An undirected weighted graph (UWG) is regularly adopted to portray the interactions among a solo set of nodes from big data-connected applications such as the interactive confidence between proteins in a protein network. A graph convolutional network (GCN) is able to represent a UWG for subsequent pattern analysis tasks such as missing link estimation. However, existing GCNs mostly neglect the local collaborative information hidden in connected node pairs, which leads to severe information loss. To address this issue, this study proposes a node-collaboration-informed graph convolutional network (NGCN) model for implementing the precise UWG representation learning with threefold ideas: 1) extracting the nodes' global graph characteristics via incorporating the residual connection and weighted representation propagation into the GCN module; 2) learning the nodes' local collaborative information from the observed interactive node pairs via a symmetric latent factor analysis (SLFA) module; and 3) designing an effective strategy to fuse the nodes' global graph characteristics and local collaborative information adaptively for highly accurate representation to the target UWG. Its high representation ability to target UWG is proved in theory. Empirical studies on six UWGs generated by real-world applications indicate that owing to its elegant modeling for the node collaborations, the proposed NGCN significantly outperforms several leading-edge models in estimation accuracy to the missing links of a UWG. Its high scalability ensures its compatibility with other GCN extensions, which will be investigated in the future.
