Signed graphs in data sciences via communicability geometry
Fernando Diaz-Diaz Ernesto Estrada
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.