Global Network Properties

Analysis of Biological Networks

Volumn , Issue , 2007, Pages 29-63

  Steuer, Ralf ^a   López, Gorka Zamora ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Average or characteristic path length; Biological phenomena and processes; Floyd Warshall algorithm

Indexed keywords

EID: 84889350276     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470253489.ch3     Document Type: Chapter

References (76)

1. R. Albert and A.-L. Barab́asi. Statistical mechanics of complex networks. Reviews of Modern Physics, 74:47-97, 2002.
2. R. Albert, H. Jeong, and A.-L. Barab́asi. Error and attack tolerance of complex networks. Nature, 406:378-382, 2000.
3. L. A. N. Amaral, A. Scala, M. Barthelemy, and H. E. Stanley. Classes of small world networks. Proceedings of the National Academy of Science (USA), Vol. 97(21), 11149-11152, 2000.
4. M. Arita. Scale-freeness and biological networks. Journal of Biochemistry, 138(1):1-4, 2005.
5. Y. Artzy-Randrup, S. J. Fleishman, N. Ben-Tal, and L. Stone. Comment on "network motifs: Simple building blocks of complex networks" and "superfamilies of evolved and designed networks." Science, 305(5687):1107c, 2004.
6. J. Bang-Jensen and G. Gutin. Digraphs: Theory, Algorithms and Applications. Springer Monographies in Mathematics. Springer-Verlag, London, 2000.
7. A.-L. Barab́asi and R. Albert. Emergence of scaling in random networks. Science, 286:509-512, 1999.
8. A.-L. Barab́asi and Z. N. Oltvai. Network biology: Understanding the cell's functional organization. Nature Reviews Genetics, 5:101-113, 2004.
9. V. Batagelj and A. Mrvar. Pajek-program for large network analysis. Connections, 21(2):47-57, 1998.
10. D. S. Callaway, M. E. J. Newman, S. Strogatz, and D. J. Watts. Network robustness and fragility: Percolation on random graphs. Physics Review Letters, 85(25):5468-5471, 2000.
11. D. Camacho, A. de la Fuente, and P. Mendes. The origin of correlations in metabolomics data. Metabolomics, 1:53-63, 2005.
12. J. M. Carlson and J. Doyle. Highly optimized tolerance: Robustness and design in complex systems. Phys. Rev. Lett., 84(11):2529-2532, 2000.
13. R. Cohen and S. Havlin. Scale-free networks are ultrasmall. Physics Review Letters, 90:058701, 2003.
14. L. da F. Costa. The hierarchical backbone of complex networks. Physics Review Letters, 93:098702, 2004.
15. J. Davidsen, H. Ebel, and S. Bornholdt. Emergence of a small-world from local interactions: Modeling acquaintance networks. Physics Review Letters, 88(12):128701, 2002.
16. D. J. de Solla Price. Network of scientific papers: The pattern of bibliographic references indicates the nature of the scientific research front. Science, 149:510-515, 1965.
17. S. N. Dorogovtsev and J. F. F. Mendes. Evolution of networks. Advances in Physics, 51(4):1079-1187, 2002.
18. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin. Size-dependent degree distribution of a scale-free growing network. Physical Review E, 63(6):062101, 2001.
19. V. M. Eguiluz, D. R. Chialvo, G. Cecchi, M. Baliki, and A. V. Apkarian. Scalefree brain functional networks. Physical Review Letters, 94:018102, 2005.
20. P. Erdös and A.Ŕenyi. On random graphs. Publicationes Mathematicae, 6:290-297, 1959.
21. I. J. Farkas, I. Deŕenyi, A.-L. Barab́asi, and T. Vicsek. Spectra of 'real-world' graphs: Beyond the semicircle law. Physical Review E, 64(2):026704, 2001.
22. D. A. Fell and A. Wagner. The small-world of metabolism. Nature Biotechnology, 18:1121-1122, 2000.
23. J. Förster, I. Famili, P. Fu, B. O. Palsson, and J. Nielsen. Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Research, 13:244-253, 2003.
24. M. Girvan and M. E. J. Newman. Community structure in social and biological networks. Proceedings of the National Academy of Science USA, 99(12):7821-7826, 2002.
25. M. L. Goldstein, S. A. Morris, and G. G. Yen. Problems with fitting to the power-law distribution. The European Physical Journal B, 41(2):255-258, 2004.
