# Predicting Critical Nodes in Temporal Networks by Dynamic Graph Convolutional Networks
## 2 Related Works  
To deal with the problems of identifying critical nodes in temporal networks, many methods based on structure and propagation dynamics have been proposed, and an intuitive idea is to extend methods in static networks such as degree, closeness and betweenness centrality to temporal networks. By this idea, [PERSON] et al. [31] proposed the time-ordered graph, embedding dynamic networks into directed and static networks. This enables us to extend network properties in a very natural way to the dynamic case. [PERSON] et al. [28] proposed the temporal version of dynamic-sensitive centrality, which extends dynamic-sensitive centrality [32] to temporal networks by the Markov chain for the epidemic model, and the numerical simulation shows that the new centrality performs much better than some topological structural centralities. By coupling centrality matrices in each snapshot into a supracrality matrix, [PERSON] et al. [33] proposed an extension framework for static centrality measures such as eigenvector-based centrality and introduced the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. [PERSON] et al. [34] defined a supra-evolution matrix to describe the structure of temporal networks. with using of the time series analysis, the relationships between different time layers can be learned automatically. Based on the special form of the supra-evolution matrix, the eigenvector centrality calculating problem is turned into the calculation of eigenvectors of several low-dimensional matrices through iteration, which effectively reduces the computational complexity. This type of method can find critical nodes in the current temporal network but can not predict the importance of nodes in the future. To find the most influential nodes, [PERSON] et al. proposed a method [35] which measures the impact of each node by the triangle property based on 2-hop neighbors. [PERSON] et al. proposed an attenuation-based supra-adjacency matrix (ASAM) [36] to model temporal networks and evaluated the importance of nodes in temporal network by calculating the eigenvector centrality of the nodes in each time layer. [PERSON] et al. proposed a temporal gravity model [37] which treats basic node properties as the mass and temporal characteristics as the distance to identify important nodes in temporal networks.  
In recent years, graph neural networks (GNNs) have become research hotspots and have been used to solve graph-related problems, such as graph [38; 39] and node [26; 27] classification. Among them, DGNN [40] has recently prevailed deep learning models used to deal with temporal graphs, which often make use of a graph neural network (GNN) [41] and recurrent neural network (RNN) [42]. GCRN-M [43] stacks a spectral GCN [44] and a standard LSTM to predict structured sequences of data. DyGGNN [45] uses a gated graph neural network (GGNN) [46] combined with a standard LSTM to learn the evolution of dynamic graphs. [PERSON] et al. [47] present GC-LSTM, which performs a spectral GCN on the hidden layer of the standard LSTM for dynamic link prediction. At present, DGNNs are mainly aimed at learning representations of entire dynamic graphs, such as DGNN, GCRN-M and DyGGN. The learning framework specific to nodes in temporal networks is still lacking. A novel framework which defined a GNN based model that learns the implicit features of nodes on a representative set is proposed by [PERSON] et al. [48], but this representation does not apply to temporal networks. The above works cannot embed the nodes of temporal networks well. In this paper, a novel and effective learning framework DGCN is proposed to embed nodes in temporal networks.