Topological Strata of Weighted Complex Networks

PLoS ONE

Volumn 8, Issue 6, 2013, Pages

  Petri, Giovanni ^a   Scolamiero, Martina ^a,b   Donato, Irene ^a,b   Vaccarino, Francesco ^a,b  

^a ISI FOUNDATION   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CLASSIFICATION; GENETIC VARIABILITY; MATHEMATICAL COMPUTING; MATHEMATICS; MOLECULAR DYNAMICS; MOLECULAR GENETICS; STATISTICAL ANALYSIS; STRUCTURAL HOMOLOGY; STRUCTURE ANALYSIS; THEORY; HUMAN; SOCIAL SUPPORT; THEORETICAL MODEL;

HUMANS; MODELS, THEORETICAL; SOCIAL SUPPORT;

EID: 84879275745     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0066506     Document Type: Article

References (54)

1. Newman MEJ, (2003) The structure and function of complex networks. SIAM Rev 45: 167-256.
2. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DH, (2006) Complex networks: Structure and dynamics. Phys Rep 424: 175-308.
3. Dorogovtsev SN, Goltsev AV, Mendes JFF (2008) Critical phenomena in complex networks. Rev Mod Phys: 1275-1335.
4. Barrat A, Barthélemy M, Pastor-Satorras R, Vespignani A, (2004) The architecture of complex weighted networks. Proc Natl Acad Sci USA 101: 3747-3752.
5. Barabási A, (1999) Emergence of scaling in random networks. Science 286: 509-512.
6. Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, et al. (2002) Network motifs: Simple building blocks of complex networks. Science 298: 824-827.
7. Vázquez A, Dobrin R, Sergi D, Eckmann JP, Oltvai ZN, et al. Proc Nat Acad Sci USA 101: 17940-17945.
8. Mahadevan P, Krioukov D, Fall K, Vahdat A, (2006) Systematic topology analysis and generation using degree correlations. ACM SIGCOMM 36: 135-146.
9. Conradi C, Flockerzi D, Raisch J, Stelling J, (2007) Subnetwork analysis reveals dynamic features of complex (bio)chemical networks. 104: 19175-19180.
10. Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV, (2005) Scale-free brain functional networks. Phys Rev Lett 92: 028102.
11. Song WM, Di Matteo T, Aste T (2012) Hierarchical information clustering by means of topologi3 cally embedded graphs. PloS One 7, e31929.
12. Tumminello M, Aste T, Di Matteo T, Mantegna RN, (2005) A tool for filtering information in complex systems. Proc Natl Acad Sci USA 102: 10421-10426.
13. Chalupa J, Leath PL, Reich GR (1979) Bootstrap percolation on a bethe lattice. J Phys C.
14. Serrano M, Boguñá M, Vespignani A, (2009) Extracting the multiscale backbone of complex weighted networks. Proc Nat Acad Sci USA 106: 6483.
15. Ghrist R (2008) Barcodes: The persistent topology of data. B AM Math Soc 45.
16. Carlsson G, Zomorodian A, (2005) Persistent homology- a survey. Discrete Comput Geom 33: 249-274.
17. Carlsson G, (2009) Topology and data. B Am Math Soc 46: 255-308.
18. Petri G, Scolamiero M, Donato I, Vaccarino F (2013) Metric and weighted clique persistent ho3 mology for complex networks. In: Proceedings of the European Conference on Complex Systems 2012.
19. Lum P, Singh G, Lehman A, Ishkanov T, Vejdemo-Johansson M,et al. Scientific Reports.
20. Hyekyoung L, Chung M, Hyejin K, Bung-Nyun K, L DS (2011) Discriminative persistent homol4 ogy of brain networks. In: Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on. 841-844. doi:10.1109/ISBI.2011.5872535.
21. Nicolau M, Levine A, Carlsson G, (2011) Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proceedings of the National Academy of Sciences 108: 7265-7270.
22. Weygaert R, Vegter G, Edelsbrunner H, Jones B, Pranav P, et al. (2011) Alpha, betti and the megaparsec universe: On the topology of the cosmic web. In: Gavrilova M, Tan C, Mostafavi M, editors, Transactions on Computational Science XIV, Springer Berlin Heidelberg, volume 6970 of Lecture Notes in Computer Science. 60-101. doi:10.1007/978-3-642-25249-5 3. URL http://dx.doi.org/10.1007/978-3-642-25249-5_3.
