Capped Alternative-Path Action on Graphs II: Curvature-Guided Capacity Planning and Rapid Failure-Recovery Decision Support for Telecommunications Networks, Validated on 276 Real Topologies

We transform a validated, regularized graph statistical-mechanics model (Paper I, doi:10.5281/zenodo.20982419) into two practical decision-support tools for telecommunications infrastructure, evaluated on 276 real-world network topologies (Internet Topology Zoo). • 𝐓𝐰𝐨 𝐝𝐞𝐜𝐢𝐬𝐢𝐨𝐧-𝐬𝐮𝐩𝐩𝐨𝐫𝐭 𝐭𝐨𝐨𝐥𝐬 are introduced:– A greedy optimization that ranks candidate links by their improvement of discrete (Forman–Ricci) curvature, a validated proxy for structural robustness, under a fixed budget.– A self-calibrating geographic cost term: distances within a network’s historical maximum link length are free, while longer links are linearly penalized. • The geographic term is 𝐟𝐮𝐥𝐥𝐲 𝐝𝐚𝐭𝐚-𝐝𝐫𝐢𝐯𝐞𝐧, requiring no external $/km estimates and adding no measurable computational cost. • Across all 276 networks:– Mean curvature: −3.23– Median curvature: −2.59– Only 3.3% exhibit positive mean curvature, almost exclusively small, near-complete clustersThese values align closely with the synthetic sparse random baseline from the companion model. • In five case studies (Turkey, Croatia, Latvia, Norway, Greece):– The most critical node is the national capital in 4/5 networks.– Its removal fragments the system into 18–57 disconnected components with no immediate recovery.– A secondary critical node allows fast recovery (0.04–0.2 seconds) with realistic link lengths. • In two cases, unconstrained optimization proposed unrealistically long links; the geographic term 𝐞𝐥𝐢𝐦𝐢𝐧𝐚𝐭𝐞𝐬 𝐚𝐥𝐥 𝐯𝐢𝐨𝐥𝐚𝐭𝐢𝐨𝐧𝐬 (0/8 and 0/3) without added cost. • Norway’s Uninett2010 network shows 𝐧𝐨 𝐬𝐢𝐧𝐠𝐥𝐞 𝐜𝐚𝐭𝐚𝐬𝐭𝐫𝐨𝐩𝐡𝐢𝐜 𝐟𝐚𝐢𝐥𝐮𝐫𝐞 𝐩𝐨𝐢𝐧𝐭, highlighting structural resilience. Scope clarification:Distance is explicitly treated as a proxy for capital cost, not a real economic estimate. The proposed methods provide rapid decision support for network operations, not a replacement for packet-level routing protocols. 𝐂𝐨𝐝𝐞 𝐚𝐧𝐝 𝐟𝐮𝐥𝐥 𝐫𝐞𝐩𝐫𝐨𝐝𝐮𝐜𝐢𝐛𝐢𝐥𝐢𝐭𝐲 𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥𝐬 𝐢𝐧𝐜𝐥𝐮𝐝𝐞𝐝.Licensed under PolyForm Noncommercial 1.0.0, covering all algorithms and implementations across languages and hardware platforms.