DocumentCode :
3163760
Title :
Tree-Like Structure in Large Social and Information Networks
Author :
Adcock, Aaron B. ; Sullivan, Blair D. ; Mahoney, Michael W.
Author_Institution :
Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA
fYear :
2013
fDate :
7-10 Dec. 2013
Firstpage :
1
Lastpage :
10
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.
Keywords :
data mining; information networks; social networking (online); trees (mathematics); Gromov d-hyperbolicity; core-periphery property; cut structure; geometric group theory; hierarchical structure; information network; k-core heuristic; large social networks; metric structure; realistic informatics graphs; structural graph theory; tree decompositions; tree width; tree-like structure; Erbium; Extraterrestrial measurements; Facebook; Graph theory; Informatics; Peer-to-peer computing; hyperbolicity; information networks; k-core; network science; network structure; tree decompositions;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Data Mining (ICDM), 2013 IEEE 13th International Conference on
Conference_Location :
Dallas, TX
ISSN :
1550-4786
Type :
conf
DOI :
10.1109/ICDM.2013.77
Filename :
6729484
Link To Document :
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