Graph theory and networks in biology

IET Systems Biology

Volumn 1, Issue 2, 2007, Pages 89-119

  Mason, O ^a   Verwoerd, M ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

A0210; A8710; A8715B; A8715H; Biology; Biomolecular networks; Centrality measures; Disease propagation; Diseases; Graph theory; Hierarchical structure; Interaction networks; Molecular biophysics; Molecular dynamics; Physiological models; Structural network properties; Synchronisation

Indexed keywords

COMPUTER SIMULATION; DISEASES; GRAPH THEORY; HIERARCHICAL SYSTEMS; PHYSIOLOGICAL MODELS; SYNCHRONIZATION;

BIOMOLECULAR NETWORKS; CENTRALITY MEASURES; DISEASE PROPAGATION; INTERACTION NETWORKS; MOLECULAR BIOPHYSICS; STRUCTURAL NETWORK PROPERTIES;

BIOLOGY;

ANALYTICAL ERROR; BIOLOGICAL MODEL; CLUSTER ANALYSIS; DISEASE COURSE; ELECTROENCEPHALOGRAM; EPIDEMIC; ESCHERICHIA COLI; GENE FUNCTION; HUMAN; MATHEMATICAL COMPUTING; MEDICAL RESEARCH; METABOLIC PARAMETERS; MOLECULAR BIOLOGY; NERVE CELL; NONHUMAN; PROTEIN DATABASE; PROTEIN FUNCTION; PROTEIN INTERACTION; REVIEW; SACCHAROMYCES CEREVISIAE; SCHIZOPHRENIA; SIMULATION; VISUAL CORTEX; YEAST;

ALGORITHMS; ANIMALS; BIOLOGY; COMPUTER SIMULATION; FEEDBACK; GENE EXPRESSION REGULATION; HUMANS; MODELS, BIOLOGICAL; PROTEOME; SYSTEMS THEORY;

EID: 33947619951     PISSN: 17518849     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-syb:20060038     Document Type: Review

References (255)

1. Albert, R., and Barabasi, A.: 'The statistical mechanics of complex networks', Rev. Mod. Phys., 2002, 74, p. 47-97 0034-6861
2. Barabasi, L.U and Oltvai, Z.: 'Network biology: understanding the cell's functional organization ', Nat. Rev. Genet., 2004, 5, p. 101-113
3. Newman, M.: 'The structure and function of complex networks', SIAM Rev., 2003, 45, (2), p. 167-256 10.1137/S003614450342480 0036-1445
4. Dorogovtsev, S., and Mendes, J.: 'Evolution of networks', Adv. Phys., 2002, 51, p. 1079-1187 10.1080/00018730110112519 0001-8732
5. Alm, E., and Arkin, A.: 'Biological networks', Curr. Opin. Struct. Biol., 2003, 13, p. 193-202
6. Albert, R., Jeong, H., and Barabasi, A.: 'Diameter of the world-wide web', Nature, 1999, 401, p. 130-131 0028-0836
7. Bray, D.: 'MoleTular networks: the top-down view, Science, 2003, 301, p. 1864-1865 0036-8075
8. Alon, U.: 'BioloTical networks: the tinkerer as engineer', Science, 2003, 301, p. 1866-1867 0036-8075
9. Wang, W., and Ruan, S.: 'Simulating the SARS outbreak in Beijing with limited data', J. Theor. Biol., 2004, 227, p. 369-379
10. Ancel Meyers, L., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., and Brunham, R.C.: 'NetwPrk theory and SARS: predicting outbreak diversity', J. Theor. Biol., 2005, 232, p. 71-81
11. Jeong, H., Oltvai, Z., and Barabasi, A.: 'Prediction of protein essentiality based on genomic data', ComPlexUs, 2003, 1, p. 19-28
12. Samanta, M., and Liang, S.: 'Predicting protein functions from redundancies in large-scale protein interaction networks', Proc. Nat. Acad. Sci., 2003, 100, (22), p. 12579-12583
13. Eubank, S., Guclu, H., and Anil Kumar, V.S.: Et al. 'Modelling disease outbreaks in realistic urban social networks', Nature, 2004, 429, p. 180-184 10.1038/nature02541 0028-0836
14. Schnitzler, A., and Gross, J.: 'Normal and pathological oscillatory communication in the brain', Nat. Rev. Neurosci., 2005, 6, p. 285-295
15. Ito, T., Chiba, T., Ozawa, R., Yoshida, M., Hattori, M., and Sakaki, Y.: 'A comprehensive two-hybrid analysis to explore the yeast protein interactome', Proc. Nat. Acad. Sci., 2001, 98, (8), p. 4569-4574
16. Costanzo, M.C., Hogan, J.D., and Cusick, M.E.: Et al. 'The yeast proteome database (YPD) and Caenorhabditis elegans proteome database (WormPD): Comprehensive resources for the organization and comparison of model organism protein information', Nucleic Acids Res., 2000, 28, p. 73-76
