Polarization and multiscale structural balance in signed networks

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.