{"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/three-faces-of-node-importance-in-network","title":"Three faces of node importance in network epidemiology: Exact results for small graphs","arxiv_id":"1708.06456","date":"2017-10-14","proceeding":null,"authors":[],"abstract":"We investigate three aspects of the importance of nodes with respect to\nSusceptible-Infectious-Removed (SIR) disease dynamics: influence maximization\n(the expected outbreak size given a set of seed nodes), the effect of\nvaccination (how much deleting nodes would reduce the expected outbreak size)\nand sentinel surveillance (how early an outbreak could be detected with sensors\nat a set of nodes). We calculate the exact expressions of these quantities, as\nfunctions of the SIR parameters, for all connected graphs of three to seven\nnodes. We obtain the smallest graphs where the optimal node sets are not\noverlapping. We find that: node separation is more important than centrality\nfor more than one active node, that vaccination and influence maximization are\nthe most different aspects of importance, and that the three aspects are more\nsimilar when the infection rate is low.","url_abs":"http://arxiv.org/abs/1708.06456v3","url_pdf":"http://arxiv.org/pdf/1708.06456v3.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":"three-faces-of-node-importance-in-network","repo_url":"https://github.com/pholme/exact-importance","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"epidemiology","task_name":"Epidemiology"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}