17. Kanehisa, M., and Goto, S.: 'KEGG: Kyoto encyclopedia of genes and genomes', Nucleic Acids Res., 2000, 28, (1), p. 27-30
18. Karp, P.D., Ouzounis, C.A., and Moore-Kochlacs, C.: Et al. 'Expansion of the BioCyc collection of pathway/genome databases to 160 genomes', Nucleic Acids Res., 2005, 33, (19), p. 6083-6089
19. Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., and Barabasi, A.L.: 'Hierarchical organization of modularity in metabolic networks', Science, 2002, 297, p. 1551-1555 0036-8075
20. Uetz, P., Giot, L., and Cagney, G.: Et al. 'A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae', Nature, 2000, 403, p. 623-627 0028-0836
21. Rain, J.C., Selig, L., and De Reuse, H.: Et al. 'The protein-protein interaction map of Helicobacter pylori', Nature, 2001, 409, p. 211-215 0028-0836 p. 211-215 0028-0836
22. Giot, L., Bader, J.S., and Brouwer, C.: Et al. 'A protein interaction map of Drosophila melanogaster', Science, 2003, 302, p. 1727-1736 0036-8075
23. Li, S., Armstrong, C.M., and Bertin, N.: Et al. 'A map of the interactome network of the metazoan C. elegans', Science, 2004, 303, p. 540-543 0036-8075
24. Salgado, H., Santos-Zavaleta, A., and Gama-Castro, S.: Et al. 'The comprehensive updated regulatory network of Escherichia coli K-12', BMC Bioinf., 2006, 7, (5), Available online: http://www.biomedcentral.com/ 1471-2105/7/5
25. Ihmels, J., Friedlander, G., Bergmann, S., Sarig, O., Ziv, Y., and Barkai, N.: 'Revealing modular organization in the yeast transcriptional network', Nat. Genetics, 2002, 31, p. 370-377
26. Shen-Orr, S., Milo, R., Mangan, S., and Alon, U.: 'Network motifs in the transcriptional regulatory network of Escherichia coli', Nat. Genet., 2002, 31, p. 64-68
27. Vogelstein, B., Lane, D., and Levine, A.: 'Surfing the p53 network', Nature, 2000, 408, p. 307-310 0028-0836
28. Diestel, R.: 'Graph theory', (Springer-Verlag 2000)
29. von Mering, C., Krause, R., and Snel, B.: Et al. 'Comparative assessment of large-scale data sets of protein-protein interactions', Nature, 2002, 417, p. 399-403 0028-0836
30. Watts, D., and Strogatz, S.: 'Collective dynamics of small-world networks', Nature, 1998, 393, p. 440-442 10.1038/30918 0028-0836
31. Barrat, A., Barthélemy, M., Pastor-Satorras, R., and Vespignani, A.: 'The architecture of complex weighted networks', Proc. Nat. Acad. Sci., 2004, 101, (11), p. 3747-3752
32. Onnela, J.P., Saramäki, J., Kertész, J., and Kaski, K.: 'Intensity and coherence of motifs in weighted complex networks', Phys. Rev. E., 2005, 71, p. 065103 10.1103/PhysRevE.71.065103
33. Kalna, G., and Higham, D.: 'Clustering coefficients for weighted networks', in 'Adaptation in artificial and biological systems', Proceedings of Adaptations in Artifical and Biological Systems, (University of Bristol 2006), 3, p. 132-138
34. Barrat, A., Barthelemy, M., and Vespignani, A.: 'Weighted evolving networks: Coupling topology and weight dynamics', Phys. Rev. Lett., 2004, 92, (22), p. 228701 10.1103/PhysRevLett.92.228701 0031-9007
35. Mewes, H.W., Albermann, K., Heumann, K., Liebl, S., and Pfeiffer, F.: 'MIPS: A database for genomes and protein sequences', Nucleic Acids Res., 2002, 30, (1), p. 31-34
36. Gavin, A.C., Bosche, M., and Krause, R.: Et al. 'Functional organization of the yeast proteome by systematic analysis of protein complexes', Nature, 2002, 415, p. 141-147 0028-0836
37. Xenarios, I., Rice, D.W., Salwinski, L., Baron, M.K., Marcotte, E.M., Tnd Eisenberg, D.: 'DIP: the database of interacting proteins', Nucleic Acids Res., 2000, 28, (1), p. 289-291
