This article deals with the characterization and detection of community and faction structures in signed
networks. We approach the study of these mesoscale structures through the lens of the Gremban expansion.
This graph operation lifts a signed graph to a larger unsigned graph, and allows the extension of standard
techniques from unsigned to signed graphs. We develop the combinatorial and algebraic properties of the
Gremban expansion, with a focus on its inherent involutive symmetry. The main technical result is a
bijective correspondence between symmetry-respecting cut-sets in the Gremban expansion, and regular cut-
sets and frustration sets in the signed graph (i.e., the combinatorial structures that underlie communities
and factions respectively). This result forms the basis for our new approach to community–faction detection
in signed networks, which makes use of spectral clustering techniques that naturally respect the required
symmetries. We demonstrate how this approach distinguishes the two mesoscale structures, how to generalize
the approach to multi-way clustering and discuss connections to network dynamical systems.