Endogenous emergence of small-world remoteness under utility-driven adaptive rewiring

Small-world networks (SWNs) have most often been characterized by an exogenously imposed rewiring probability or empirically measured remoteness parameters. We propose an adaptive network formation model in which remoteness emerges endogenously from decentralized utility-driven rewiring. Agents are located on a degree-preserving Watts–Strogatz ring lattice and evaluate cross-cluster links using a tradeoff between (i) distance-dependent novelty gain, (ii) distance-dependent friction loss, and (iii) normative clustering pressure. We show analytically that the agent-level utility we specify admits a unique interior maximizer in link distance, implying a non-degenerate equilibrium remoteness level. Monte Carlo simulations confirm robust convergence to a stable interior regime concentrated near ρ ≈ 0.4. The results indicate that oft-cited small-world ranges of efficient network remoteness can arise without assigning a rewiring probability ex ante.