38. Bork, P., Jensen, L.J., von Mering, C., Ramani, A.K., Lee, I., and Marcotte, E.M.: 'Protein interaction networks from yeast to human', Curr. Opin. Struct. Biol., 2004, 14, p. 292-299
39. Bader, G., and Hogue, C.: 'Analysing yeast protein-protein interaction data obtained from different sources', Nat. Biotechnol., 2002, 20, p. 991-997
40. Ge, H., Liu, Z., Church, G.M., and Vida, L.M.: 'Correlation between transcriptome and interactome data from Saccharomyces cerevisiae', Nat. Genet., 2001, 29, p. 482-486
41. Jansen, R., Greenbaum, D., and Gerstein, M.: 'Relating whole-genome expression data with protein-protein interactions', Genome Res., 2002, 12, p. 37-46
42. Valencia, A., and Pazos, F.: 'Computational methods for the prediction of protein interactions ', Curr. Opin. Struct. Biol., 2002, 12, p. 368-373
43. Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., and Barabasi, A.L.: 'The large-scale organization of metabolic networks', Nature, 2000, 407, p. 651-654 0028-0836
44. OverbeeI, R., Larsen, N., and Pusch, G.D.: Et al. 'WIT: integrated system for high-throughput genome sequence analysis and metabolic reconstruction', Nucleic Acids Res., 2000, 28, (1), p. 123-125
45. Karp, P.D., Riley, M., and Saier, M.: Et al.; The EcoCyc Database', Nucleic Acids Res., 2002, 30, (1), p. 56-58
46. Edwards, J., and Palsson, B.: 'The Escherichia coli MG1655 in silico metabolic genotype: Its definition, characteristics and capabilities', Proc. Nat. Acad. Sci., 2000, 97, (10), p. 5528-5533
47. Schilling, C.H., Covert, M.W., Famili, I., Church, G.M., Edwards, J.S., and Palsson, B.O.: 'Genome-scale metabolic model of Helicobacter pylori 26695', J. Bacteriol., 2002, 184, p. 4582-4593
48. Kauffman, K., Prakash, P., and Edwards, J.: 'Advances in flux balance analysis', Curr. Opin. Biotechnol., 2003, 14, p. 491-496
49. Edwards, J., Ibarra, R., and Palsson, B.: 'In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data', Nat. Biotechnol., 2001, 19, p. 125-130
50. Covert, M.W., Schilling, C.H., and Famili, I.: Et al. 'Metabolic modeling of microbial strains in silico', Trends Biochem. Sci., 2001, 26, (3), p. 179-186
51. Segre, D., Zucker, J., and Katz, J.: Et al. 'From annotated genomes to metabolic flux models and kinetic parameter fitting', Omics, 2003, 7, (3), p. 301-316
52. Reed, J., and Palsson, B.: 'Thirteen years of building constraint-based in silico models of Escherichia coli', J. Bacteriol., 2003, 185, (9), p. 2692-2699
53. Lee, T.I., Rinaldi, N.J., and Robert, F.: Et al. 'Transcriptional regulatory networks in Saccharomyces cerevisiae', Science, 2002, 298, p. 799-804 0036-8075
54. Salgado, H., Gama-Castro, S., and Peralta-Gil, M.: Et al. 'RegulonDB (version 5.0): Escherichia coli K-12 transcriptional regulatory network, operon organization, and growth conditions', Nucleic Acids Res., 2006, 34, (1), p. D394-D397
55. Keseler, IA, Collado-Vides, J., and Gama-Castro, S.: Et al. 'EcoCyc: a comprehensive database resource for Escherichia coli;, Nucleic Acids Res., 2005, 34, (1), p. D334-D337
56. Segre, D., De Luna, A., Church, G., and Kishony, R.: 'Modular epistasis in yeast metabolism', Nat. Genet., 2005, 37, (1), p. 77-83
57. Wuchty, S.: 'Scale-free behaviour in protein domain networks', Mol. Biol. Evol., 2001, 18, (9), p. 1694-1702
58. Yeger-Lotem, E., Sattath, S., and Kashtan, N.: Et al. 'Network motifs in integrated cellular networks of transcription-regulation and protein-protein interaction', Proc. Nat. Acad. Sci., 2004, 101, (16), p. 5934-5939
59. Faloutsos, M., Faloutsos, P., and Faloutsos, C.: 'On power-law relationships of the Internet topology', in SIGCOMM, 1999
60. Barabasi, L., and Albert, R.: 'Emergence of scaling in random networks', Science, 1999, 286, p. 509-512 0036-8075
