Symmetrization for Embedding Directed Graphs

Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for(undirected) graphs (while preserving important properties) (Liang et al. 2018). However, most of the work to date on embedding graphs has targeted undirected networks and very little has focused on the thorny issue of embedding directed networks. In this paper, we instead propose to solve the directed graph embedding problem via a two-stage approach: inthe first stage, the graph is symmetrized in one of several possible ways, and in the second stage, the soobtained symmetrizedgraph is embedded using any state-ofthe-art (undirected) graph embedding algorithm. Note that it is not the objective of this paper to propose a new (undirected) graphembedding algorithm or discuss the strengths and weaknesses of existing ones; all we are saying is that whichever be the suitable graph embedding algorithm, it will fit in the above proposed symmetrization framework. Satuluri et al. proposed various ways (such as Bibliometric andDegree-discounted symmetrization) of symmetrizing a directed graph into an undirected graph, while information aboutdirectionality is incorporated via weights on the edges of the transformed graph (or applying a re-weighting scheme in case of already weighted graphs) (Satuluri and Parthasarathy 2011).