Symmetrization for Embedding Directed Graphs
This addresses the challenge of representing directed networks for applications in network analysis, though it is incremental as it builds on existing undirected methods.
The paper tackles the problem of embedding directed graphs, which has received little attention compared to undirected graphs, by proposing a two-stage symmetrization framework that converts directed graphs into undirected ones for use with existing embedding algorithms.
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). 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: in the first stage, the graph is symmetrized in one of several possible ways, and in the second stage, the so-obtained symmetrized graph is embedded using any state-of-the-art (undirected) graph embedding algorithm. Note that it is not the objective of this paper to propose a new (undirected) graph embedding 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.