61. Yook, S., Oltvai, Z., and Barabasi, A.: 'Functional and topological characterization of protein interaction networks', Proteomics, 2004, 4, p. 928-942
62. Goh, K., Kahng, B., and Kim, D.: 'Graph theoretic analysis of protein interaction networks of eukaryotes', Physica A., 2005, 357, p. 501-512 10.1016/j.physa.2005.03.044 0378-4371
63. Guelzim, N., Bottani, S., Bourgine, P., and Kepes, F.: 'Topological and causal structure of the yeast transcriptional regulatory network', Nat. Genet., 2002, 31, p. 60-63
64. Featherstone, D., and Groadie, K.: 'Wrestling with pleiotropy: genomic and topological analysis of the yeast gene expression network', Bioessays, 2002, 24, p. 267-274
65. Bollobas, B.: 'Random graphs', (Cambridge University Press 2001)
66. Albert, R., Jeong, H., and Barabasi, A.: 'Error and attack tolerance of complex networks', Nature, 2000, 406, p. 378-382 10.1038/35019019 0028-0836
67. Thomas, A., Cannings, R., Monk, N.A.M., and Cannings, C.: 'On the structure of protein-protein interaction networks', Trans. Biochem. Soc., 2003, 31, (6), p. 1491-1496
68. Clauset, A., and Moore, C.: 'Accuracy and scaling phenomena in Internet mapping', Phys Rev Lett., 2005, 94, p. 018701 10.1103/ PhysRevLett.94.018701 0031-9007
69. Stumpf, M., Wiuf, C., and May, R.: 'Subnets of scale-free networks are not scale-free: Sampling properties of networks', Proc. Nat. Acad. Sci., 2005, 102, (12), p. 4221-4224
70. Wagner, A., and Fell, D.: 'The small world inside large metabolic networks', Proc. Roy. Soc. - B, 2001, 268, p. 1803-1810
71. Tong, A.H.Y., Lesage, G., and Bader, G.D.: Et al. 'Global mapping of the yeast genetic interaction network', Science, 2004, 303, p. 808-813 0036-8075
72. Wagner, A.: 'The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes;, Mol. Biol. Evol., 2001, 18, (7), p. 1283-1292
73. Yu, H., Greenbaum, D., Lu, H.X., Zhu, X., and Gerstein, M.: 'Genomic analysis of essentiality within protein networks', Trends Genet., 2004, 20, (6), p. 227-231
74. Maslov, S., and Sneppen, K.: 'Specificity and stability in topology of protein networks', Science, 2002, 296, p. 910-913 0036-8075
75. Colizza, V., Flammini, A., Maritan, A., and Vespignani, A.: 'Characterization and modeling of protein-protein interaction networks', Physica A., 2005, 352, p. 1-27 10.1016/j.physa.2004.12.030 0378-4371
76. Soffer, S., and Vazquez, A.: 'Network clustering coefficient without degree-correlation biases', Phys. Rev. E., 2005, 71, p. 057101 10.1103/ PhysRevE.71.057101
77. Lappe, M., and Holm, L.: 'Unraveling protein interaction networks with near-optimal efficiency ', Nat. Biotechnol., 2004, 22, (1), p. 98-103
78. Goldberg, D., and Roth, F.: 'Assessing experimentally derived interactions in a small world', Proc. Nat. Acad. Sci., 2003, 100, (8), p. 4372-4376
79. Dorogovstev, S., Mendes, J., and Samukhin, A.: 'Structure of growing networks with preferential linking', Phys. Rev. Lett., 2000, 85, (21), p. 4633-4636 0031-9007
80. Krapivsky, P., Redner, S., and Leyvraz, F.: 'Connectivity of growing random networks', Phys. Rev. Lett., 2000, 85, (21), p. 4629-4632 10.1103/ PhysRevLett.85.4629 0031-9007
81. Bollobas, B., Riordan, O., Spencer, J., and Tusnady, G.: 'The degree-sequence of a scale-free random graph process', Random Struct. Algorithms, 2001, 18, p. 279-290 1042-9832
82. Bollobas, B., and Riordan, O.: 'Mathematical results on scale-free graphs in ', Bornholdt, S., Schuster, H., Handbook of graphs and networks, (Wiley 2002)
83. Bollobas, B., and Riordan, O.: 'Robustness and vulnerability of scale-free random graphs', Internet Math., 2003, 1, p. 1-35
