{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/random-walk-models-of-network-formation-and","title":"Random Walk Models of Network Formation and Sequential Monte Carlo Methods for Graphs","arxiv_id":"1612.06404","date":"2016-12-19","proceeding":null,"authors":["Benjamin Bloem-Reddy","Peter Orbanz"],"abstract":"We introduce a class of generative network models that insert edges by\nconnecting the starting and terminal vertices of a random walk on the network\ngraph. Within the taxonomy of statistical network models, this class is\ndistinguished by permitting the location of a new edge to explicitly depend on\nthe structure of the graph, but being nonetheless statistically and\ncomputationally tractable. In the limit of infinite walk length, the model\nconverges to an extension of the preferential attachment model---in this sense,\nit can be motivated alternatively by asking what preferential attachment is an\napproximation to. Theoretical properties, including the limiting degree\nsequence, are studied analytically. If the entire history of the graph is\nobserved, parameters can be estimated by maximum likelihood. If only the final\ngraph is available, its history can be imputed using MCMC. We develop a class\nof sequential Monte Carlo algorithms that are more generally applicable to\nsequential network models, and may be of interest in their own right. The model\nparameters can be recovered from a single graph generated by the model.\nApplications to data clarify the role of the random walk length as a length\nscale of interactions within the graph.","url_abs":"http://arxiv.org/abs/1612.06404v2","url_pdf":"http://arxiv.org/pdf/1612.06404v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"random-walk-models-of-network-formation-and","repo_url":"https://github.com/ben-br/random_walk_smc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}