Communities and bottlenecks: Trees and treelike networks have high modularity

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 6, 2012, Pages

  Bagrow, James P ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; CONNECTED GRAPH; DATA SETS; HIGH QUALITY; LOW PROBABILITY; MAXIMUM VALUES; MODEL TREES; MODULAR STRUCTURES; NONLOCAL; NULL MODEL; OBJECTIVE FUNCTIONS; RANDOM GRAPHS; TREE COMMUNITY; TREELIKE NETWORKS;

GRAPH THEORY; STATISTICAL TESTS; STRUCTURE (COMPOSITION);

FORESTRY;

FORESTS; PROBLEM SOLVING; STATISTICAL ANALYSIS;

EID: 84862893470     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.066118     Document Type: Article

References (55)

1. M. E. J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010).
2. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
3. M. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
4. A. Barrat, M. Bathélemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
5. A. Vespignani, Nat. Phys. 1745-2473 10.1038/nphys2160 8, 32 (2011).
6. J.-P. Onnela, J. Saramäki, J. Hyvönen, G. Szabó, M. A. de Menezes, K. Kaski, A.-L. Barabási, and J. Kertész, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/6/179 9, 179 (2007). (Pubitemid 47159638)
7. M. C. González, C. A. Hidalgo, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/nature06958 453, 779 (2008). (Pubitemid 351793783)
8. J. P. Bagrow, D. Wang, and A.-L. Barabási, PLoS ONE 1932-6203 10.1371/journal.pone.0017680 6, e17680 (2011).
9. H. Jeong, B. Tombor, R. Albert, Z. Oltvai, and A. Barabási, Nature (London) NATUAS 0028-0836 10.1038/35036627 407, 651 (2000).
10. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Science SCIEAS 0036-8075 10.1126/science.298.5594.824 298, 824 (2002). (Pubitemid 35231534)
11. J. Dunne, R. Williams, and N. Martinez, Ecol. Lett. 1461-023X 10.1046/j.1461-0248.2002.00354.x 5, 558 (2002). (Pubitemid 34824916)
12. A. E. Krause, K. A. Frank, D. M. Mason, R. E. Ulanowicz, and W. W. Taylor, Nature (London) NATUAS 0028-0836 10.1038/nature02115 426, 282 (2003). (Pubitemid 37463145)
13. L. S. Schulman, J. P. Bagrow, and B. Gaveau, Advs. Complex Syst. 1284-8535 10.1142/S0219525911003463 14, 829 (2011).
14. A.-L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
15. J. Kleinberg, Nature (London) NATUAS 0028-0836 10.1038/35022643 406, 845 (2000). (Pubitemid 30664249)
16. V. Colizza, A. Barrat, M. Barthelemy, and A. Vespignani, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0510525103 103, 2015 (2006). (Pubitemid 43271615)
17. D. Brockmann, L. Hufnagel, and T. Geisel, Nature (London) NATUAS 0028-0836 10.1038/nature04292 439, 462 (2006). (Pubitemid 43152835)
18. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998). (Pubitemid 28292183)
19. S. Fortunato, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.11.002 486, 75 (2010).
20. M. E. J. Newman, Nat. Phys. 1745-2473 10.1038/nphys2162 8, 25 (2011).
21. A. Clauset, C. Moore, and M. E. J. Newman, Nature (London) NATUAS 0028-0836 10.1038/nature06830 453, 98 (2008). (Pubitemid 351630323)
22. J.-P. Onnela, J. Saramäki, J. Hyvönen, G. Szabó, D. Lazer, K. Kaski, J. Kertész, and A.-L. Barabási, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0610245104 104, 7332 (2007). (Pubitemid 47185905)
23. C. Ratti, S. Sobolevsky, F. Calabrese, C. Andris, J. Reades, M. Martino, R. Claxton, and S. H. Strogatz, PLoS ONE 1932-6203 10.1371/journal.pone.0014248 5, e14248 (2010).
24. P. Expert, T. S. Evans, V. D. Blondel, and R. Lambiotte, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.1018962108 108, 7663 (2011).