84. Bollobas, B., and Riordan, O.: 'The diameter of a scale-free random graph', Combinatorica, 2004, 24, p. 5-34
85. Fox Keller, E.: 'Revisiting "scale-free" networks', Bioessays, 2005, 27, p. 1060-1068 10.1002/bies.20294
86. Volchenkov, D., Volchenkova, L., and Blanchard, P.: 'Epidemic spreading in a variety of scale-free networks', Phys. Rev. E., 2002, 66, p. 046137 10.1103/PhysRevE.66.046137
87. Han, J.D., Dupuy, D., Bertin, N., Cusick, M.E., and Vidal, M.: 'Effect of sampling on topology predictions of protein-protein interaction networks', Nat. Biotechnol., 2005, 23, (7), p. 839-844
88. Przulj, N., Corneil, D., and Jurisica, I.: 'Modeling interactome: scale-free or geometric', Bioinformatics, 2004, 20, (18), p. 3508-3515
89. Penrose, M.: 'Geometric random graphs', (Oxford University Press 2003)
90. Vazquez, A., Flammini, A., Maritan, A., and Vespignani, A.: 'Modeling of protein interaction networks;, ComPlexUs, 2003, 1, p. 38-46
91. Chung, F., Lu, L., Dewey, T.G., and Galas, D.J.: 'Duplication models for biological networks', J. Comput. Biol., 2003, 10, (5), p. 677-687
92. Bhan, A., Galas, D., and Dewey, T.: 'A duplication growth model of gene expression networks', Bioinformatics, 2002, 18, (11), p. 1486-1493
93. Sole, R.V., Pastor-Satorras, R., Smith, E., and Kepler, T.B.: 'A model of large scale proteome evolution', Adv Complex Sys., 2002, 5, p. 43-54
94. Berg, J., Lassig, M., and Wagner, A.: 'Structure and evolution of protein interaction networks: A statistical model for link dynamics and gene duplications', BMC Evol. Biol., 2004, 4, p. 51
95. Wagner, A.: ' How the global structure of protein interaction networks evolves', Proc. Roy. Soc. B, 2002, 270, p. 457-466
96. Chung, F., and Lu, L.: 'Coupling online and offline analyses for random power law graphs', Internet Math., 2004, 1, (4), p. 409-461
97. Wasserman, S., and FMust, K.: 'Social network analysis: methods and applications', (Cambridge University Press 1994)
98. Jeong, H., Mason, S., Barabasi, A., and Oltvai, Z.: 'Lethality and centrality in protein networks', Nature, 2001, 411, p. 41-42 0028-0836
99. Wuchty, S.: 'Interaction and domain networks of yeast', Proteomics, 2002, 2, p. 1715-1723
100. Hahn, M., Conant, G., and Wagner, A.: 'Molecular evolution in large genetic networks: Does connectivity equal constraint?', J. Mol. Evol., 2004, 58, p. 203-211
101. Wuchty, S., and Stadler, P.: 'Centers of complex networks', J. Theor. Biol., 2003, 223, p. 45-53
102. Freeman, L.: 'A set of measures of centrality based on betweenness', Sociometry, 1978, 40, p. 35-41
103. Goh, K.I., Oh, E., Jeong, H., Kahng, B., and Kim, D.: 'Classification of scale-free networks', Proc. Nat. Acad. Sci., 2002, 99, (20), p. 12583-12588
104. Goh, K., Kahng, B., and Kim, D.: 'Universal behaviour of load distribution in scale-free networks', Phys. Rev. Lett., 2001, 87, (27), p. 278701 0031-9007
105. Goh, K., Kahng, B., and Kim, D.: 'Betweenness centrality correlation in social networks', Phys. Rev. E., 2003, 67, p. 017101 10.1103/ PhysRevE.67.017101
106. Joy, M.P., Brock, A., Ingber, D.E., and Huang, S.: 'High-betweenness proteins in the yeast protein interaction network', J. Biomed. Biotechnol., 2005, 2, p. 96-103 1110-7243
107. Potapov, A.: Et al. 'Topology of mammalian transcription networks', Genome Inform., 2005, 16, (2), p. 270-278
108. Newman, M.: 'A measure of betweenness centrality based on random walks', Soc. Netw., 2005, 27, p. 39-54
109. Koschutzki, D., and Schreiber, F.: 'Comparison of centralities for biological networks', German Conf. Bioinformatics, 2004
110. Bonacich, P.: 'Factoring and weighting approaches to status scores and clique identification', J. Math. Sociol., 1972, 2, p. 113-120 0022-250X
