Polarization and multiscale structural balance in signed networks

Polarization, or a division into mutually hostile groups, is a common feature of social systems. It is studied in Structural Balance Theory in terms of semicycles in signed networks. However, enumerating semicycles is computationally expensive, so approximations are often needed. Here we introduce the Multiscale Semiwalk Balance approach for measuring the degree of balance (DoB) in (un)directed, (un)weighted signed networks by approximating semicycles with closed semiwalks. It allows selecting the resolution of analysis appropriate for assessing DoB motivated by the Locality Principle, 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, which leads to explainable results for networks with expected patterns (polarization in the US Congress) and a more nuanced perspective for other systems. Our work may facilitate studying polarization and structural balance in a variety of contexts and at multiple scales.