

Computing the signature of a network is both significant and challenging. Addressing the limitations of existing methods in batch processing of large-scale network signatures, in this paper we propose a novel DNN (Deep Neural Network)-based framework for estimating the all-terminal signature and reliability for networks with varying topologies. Our framework involves constructing a DNN model with four efficient and compact network topological features (the numbers of nodes, and links, the node degrees and the link connectivity) as input features and the signature as the response. Additionally, we propose to estimate the all-terminal network reliability based on the signature estimated by the DNN, termed the two-stage DNN approach, which does not require the link reliability as one of the inputs, resulting in better estimation accuracy and generation performance compared to traditional DNN approaches. A case study is conducted and the results show that the estimation accuracy of our DNN model for the signature is satisfactory, and the two-stage DNN approach for network reliability outperforms existing DNN approaches in the literature.