Access-based network growth: preferential attachment with capacity, cost, and connectivity

This study proposes a reduced-form, access-based model of network growth in which attachment depends jointly on accumulated connectivity, residual capacity, and origin–destination pair-specific link cost. The kernel contains Barabási–Albert (BA) preferential attachment, spatial attachment, and capacity-limited growth as limiting cases. At \(N=1000,\) \(α=1,\) and \(κ=2,\) the capacity-only specification ( \(β=1\) , \(K=16\) ) reduces mean maximum degree from \(82.31\) in the BA limiting case to \(16.00,\) while the spatial-only specification ( \(φ=1\) ) reduces mean edge length from \(0.521\) to \(0.351\) . Increasing \(φ\) from \(0\) to \(2\) shortens mean edge length from \(0.526\) to \(0.157,\) and increasing \(κ\) from \(1\) to \(4\) raises clustering and reduces average path length. With mean capacity near \(16\) , integer-uniform and rounded-lognormal capacities raise mean maximum degree to \(23.06\) and \(49.00\) , respectively. Crossing-handling and access-guided extensions represent junction formation and compare four configured transport-growth strategies using a common ex post access measure. The framework yields directional hypotheses for empirical calibration.