{"slug":"barabasi-1999","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":5,"sources":[{"id":"barabasi-1999","type":"primary","url":"https://doi.org/10.1126/science.286.5439.509","title":"Emergence of Scaling in Random Networks","quote":"Starting from a small number of nodes, at every time step we add a new node with m edges that link the new node to m different nodes already present in the system. To incorporate preferential attachment, we assume that the probability P that a new node will be connected to node i depends on the connectivity kᵢ of that node, so that P(kᵢ) = kᵢ / Σⱼ kⱼ.","summary":"Foundational paper introducing preferential attachment as the generative mechanism for scale-free networks, supported by web crawl, actor collaboration, and power grid data.","claim_ids":["c1","c2","c3"],"quality_score":1},{"id":"watts-1998","type":"adjacent","url":"https://miscsubjects.com/a/watts-1998","title":"Watts & Strogatz 1998: Collective Dynamics of Small-World Networks","quote":"","summary":"Predecessor work on small-world networks that established non-random topology in real networks one year before Barabási-Albert.","claim_ids":["c1"],"quality_score":0.95},{"id":"mandelbrot-1967","type":"adjacent","url":"https://miscsubjects.com/a/mandelbrot-1967","title":"Mandelbrot 1967: How Long Is the Coast of Britain?","quote":"","summary":"Mathematical source of power-law scale invariance; cited as the geometric analogue to scale-free network topology.","claim_ids":["c4"],"quality_score":0.9},{"id":"clauset-2009","type":"rival","url":"https://doi.org/10.1137/070710111","title":"Power-Law Distributions in Empirical Data","quote":"Most claimed power-law distributions in empirical data do not actually fit the power-law model well.","summary":"Large-scale statistical audit of real networks finding that most do not pass rigorous power-law tests; primary falsifier of scale-free ubiquity claims.","claim_ids":["c5","c6"],"quality_score":0.95},{"id":"bejan-1996","type":"adjacent","url":"","title":"Constructal Law (Bejan 1996)","quote":"","summary":"Theoretical framework for branching flow networks; cited as geometric dual to hub-and-spoke link topology.","claim_ids":["c4"],"quality_score":0.75}]}