  Polarization, understood as a division into mutually hostile groups, is a
common feature of social systems. It is studied in Structural Balance Theory
(SBT) in terms of semicycles in signed networks. However, enumerating
semicycles is computationally expensive, so approximations are often needed.
Here we introduce Multiscale Semiwalk Balance (MSB) approach for measuring
degree of balance (DoB) in (un)directed, (un)weighted signed networks by
approximating semicycles with closed semiwalks. It allows for selection of the
resolution of analysis appropriate for assessing DoB motivated by Locality
Principle (LP), which posits that patterns in shorter cycles are more important
than in longer ones. Our approach overcomes several limitations affecting
walk-based approximations, and provides methods for assessing DoB at various
scales, from graphs to individual nodes, and for clustering signed networks. We
demonstrate its effectiveness by applying it to real-world social systems, for
which it produces explainable results consistent with expectations based on
domain-specific knowledge.
