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• W2058600246 abstract "Although large social and information networks are often thought of as having hierarchical or tree-like structure, this assumption is rarely tested. We have performed a detailed empirical analysis of the tree-like properties of realistic informatics graphs using two very different notions of tree-likeness: Gromov's d-hyperbolicity, which is a notion from geometric group theory that measures how tree-like a graph is in terms of its metric structure, and tree decompositions, tools from structural graph theory which measure how tree-like a graph is in terms of its cut structure. Although realistic informatics graphs often do not have meaningful tree-like structure when viewed with respect to the simplest and most popular metrics, e.g., the value of d or the tree width, we conclude that many such graphs do have meaningful tree-like structure when viewed with respect to more refined metrics, e.g., a size-resolved notion of d or a closer analysis of the tree decompositions. We also show that, although these two rigorous notions of tree-likeness capture very different tree-like structures in worst-case, for realistic informatics graphs they empirically identify surprisingly similar structure. We interpret this tree-like structure in terms of the recently-characterized nested core-periphery property of large informatics graphs, and we show that the fast and scalable k-core heuristic can be used to identify this tree-like structure." @default.
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• W2058600246 date "2013-12-01" @default.
• W2058600246 modified "2023-10-10" @default.
• W2058600246 title "Tree-Like Structure in Large Social and Information Networks" @default.
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• W2058600246 doi "https://doi.org/10.1109/icdm.2013.77" @default.
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