I. Introduction
Graph is the primary representation of data with node attributes and local topological structures. For instance, graph data can be used to analyse the latent relations in social networks [1]–[3]. In general, the graph data contains structural information and content information with a high dimension. To make representation and computation easier, lots of models have been proposed for reducing the dimension of the graph data. Adjacency matrix is often used to measure the structure of a graph. In an unweighted graph, element in adjacency matrix is valued 1 if there is an edge between two nodes, valued 0, otherwise. In a weighted graph, element in adjacency matrix is the weight value between two nodes. However, the direct connection cannot reveal the structural relation among nodes precisely. Also, the adjacency matrix fails to describe the relation of two nodes without an edge. Thus, many methods have been proposed to describe the structural similarity instead of original adjacency matrix. LINE [4] uses node’s first- order proximity and second-order proximity simultaneously to distinguish nodes that are different at structure. The first-order proximity is defined as the proximity of two nodes with a direct link. The second-order proximity describes the proximity of nodes sharing some common neighbors. While, LINE fails to leverage high-order proximity of nodes. GraRep [5] defines the k-order proximity to measure the global structure to make up for the consideration of high-order proximity. Struc2vec [6] constructs a multi-layer graph using hierarchy to measure the similarity of pairs of nodes, considering the structure as the unique identification of a node.