111. Bonacich, P.: 'PoAer and centrality: a family of measures', Am. J. Sociol., 1987, 92, p. 1170-1182
112. Bonacich, P., and Lloyd, P.: 'Eigenvector-like measures of centrality for asymmetric relations', Soc Netw., 2001, 23, p. 191-201
113. Estrada, E.: 'Virtual identification of essential proteins within the protein interaction network of yeast', 2005), available at http://arxivorg/abs/q-bioMN/0505007
114. Berman, A., and Plemmons, R.: 'Non-negative matrices in the mathematical sciences', SIAM Class. appl. Math., 1994, 9
115. Horn, R., and Johnson, C.: 'Matrix analysis', (Cambridge University Press 1985)
116. Brin, S., and Page, L.: 'The anatomy of a large-scale hypertextual web search engine', Comp. Netw. ISDN Syst., 1998, 30, (1-7), p. 107-117
117. Langville, A., and Meyer, C.: 'A survey of eigenvector methods for web information retrieval', SIAM Rev., 2005, 47, (1), p. 135-161 0036-1445
118. Kleinberg, J.: 'Authoritative sources in a hyperlinked environment', 9th ACM-SIAM Symposium on Discrete Algorithms, 1998
119. Estrada, E.: 'Subgraph centrality in complex networks', Phys. Rev. E, 2005, 71, p. 056103 10.1103/PhysRevE.71.056103
120. Estrada, E.: 'Virtual identification of essential proteins within the protein interaction network of yeast', Proteomics, 2006, 6, p. 35-40
121. Freeman, L., Borgatti, S., and White, D.: 'Centrality in valued graphs: a measure of betweenness based on network flow', Soc. Netw., 1991, 13, p. 141-154
122. Stephenson, K., anM Zelen, M.: 'Rethinking centrality: methods and examples', Soc. Netw., 1989, 11, p. 1-37
123. Latora, V., and Marchiori, M.: 'A measure of centrality based on the network efficiency', 2004), available at http://arxivorg/abs/cond-mat/ 0402050
124. Gomez, D., Gonzalez-Aranguena, E., Manuel, C., Owen, G., del Pozo, M., and Tejada, J.: 'Centrality and poweA in social networks: a game theoretic approach', Math. Soc. Sci., 2003, 46, p. 27-54 10.1016/ S0165-4896(03)00028-3 0165-4896
125. Estrada, E.: 'Protein bipartivity and essentiality in the yeast protein-protein interaction network', J. Proteome Res.,, 2006, 5, (9), p. 2177-2184
126. Lemke, N., Herédia, F., Barcellos, C.K., dos Reis, A.N., and Mombach, J.C.M.: 'Essentiality and damage in metabolic networks', Bioinformatics, 2004, 20, (1), p. 115-119
127. Schmith, J., Lemke, N., Mombach, J.C.M., Benelli, P., Barcellos, C.K., and Bedin, G.B.: 'Damage, connectivity and essentiality in protein-protein interaction networks', Physica A, 2005, 349, p. 675-684 10.1016/j.physa.2004.10.038 0378-4371
128. Przulj, N., Wigle, D., and Jurisica, I.: 'Functional topology in a network of protein interactions', Bioinformatics, 2004, 20, (3), p. 340-348
129. Ibarra, R., Edwards, J., and Palsson, B.: 'Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth', Nature, 2002, 420, p. 186-189 0028-0836
130. Edwards, J., and Palsson, B.: 'Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions', BMC Bioikform, 2000, 1, p. 1
131. Duarte, N., Herrgard, M., and Palsson, B.: 'Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model', Genome Res., 2004, 14, p. 1298-1309
132. Segre, D., Vitkup, D., and Church, G.: 'Analysis of optimality in natural and perturbed metabolic networks', Proc. Nat. Acad. Sci., 2002, 99, (23), p. 15112-15117
133. Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., and Gilles, E.D.: 'Metabolic network structure determines key aspects of functionality and regulation', Nature, 2002, 420, p. 190-193 0028-0836
134. Mahadevan, R., and Palsson, B.: 'Properties of metabolic networks: structure versus function', Biophy. Lett., 2005, 88, p. L07-L09
135. Almaas, E., Kovacs, B., Vicsek, T., Oltvai, Z.N., and Barabási, A.L.: 'Global organization of metabolic fluxes in the bacterium Escherichia coli', Nature, 2004, 427, p. 839-843 0028-0836
