{"type":"ScholarlyArticle","title":"A Degeneracy Framework for Graph Similarity","authors":[{"name":"Giannis Nikolentzos","slug":"giannis-nikolentzos","given":"Giannis","family":"Nikolentzos","affiliation":"École Polytechnique , France"},{"name":"Polykarpos Meladianos","slug":"polykarpos-meladianos","given":"Polykarpos","family":"Meladianos","affiliation":"Athens University of Economics and Business , Greece"},{"name":"Stratis Limnios","slug":"stratis-limnios","given":"Stratis","family":"Limnios","affiliation":"École Polytechnique , France"},{"name":"Michalis Vazirgiannis","slug":"michalis-vazirgiannis","given":"Michalis","family":"Vazirgiannis","affiliation":"École Polytechnique , France"}],"abstract":"The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Most existing methods for graph similarity focus either on local or on global properties of graphs. However, even if graphs seem very similar from a local or a global perspective, they may exhibit different structure at different scales. In this paper, we present a general framework for graph similarity which takes into account structure at multiple different scales. The proposed framework capitalizes on the well-known k-core decomposition of graphs in order to build a hierarchy of nested subgraphs. We apply the framework to derive variants of four graph kernels, namely graphlet kernel, shortest-path kernel, Weisfeiler-Lehman subtree kernel, and pyramid match graph kernel. The framework is not limited to graph kernels, but can be applied to any graph comparison algorithm. The proposed framework is evaluated on several benchmark datasets for graph classification. In most cases, the core-based kernels achieve significant improvements in terms of classification accuracy over the base kernels, while their time complexity remains very attractive.","doi":"10.24963/ijcai.2018/360","url":"https://ijcai.org/proceedings/2018/360","pdf":"https://ijcai.org/proceedings/2018/0360.pdf","markdown":"https://ijcai.org/proceedings/2018/360.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/360","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":360,"pages":{"first":2595,"last":2601},"keywords":["Machine Learning Applications: Networks","Machine Learning: Kernel Methods","Machine Learning: Data Mining"],"videos":[],"references":[{"position":1,"raw":"[Alvarez-Hamelin et al., 2006] I.","title":null,"authors":"Alvarez-Hamelin","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"Alvarez-Hamelin, L. 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