Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in realworld graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding, two variants of adversarial approaches, adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction, graph clustering, and graph visualization tasks.

Graph clustering is a fundamental task which discovers communities or groups in networks. Recent studies have mostly focused on developing deep learning approaches to learn a compact graph embedding, upon which classic clustering methods like k-means or spectral clustering algorithms are applied. These two-step frameworks are difficult to manipulate and usually lead to suboptimal performance, mainly because the graph embedding is not goal-directed, i.e., designed for the specific clustering task. In this paper, we propose a goal-directed deep learning approach, Deep Attentional Embedded Graph Clustering (DAEGC for short). Our method focuses on attributed graphs to sufficiently explore the two sides of information in graphs. By employing an attention network to capture the importance of the neighboring nodes to a target node, our DAEGC algorithm encodes the topological structure and node content in a graph to a compact representation, on which an inner product decoder is trained to reconstruct the graph structure. Furthermore, soft labels from the graph embedding itself are generated to supervise a self-training graph clustering process, which iteratively refines the clustering results. The selftraining process is jointly learned and optimized with the graph embedding in a unified framework, to mutually benefit both components. Experimental results compared with state-of-the-art algorithms demonstrate the superiority of our method.

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding distribution of the latent codes, which unfortunately may lead to inferior representation in many cases. In this paper, we present a novel adversarially regularized framework for graph embedding. By employing the graph convolutional network as an encoder, our framework embeds the topological information and node content into a vector representation, from which a graph decoder is further built to reconstruct the input graph. The adversarial training principle is applied to enforce our latent codes to match a prior Gaussian or Uniform distribution. Based on this framework, we derive two variants of adversarial models, the adversarially regularized graph autoencoder (ARGA) and its variational version, adversarially regularized variational graph autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit other potential variations of ARGA and ARVGA to get a deeper understanding on our designs. Experimental results compared among twelve algorithms for link prediction and twenty algorithms for graph clustering validate our solutions.

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Neighborhood aggregation algorithms like spectral graph convolutional networks (GCNs) formulate graph convolutions as a symmetric Laplacian smoothing operation to aggregate the feature information of one node with that of its neighbors. While they have achieved great success in semi-supervised node classification on graphs, current approaches suffer from the over-smoothing problem when the depth of the neural networks increases, which always leads to a noticeable degradation of performance. To solve this problem, we present graph convolutional ladder-shape networks (GCLN), a novel graph neural network architecture that transmits messages from shallow layers to deeper layers to overcome the over-smoothing problem and dramatically extend the scale of the neural networks with improved performance. We have validated the effectiveness of proposed GCLN at a node-wise level with a semi-supervised task (node classification) and an unsupervised task (node clustering), and at a graph-wise level with graph classification by applying a differentiable pooling operation. The proposed GCLN outperforms original GCNs, deep GCNs and other state-of-the-art GCN-based models for all three tasks, which were designed from various perspectives on six real-world benchmark data sets.