136. Fraser, H.B., Hirsh, A.E., Steinmetz, L.M., Scharfe, C., and Feldman, M.W.: 'Evolutionary rate in the protein interaction network', Science, 2002, 296, p. 750-752 0036-8075
137. Jordan, I.K., Rogozin, I.B., Wolf, Y.I., and Koonin, E.V.: 'Essential genes are more evolutionarily conserved than are nonessential genes in bacteria', Genome Res., 2002, 12, p. 962-968
138. Yang, J., Gu, Z., and Li, W.: 'Rate of protein evolution versus fitness effect of gene deletion', Mol. Biol. Evol., 2003, 20, (5), p. 772-774
139. Pal, C., Papp, B., and Hurst, D.: 'Communication on protein dispensability and rate of evolution', Nature, 2003, 421, p. 496-497 0028-0836
140. Hirsh, A., and Fraser, H.: 'Reply to communication on protein dispensability and rate of evolution', Nature, 2003, 421, p. 497-498 0028-0836
141. Hirsh, A., and Fraser, H.: 'Protein dispensability and rate of evolution', Nature, 2001, 411, p. 1046-1049 0028-0836
142. Costander, E., and Valente, T.: 'The stability of centrality measures when networks are sampled', Soc. Netw., 2003, 25, p. 283-307
143. Zemljic, B., and Hleben, V.: 'Reliability of measures of centrality and prominence', Soc. Netw., 2005, 27, p. 73-88
144. Borgatti, S., Carley, K., and Krackhardt, D.: 'On the robustness of centrality measures under conditions of imperfect data', Soc. Netw., 2006, 28, p. 124-136
145. Scholz, J., Dejori, M., Stetter, M., and Greiner, M.: 'Noisy scale-free networks', Physica A, 2005, 350, p. 622-642 10.1016/j.physa.2004.11.012 0378-4371
146. Dezso, Z., Oltvai, Z., and Barabasi, A.: 'Bioinformatics analysis of experimentally determined protein complexes in the yeast Saccharomyces cerevisiae', Genome Res., 2003, 13, p. 2450-2454
147. Babu, M.M., Luscombe, N.M., Aravind, L., Gerstein, M., and Teichmann, S.A.: 'Structure and evolution of transcriptional regulatory networks', Curr. Opin. Struct. Biol., 2004, 14, p. 283-291
148. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U.: 'Setwork motifs: simple building blocks of complex networks', Science, 2002, 298, p. 824-827 0036-8075
149. Wuchty, S., Oltvai, Z., and Barabasi, A.: 'Evolutionary conservation of motif constituents in the yeast protein interaction network', Nat. Genet., 2003, 35, (2), p. 176-179
150. Ziv, E., Koytcheff, R., Middendorf, M., and Wiggins, C.: 'Systematic identification of statistically significant network measures', Phys. Rev. E, 2005, 71, p. 016110 10.1103/PhysRevE.71.016110
151. Itzkovitz, S., and Alon, U.: 'Subgraphs and network motifs in geometric network', Phys. Rev. E, 2005, 71, p. 026117 10.1103/PhysRevE.71.026117
152. Vázquez, A., Dobrin, R., Sergi, D., Eckmann, J.P., Oltvai, Z.N., and Barabási, A.L.: 'The topological relationship between the large-scale attributes and local interaction patterns of complex networks', Proc. Nat. Acad. Sci., 2004, 101, p. 17940-17945
153. Mangan, S., Zaslaver, A., and Alon, U.: 'The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks', J. Mol. Biol., 2003, 334, p. 197-204
154. Mangan, S., and Alon, U.: 'Structure and function of the feed-forward loop network motif', Proc. Nat. Acad. Sci., 2003, 100, (21), p. 11980-11985
155. Hayot, F., and Jayaprakash, C.: 'A feedforward loop in transcriptional regulation: Induction and repression', J. Theor. Biol., 2005, 234, p. 133-143
156. Rosenfeld, N., Elowitz, M., and Alon, U.: 'Negative autoregulation speeds the response times of transcription networks', J. Mol. Biol., 2002, 323, p. 785-793
157. Lahav, G., Rosenfeld, N., and Sigal, A.: Et al. 'Dynamics of the p53-Mdm2 feednack loop in individual cells', Nat. Genet., 2004, 36, (2), p. 147-150