23. Opsahl T, Colizza V, Panzarasa P, Ramasco JJ, (2008) Prominence and control: The weighted rich-club effect. Phys Rev Lett 101: 168702.
24. Pajevic D, Plenz S, (2012) The organization of strong links in complex networks. Nat Phys 8: 429-436.
25. Barthelemy M, (2011) Spatial networks. Phys Rep 499: 1-101.
26. Antonioni A, Tomassini M, (2012) Degree correlations in random geometric graphs. Phys Rev E 86: 037101.
27. Barrat A, Barthelemy M, Vespignani A, (2005) The effects of spatial constraints on the evolution of weighted complex networks. J Stat Mech 05: P05003.
28. Palla G, Derényi I, Farkas I, Vicsek T (2005) The effects of spatial constraints on the evolution of weighted complex networks.
29. Stehlé J, Voirin N, Barrat M, Cattuto C, Isella L, et al. (2011) High-resolution measurements of face-to-face contact patterns in a primary school. PLoS One 6: e23176.
30. Gfeller D, De Los Rios P, (2007) Spectral coarse graining of complex networks. Phys Rev Lett 99: 38701.
31. Chavez M, Hwang DU, Amann A, Hentschel HGE, Boccaletti S, (2005) Synchronization is enhanced in weighted complex networks. Phys Rev Lett 94: 218701.
32. Farkas IJ, Derenyi I, Barabási AL, Vicsek T (2001) Spectra of real-world" graphs: Beyond the semicircle law. Phys Rev E 64.
33. Jun WU, Barahona M, Yue-Jin T, Hong-Zhong D, (2010) Natural connectivity of complex networks. Chin Phys Lett 27: 078902.
34. Barahona M, Pecora LM, (2002) Synchronization in small-world systems. Phys Rev Lett 89: 054101.
35. MacArthur BD, Sánchez-Garca RJ, (2009) Spectral characteristics of network redundancy. Phys Rev E 80: 026117.
36. Colizza V, Flammini A, Serrano MA, Vespignani A, (2006) Detecting rich-club ordering in complex networks. Nat Phys 2: 110-115.
37. Boguñá M PF, Krioukov D, (2010) Sustaining the internet with hyperbolic mapping. Nat Comms 1: 1-8.
38. Grady D, Thiemann C, Brockmann D, (2012) Robust classification of salient links in complex networks. Nat Comm 3: 864.
39. Carlsson G, Zomorodian A, (2009) Theory of multidimensional persistence. Discr Comput Geom 42: 71-93.
40. Watts D, Strogatz SH, (1998) Collective dynamics of 'small-world' networks. Nature 393: 440-442.
41. Opsahl T, Panzarasa P, (2009) Clustering in weighted networks. Soc Net 31: 155-163.
42. Opsahl T (2010) Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Soc Net.
43. Gardner T, di Bernardo D, Lorenz D, Collins J, (2003) Inferring genetic networks and identifying compound mode of action via expression profiling. Science 301: 102-105.
44. Newman MEJ, (2001) The structure of scientific collaboration networks. Proc Natl Acad Sci USA 98: 404-409.
45. Petri G (2013). Holes- python package for persistent homology calculations. URL http://lordgrilo.github.com/Holes/.
46. Barthélemy M (2011) Spatial networks. Phys Rep 499.
47. Penrose M (2003) Random Geometric Graphs. Oxford, UK: Oxford University Press.
48. Palla Gea (2007) Directed network modules. New J Phys 9.
49. Munkres JR (1984) Elements of Algebraic Topology. 2725 Sand Hill Road Menlo Park, California 94025: Addison-Wesley Publishing Company.
50. Steiner DC, Edelsbrunner H, Harer J, (2007) Stability of persistence diagrams. Discrete Comput Geom 37: 103-120.
51. Tausz A, Vejdemo-Johansson M, Adams H (2011). Javaplex: A research software package for persistent (co)homology. "Software available at http://code.google.com/javaplex".
52. de Silva V, Carlsson G (2004) Topological estimation using witness complexes. Symp Point- Based Graphics, ETH Zurich.
53. Bauer U, Kerber M, Reininghaus J (2013) Clear and compress: Computing persistent homology in chunks. arXiv: 13030477.
54. Zomorodian A (2010) The tidy set: a minimal simplicial set for computing homology of clique complexes. Proceedings of the 2010 annual symposium on Computational geometry: 257-266.