Tree-like structure in large social and information networks

Proceedings - IEEE International Conference on Data Mining, ICDM

Volumn , Issue , 2013, Pages 1-10

  Adcock, Aaron B ^a   Sullivan, Blair D ^b   Mahoney, Michael W ^c  

^a Stanford University   (United States)

^b North Carolina State University   (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

hyperbolicity; information networks; k core; network science; network structure; tree decompositions

Indexed keywords

EID: 84894683815     PISSN: 15504786     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICDM.2013.77     Document Type: Conference Paper

References (40)

1. Supporting website. http://snap.stanford.edu/data/index.html.
2. L. A. Adamic and N. Glance. The political blogosphere and the 2004 U.S. election: divided they blog. In Proceedings of the 3rd international workshop on Link discovery, pages 36-43. ACM, 2005.
3. A. B. Adcock, B. D. Sullivan, O. R. Hernandez, and M. W. Mahoney. Evaluating OpenMP tasking at scale for the computation of graph hyperbolicity. In Proceedings of the 9th International Workshop on OpenMP (IWOMP 2013), pages 71-83, 2013.
4. J. Ignacio Alvarez-Hamelin, L. Dall'Asta, A. Barrat, and A. Vespignani. Large scale networks fingerprinting and visualization using the k-core decomposition. In Proceedings of NIPS, 2005.
5. J. Ignacio Alvarez-Hamelin, L. Dall'Asta, A. Barrat, and A. Vespignani. K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases. Networks and Heterogeneous Media, 3(2):371-293, 2008.
6. P. R. Amestoy, T. A. Davis, and I. S. Duff. Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Transactions on Mathematical Software, 30(3):381-388, 2004.
7. E. Amir. Approximation algorithms for treewidth. Algorithmica, 56(4):448-479, 2010.
8. S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics, 23(1):11-24, 1989.
9. V. Batagelj and A. Mrvar. Pajek - analysis and visualization of large networks. In Graph Drawing Software, pages 77-103. Springer, 2003.
10. V. Batagelj and M. Zaversnik. An O(m) algorithm for cores decomposition of networks. CoRR, cs.DS/0310049, 2003.
11. H. L. Bodlaender. A linear-time algorithm for finding treedecompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996.
12. M.R. Bridson and A. Häfliger. Metric Spaces of Non-Positive Curvature. Grundlehren Der Mathematischen Wissenschaften. Springer, 2009.
13. W. Chen, W. Fang, G. Hu, and M. W. Mahoney. On the hyperbolicity of small-world and tree-like random graphs. In press at: Internet Mathematics. Also available at: arXiv:1201.1717.
14. V. Chepoi, F. Dragan, B. Estellon, M. Habib, and Y. Vax̀es. Diameters, centers, and approximating trees of δ-hyperbolic geodesic spaces and graphs. In Proceedings of the 24th Annual Symposium on Computational Geometry, pages 59-68, 2008.
15. F.R.K. Chung and L. Lu. Complex Graphs and Networks. American Mathematical Society, 2006.
16. P. Colomer-de Simon, A. Serrano, M. G. Beiro, J. Ignacio Alvarez-Hamelin, and M. Boguna. Deciphering the global organization of clustering in real complex networks. CoRR, abs/1306.0112, 2013.
17. R. Diestel. Graph Theory. Graduate Texts in Mathematics. Springer, 2006.
18. P. Erdos and Alfred R. On the evolution of random graphs. Publ. Math. Inst. Hungary. Acad. Sci., 5:17-61, 1960.
19. J. A. George. Nested dissection of a regular finite element mesh. SIAM Journal of Numerical Analysis, 10:345-363, 1973.
20. J. R. Gilbert and R. E. Tarjan. The analysis of a nested dissection algorithm. Numerische Mathematik, 50(4):377-404, 1986.
21. M. Gromov. Hyperbolic groups. In Essays in Group Theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 75-263. Springer-Verlag, 1987.
22. I.V. Hicks, A. Koster, and E. Kolotoglu. Branch and tree decomposition techniques for discrete optimization. INFORMS TutORials in Operation Research, 2005:1-29, 2005.
23. E. A. Jonckheere, P. Lohsoonthorn, and F. Ariaei. Scaled Gromov four-point condition for network graph curvature computation. Internet Mathematics, 7(3):137-177, 2011.
24. E. A. Jonckheere, P. Lohsoonthorn, and F. Bonahon. Scaled Gromov hyperbolic graphs. Journal of Graph Theory, 57(2):157-180, 2008.
25. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput., 20(1):359-392, 1998.
26. M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. E. Stanley, and H. A. Makse. Identification of influential spreaders in complex networks. Nature Physics, 6:888-893, 2010.
27. R. Kleinberg. Geographic routing using hyperbolic space. In Proceedings of the 26th IEEE International Conference on Computer Communications, pages 1902-1909, 2007.
28. D. Koller and N. Friedman. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009.
29. D. V. Krioukov, F. Papadopoulos, M. Kitsak, A. Vahdat, and M. Boguñá. Hyperbolic geometry of complex networks. CoRR, abs/1006.5169, 2010.
30. J. Leskovec, K.J. Lang, A. Dasgupta, and M.W. Mahoney. Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics, 6(1):29-123, 2009. Also available at: arXiv:0810.1355.
31. H. M. Markowitz. The elimination form of the inverse and its application to linear programming. Management Science, 3(3):255-269, 1957.
32. T. Martin, B. Ball, B. Karrer, and M. E. J. Newman. Coauthorship and citation in scientific publishing. CoRR, abs/1304.0473, 2013.
33. F. Montgolfier, M. Soto, and L. Viennot. Treewidth and hyperbolicity of the internet. In Proceedings of the 10th IEEE International Symposium on Network Computing and Applications (NCA), pages 25-32, 2011.
34. O. Narayan and I. Saniee. Large-scale curvature of networks. Phys. Rev. E, 84:066108, Dec 2011.
35. N. Robertson and P.D Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7(3):309-322, 1986.
36. H. Röhrig. Tree decomposition: a feasibility study. Master's thesis, Universität des Saarlandes, Saarbrücken, Germany, 1998.
37. P.D. Seymour and R. Thomas. Call routing and the ratcatcher. Combinatorica, 14(2):217-241, 1994.
38. Y. Shavitt and T. Tankel. Hyperbolic embedding of internet graph for distance estimation and overlay construction. IEEE/ACM Trans. Netw., 16(1):25-36, 2008.
39. A. L. Traud, P. J. Mucha, and M. A. Porter. Social structure of Facebook networks. CoRR, abs/1102.2166, 2011.
40. D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature, 393:440-442, 1998.