Signed graphs are an emergent way of representing data in a variety of contexts were conflicting interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability geometry for signed graphs, proving that metrics in this space, such as the communicability distance and angles, are Euclidean and spherical. We then apply these metrics to solve several problems in data analysis of signed graphs in a unified way. They include the partitioning of signed graphs, dimensionality reduction, finding hierarchies of alliances in signed networks as well as the quantification of the degree of polarization between the existing factions in systems represented by this type of graphs.

翻译：符号图是一种在存在冲突交互的各种数据场景中表示数据的新兴方式，包括生物、生态和社会系统中的数据。本文提出了符号图的通信几何概念，证明了该空间中的度量（如通信距离和角度）具有欧几里得性与球面性。进而将这些度量统一应用于符号图数据分析中的若干问题，包括符号图分割、降维、符号网络中联盟层次结构的发现，以及此类图所代表系统中现有派系间极化程度的量化。