25. C. Thiemann, F. Theis, D. Grady, R. Brune, and D. Brockmann, PLoS ONE 1932-6203 10.1371/journal.pone.0015422 5, e15422 (2010).
26. J. P. Bagrow and E. M. Bollt, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.046108 72, 046108 (2005). (Pubitemid 43273103)
27. A. Clauset, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.026132 72, 026132 (2005). (Pubitemid 41520947)
28. J. P. Bagrow, J. Stat. Mech. 10.1088/1742-5468/2008/05/P05001 (2008) P05001.
29. G. Palla, I. Derényi, I. Farkas, and T. Vicsek, Nature (London) NATUAS 0028-0836 10.1038/nature03607 435, 814 (2005). (Pubitemid 40839731)
30. Y.-Y. Ahn, J. P. Bagrow, and S. Lehmann, Nature (London) NATUAS 0028-0836 10.1038/nature09182 466, 761 (2010).
31. B. Ball, B. Karrer, and M. E. J. Newman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.036103 84, 036103 (2011).
32. S. Sreenivasan, R. Cohen, E. López, Z. Toroczkai, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.036105 75, 036105 (2007). (Pubitemid 46375529)
33. B. Bollobás, Modern Graph Theory (Springer, Berlin, 1998).
34. M. E. J. Newman and M. Girvan, Phys. Rev. E 1539-3755 10.1103/PhysRevE.69.026113 69, 026113 (2004).
35. M. E. J. Newman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.066133 69, 066133 (2004).
36. S. Fortunato and M. Barthelemy, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0605965104 104, 36 (2007). (Pubitemid 46075032)
37. A. Lancichinetti and S. Fortunato, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.066122 84, 066122 (2011).
38. J. Reichardt and S. Bornholdt, Phys. D PDNPDT 0167-2789 10.1016/j.physd.2006.09.009 224, 20 (2006). (Pubitemid 44751206)
39. J. Reichardt and S. Bornholdt, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.016110 74, 016110 (2006). (Pubitemid 44091255)
40. R. Guimera, M. Sales-Pardo, and L. A. N. Amaral, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.025101 70, 025101 (2004).
41. B. H. Good, Y.-A. de Montjoye, and A. Clauset, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.046106 81, 046106 (2010).
42. V. Blondel, J. Guillaume, R. Lambiotte, and E. Lefebvre, J. Stat. Mech. 1742-5468 10.1088/1742-5468/2008/10/P10008 (2008 2008) P10008.
43. M. Rosvall and C. T. Bergstrom, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0706851105 105, 1118 (2008). (Pubitemid 351397014)
44. T. Harris, The Theory of Branching Processes (Dover, New York, 2002).
45. North Dakota State University, The Mathematics Genealogy Project http://genealogy.math.ndsu.nodak.edu.
46. R. D. Malmgren, J. M. Ottino, and L. A. N. Amaral, Nature NATUAS 0028-0836 10.1038/nature09040 (London) 465, 622 (2010).
47. A. Lancichinetti, F. Radicchi, and J. J. Ramasco, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.046110 81, 046110 (2010).
48. A. Mirshahvalad, J. Lindholm, M. Derlén, and M. Rosvall, PLoS ONE 1932-6203 10.1371/journal.pone.0033721 7, e33721 (2012).
49. J. P. Bagrow, S. Lehmann, and Y.-Y. Ahn, arXiv: 1102.5085.
50. H. Yu, P. Braun, M. Yldrm, I. Lemmens, K. Venkatesan, J. Sahalie, T. Hirozane-Kishikawa, F. Gebreab, N. Li, and N. Simonis, Science SCIEAS 0036-8075 10.1126/science.1158684 322, 104 (2008).
51. Gene Ontology Consortium, Nucleic Acids Res. NARHAD 0305-1048 10.1093/nar/gkm883 36, D440 (2008). (Pubitemid 351149763)
52. A.-C. Gavin, Nature (London) NATUAS 0028-0836 10.1038/nature04532 440, 631 (2006).
53. N. J. Krogan, Nature (London) NATUAS 0028-0836 10.1038/nature04670 440, 637 (2006).
54. H. Yu, Science SCIEAS 0036-8075 10.1126/science.1158684 322, 104 (2008).
55. A. L. Traud, E. D. Kelsic, P. J. Mucha, and M. A. Porter, SIAM Rev. SIREAD 0036-1445 10.1137/080734315 53, 526 (2011).