26. M. Gustafsson. Large-scale topology, stability and biology of gene networks, volume 1256 of Link̈oping Studies in Science and Technology Thesis. Link̈opings university, Norrk̈opping, 2006.
27. M. Gustafsson, M. Hörnquist, and A. Lombardi. Comparison and validation of community structures in complex networks. Physica A, 367:559-576, 2006.
28. H. Herzel. How to quantify 'small-world networks'? Fractals, 6(4):301-303, 1998.
29. P. Holme, B. J. Kim, C. N.Yoon, and S. K. Han. Attack vulnerability of complex networks. Physical Review E, 65:056109, 2002.
30. P. J. Ingram, M. P. H. Stumpf, and J. Stark. Network motifs: structure does not determine function. BMC Genomics, 7:108, 2006.
31. S. Itzkovitz, R. Milo, N. Kashtan, G. Ziv, and U. Alon. Subgraphs in random networks. Physical Review E, 68(2):026127, 2003.
32. H. Jeong, S. P. Mason, A.-L. Barab́asi, and Z. N. Oltvai. Lethality and centrality in protein networks. Nature (Brief Communications), 411:41-42, 2001.
33. H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barab́asi. The large-scale organization of metabolic network. Nature, 407:651-654, 2000.
34. N. Kashtan and U. Alon. Spontaneous evolution of modularity and network motifs. Proceedings of the National Academy of Science USA, 102(39):13773-13778, 2005.
35. H. Kitano. Biological robustness. Nature Review Genetics, 5:826-837, 2004.
36. K. Klemm and V. M. Eguíluz. Highly clustered scale-free networks. Physical Review E, 65:036123, 2002.
37. E. Klipp, W. Liebermeister, and C. Wierling. Inferring dynamic properties of biochemical reaction networks from structural knowledge. Genome Informatics Series, 15(1):125-137, 2004.
38. P. L. Krapivsky, S. Redner, and F. Leyvraz. Connectivity of growing random networks. Physics Review Letters, 85(21):4629-4632, 2000.
39. T. I. Lee, N. J. Rinaldi, F. Robert, D. T. Odom, Z. Bar-Joseph, G. K. Gerber, N. M. Hannett, C. T. Harbison, C. M. Thompson, I. Simon, J. Zeitlinger, E. G. Jennings, H. L. Murray, D. B. Gordon, B. Ren, J. J. Wyrick, J.-B. Tagne, T. L. Volkert, E. Fraenkel, D. K. Gifford, and R. A. Young. Transcriptional regulatory networks in Saccharomyces cerevisiae. Science, 298:799-804, 2002.
40. A. Li and S. Horvath. Network neighborhood analysis with the multi-node topological overlap measure. Bioinformatics, 23(2):222-231, 2007.
41. H. Ma and A.-P. Zeng. Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics, 19(2):270-277, 2003.
42. P. Mendes, D. Camacho, and A. de la Fuente. Modelling and simulations for metabolomics data analysis. Biochemical Society Transactions, 33(6):1427-1429, 2005.
43. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. Ayzenshtat, M. Sheffer, and U. Alon. Superfamilies of evolved and designed networks. Science, 303(5663): 1538-1542, 2004.
44. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon. Network motifs: Simple building blocks of complex networks. Science, 298:824-827, 2002.
45. M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2):226-251, 2004.
46. K. Morgenthal, W. Weckwerth, and R. Steuer. Metabolomic networks in plants: Transitions from pattern recognition to biological interpretation. BioSystems, 83(2-3):108-117, 2006.
47. M. Morohashi, A. E.Winn, M. T. Borisuk, H. Bolouri, J. Doyle, and H. Kitano. Robustness as a measure of plausibility in models of biochemical networks. Journals of Theoretical Biology, 216:19-30, 2002.
48. S. Mossa, M. Barth́eĺemy, H. E. Stanley, and L. A. N. Amaral. Truncation of power law behavior in scale-free network models due to information filtering. Physics Review Letters, 88:138701, 2002.
49. M. E. J. Newman. Assortative mixing in networks. Physics Review Letters, 89:208701, 2002.
50. M. E. J. Newman. The structure and function of complex networks. SIAM REVIEW, 45(2):167-256, 2003.
