Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.

本研究解决了现有图表示学习方法对有符号图的处理不足的问题。通过提出两种新方法SG2V和WSGCN，分别对整体图和签名图的嵌入进行了有效扩展。研究结果表明，新方法在表示学习任务中显著提高了性能，尤其是WSGCN达到了81.20的F度量分数，显示出更优的效果。

整个图的表示学习用于有符号网络的分类