Graph Embedding Based on Euclidean Distance Matrix and its Applications

Zhihong Liu, Huiyu Li, Ruixin Li, Yong Zeng, Jianfeng Ma

Abstract: Graph embedding converts a graph into a multi-dimensional space in which the graph structural information or graph properties are maximumly preserved. It is an effective and efficient way to provide users a deeper understanding of what is behind the data and thus can benefit a lot of useful applications. However, most graph embedding methods suffer from high computation and space costs. In this paper, we present a simple graph embedding method that directly embeds the graph into its Euclidean distance space. This method does not require the learned representations to be low dimensional, but it has several good characteristics. We find that the centrality of nodes/edges can be represented by the position of nodes or the length of edges when a graph is embedded. Besides, the edge length is closely related to the density of regions in a graph. We then apply this graph embedding method into graph analytics, such as community detection, graph compression, and wormhole detection, etc. Our evaluation shows the effectiveness and efficiency of this embedding method and contends that it yields a promising approach to graph analytics.