New model grows networks by balancing capacity, cost and connectivity

A new open-access study in Applied Network Science proposes a model of network growth in which new links attach not simply to the most connected nodes, but through a combined kernel that weighs accumulated connectivity, residual capacity, and origin–destination pair-specific link cost. The work, published on 23 October 2026 by David Levinson, Somwrita Sarkar, Nazanin Tajik and Alireza Ermagun, is described as a reduced-form, access-based framework for how transport-like networks might grow.

A key feature of the model is that well-known growth rules emerge as limiting cases. The authors show that their kernel contains Barabási–Albert preferential attachment, spatial attachment, and capacity-limited growth as special cases, allowing the three mechanisms to be blended in a single specification rather than treated as competing alternatives.

The reported simulations, run at N=1000, α=1 and κ=2, quantify how each mechanism reshapes structure. In the capacity-only specification (β=1, K=16), the mean maximum degree falls from 82.31 in the Barabási–Albert limiting case to 16.00. In the spatial-only specification (φ=1), mean edge length drops from 0.521 to 0.351, showing that distance-sensitive attachment shortens the links the network adds.

The parameters act continuously rather than as switches. Increasing φ from 0 to 2 shortens mean edge length from 0.526 to 0.157, while increasing κ from 1 to 4 raises clustering and reduces average path length. These are model outputs from the simulations, not measurements of real-world networks.

Capacity itself need not be uniform. With mean capacity near 16, the authors compare distributions: integer-uniform capacities raise the mean maximum degree to 23.06, and rounded-lognormal capacities raise it to 49.00, against the fixed-capacity value of 16.00. How capacity is distributed across nodes, not just its average, therefore shapes how concentrated the network’s hubs become.

The framework also includes crossing-handling and access-guided extensions that represent junction formation, and it uses a common ex post access measure to compare four configured transport-growth strategies. The authors position the model as a source of directional hypotheses for empirical calibration, rather than as a calibrated description of any specific network.

Subject of Research: A reduced-form access-based model of network growth combining preferential attachment, spatial cost and capacity limits

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

Article References: Levinson, D., Sarkar, S., Tajik, N., & Ermagun, A. (2026). Access-based network growth: preferential attachment with capacity, cost, and connectivity. Applied Network Science. https://doi.org/10.1007/s41109-026-00842-y

Image Credits: AI Generated

DOI: 10.1007/s41109-026-00842-y

Keywords: network growth, preferential attachment, Barabási–Albert model, spatial networks, capacity constraints, link cost, clustering, path length, transport networks, access measure, simulation model, Access-based