DSP: A Statistically-Principled Structural Polarization Measure

Social and information networks may become polarized, leading to echo chambers and political gridlock. Accurately measuring this phenomenon is a critical challenge. Existing measures often conflate genuine structural division with random topological features, yielding misleadingly high polarization scores on random networks, and failing to distinguish real-world networks from randomized null models. We introduce DSP, a Diffusion-based Structural Polarization measure designed from first principles to correct for such biases. DSP removes the arbitrary concept of 'influencers' used by the popular Random Walk Controversy (RWC) score, instead treating every node as a potential origin for a random walk. To validate our approach, we introduce a set of desirable properties for polarization measures, expressed through reference topologies with known structural properties. We show that DSP satisfies these desiderata, being near-zero for non-polarized structures such as cliques and random networks, while correctly capturing the expected polarization of reference topologies such as monochromatic-splittable networks. Our method applied to U.S. Congress datasets uncovers trends of increasing polarization in recent years. By integrating a null model into its core definition, DSP provides a reliable and interpretable diagnostic tool, highlighting the necessity of statistically-grounded metrics to analyze societal fragmentation.