51. M. E. J. Newman and M. Girvan. Finding and evaluating community structure in networks. Physical Review E, 69:026113, 2004.
52. M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64:026118 [17 pages], 2001.
53. R. Pastor-Satorras, A. V́azquez, and A. Vespignani. Dynamical and correlation properties of the internet. Physics Review Letters, 87(25):258701, 2001.
54. L. M. Pecora and T. L. Carroll. Master stability function for synchronized coupled systems. Physics Review Letters, 80(10):2109-2112, 1998.
55. R. J. Prill, P. A. Iglesias, and A. Levchenko. Dynamic properties of network motifs contribute to biological network organization. PLoS Biology, 3(11):1881-1892, 2005.
56. A. Ramezanpour, V. Karimipour, and A. Mashaghi. Generating correlated networks from uncorrelated ones. Physical Review E, 67:046107, 2003.
57. E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barab́asi. Hierachical organization of modularity in metabolic networks. Science, 297:1551-1555, 2002.
58. E. Ravasz and A.-L. Barab́asi. Hierarchical organization in complex networks. Physical Review E, 67(2):026112, 2003.
59. S. S. Shen-Orr, R. Milo, S. Mangan, and U. Alon. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31:64-68, 2002.
60. J. Stelling, U. Sauer, Z. Szallasi, F. J. Doyle III, and J. Doyle. Robustness of cellular function. Cell, 118:675-685, 2004.
61. R. Steuer. Nonlinear dynamics and molecular biology: From gene expression to metabolic networks. Ph.D. thesis, University Potsdam, 2005.
62. R. Steuer. On the analysis and interpretation of correlations in metabolomic data. Briefings in Bioinformatics, 7(2):151-158, 2006.
63. R. Steuer. Computational approaches to the topology, stability and dynamics of metabolic networks. Phytochemistry, 68(16-18), pp. 2139-2151, 2007.
64. R. Steuer, C. O. Daub, J. Selbig, and J. Kurths. Measuring distances between variables by mutual information. In D. Baier and K.-D. Wernecke, editors, Innovations in Classification, Data Science, and Information Systems, volume Proc. 27th Annual GfKl Conference, pages 81-90. Springer-Verlag, Berlin, 2004.
65. R. Steuer, T. Gross, J. Selbig, and B. Blasius. Structural kinetic modeling of metabolic networks. Proceedings of the National Academy of Science USA, 103(32):11868-11873, 2006.
66. R. Steuer, J.Kurths, C. O. Daub, J.Weise, and J. Selbig. The mutual information: Detecting and evaluating dependencies between variables. Bioinformatics, 18(Suppl. 2):S231-S240, 2002.
67. R. Steuer, J.Kurths, O. Fiehn, and W. Weckwerth. Observing and interpreting correlations in metabolomic networks. Bioinformatics, 19(8):1019-1026, 2003.
68. R. Steuer, A. Nunes-Nesi, A. R. Fernie, T. Gross, B. Blasius, and J. Selbig. From structure to dynamics of metabolic pathways: Application to the plant mitochondrial TCA cycle. Bioinformatics, 23(1), pp. 1378-1385, 2007.
69. L. J. Sweetlove and A. R. Fernie. Regulation of metabolic networks: Understanding metabolic complexity in the systems biology era. New Phytologist, 168:9-24, 2005.
70. A. Trusina, S. Maslov, P. Minnhagen, and K. Sneppen. Hierarchy measures in complex networks. Physics Review Letters, 92(17):178702, 2004.
71. A.Wagner and D. A. Fell. The small-world inside large metabolic networks. Proceedings of the Royal Society of London B., 268:1803-1810, 2001.
72. D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature, 393:440-442, 1998.
73. R. Xulvi-Brunet and I. M. Sokolov. Reshuffling scale-free networks: from random to assortative. Physical Review E, 70:066102, 2004.
74. C. Zhou, A. E. Motter, and J. Kurths. Universality in the synchronization of weighted random networks. Physics Review Letters, 96:034101, 2006.
75. H. Zhou. Network landscape from a Brownian particle's perspective. Physical Review E, 67:041908, 2003.
76. E. Ziv, M. Middendorf, and C. H. Wiggins. Information-theoretic approach to network modularity. Physical Review E, 71:04611, 2005.