Model
Pick random discordant edge (i,j):
with prob φ: i rewires to random k
with prob 1-φ: i adopts j's opinion
Phase transition at φ* :
φ < φ*: consensus
φ > φ*: fragmentation
φ* ≈ 1/(1 + 2⟨k⟩δ)
Controls: rewiring rate φ
and tolerance width δ
Holme & Newman (2006): when agents rewire too readily (high φ), the network fragments into echo chambers before consensus can form. Below the critical φ*, agents influence each other enough to reach full consensus. This models political polarization, filter bubbles, and social fragmentation dynamics.