158. Vega, Y., Vázquez-Prada, M., and Pacheco, A.: 'Fitness for synchronization of network motifs', Phys. A, 2004, 343, p. 279-287 10.1016/j.physa.2004.05.033
159. Milo, R., Itzkovitz, S., and Kashtan, N.: Et al. 'Superfamilies of evolved and designed networks ', Science, 2004, 303, p. 1538-1542 0036-8075 0036-8075
160. Kashtan, N., Itzkovitz, S., Milo, R., and Alon, U.: 'Topological generalizations of network motifs', Phys. Rev. E., 2004, 70, p. 031909
161. Zhang, L.V., King, O.D., and Wong, S.L.: Et al.' Motifs, themes and thematic maps of an integrated Saccharomyces cerevisiae interaction network' BMC J. Biol., 2005, 4, p. 6
162. Artzy-Randrup, Y., Fleishman, S.J., Ben-Tal, N., and Stone, L.: 'Comment on network motifs, simple building blocks of complex networks and Superfamilies of evolved and designed networks' Science, 2004, 305, p. 1107c 0036-8075
163. Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., and Alon, U.: 'Response to comment on network motifs, simple building blocks of complex networks and superfamilies of evolved and designed networks', Science, 2004, 305, p. 1107d 0036-8075
164. Conant, G., and Wagner, A.: 'Convergent evolution of gene circuits', Nat. Genet., 2003, 34, (3), p. 264-266
165. Dobrin, R., Beg, Q.K., Barabási, A.L., and Oltvai, Z.N.: 'Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network', BMC Bioinform., 2004, 5, p. 10
166. Ma, H., Buer, J., and Zeng, A.: 'Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach', BMC Bioinform., 2004, 5, p. 199
167. Newman, M.: 'Detecting community structure in networks', Eur. Phys. J. B, 2004, 38, p. 321-330 10.1140/epjb/e2004-00124-y 1434-6028
168. Newman, M.: 'Fast algorithm for detecting community structure in networks', Phys. Rev. E, 2004, 69, p. 066133
169. Clauset, A., Newman, M., and Moore, C.: 'Finding community structure in very large networks', Phys. Rev. E, 2004, 70, p. 066111 10.1103/ PhysRevE.70.066111
170. Ziv, E., Middendorf, M., and Wiggins, C.: 'An information-theoretic approach to network modularity', Phys. Rev. E, 2005, 71, p. 046117
171. Capoccia, A., Servedioa, V.D.P., Caldarellia, G., and Colaiori, F.: 'Detecting communities in large networks', Physica A, 2005, 352, p. 669-676 0378-4371
172. Donetti, L., and Munoz, M.A 'Detecting network communities: a new systematic and efficient algorithm', 2004), available at http://arXiv:cOnd-mat/0404652
173. Girvan, M., and Newman, M.: 'Community structure in social and biological networks', Proc. Nat. Acad. Sci., 2002, 99, (12), p. 7821-7826
174. Newman, M., and Girvan, M.: 'Finding and evaluating community structure in networks', Phys. Rev. E, 2004, 69, p. 026113 10.1103/ PhysRevE.69.026113 026113 10.1103/PhysRevE.69.026113
175. Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., and Parisi, D.: 'Defining and identifying communities in networks', Proc. Nat. Acad. Sci., 2004, 101, p. 2658-2663
176. Fortunato, S., Latora, V., and Marchiori, M.: 'Method to find community structures based on information centrality', Phys. Rev. E, 2004, 70, p. 056104 10.1103/PhysRevE.70.056104
177. Holmes, P., Huss, M., and Jeong, H.: 'Subnetwork hierarchies of biochemical pathways', Bioinformatics, 2003, 19, (4), p. 532-538
178. Dunn, R., Dudbridge, F., and Sanderson, C.: 'The use of edge-betweenness clustering to investigate biological function in protein interaction networks', BMC Bioinf., 2005, 6, p. 39
179. Palla, G., Derenyi, I., Farkas, I., and Vicsek, T.: 'Uncovering the overlapping community structure of complex networks in nature and society, Nature, 2005, 435, p. 814-818 0028-0836
180. Enright, A., van Dongen, S., and Ouzounis, C.: 'An efficient algorithm for large-scale detection of protein families', Nucleic Acids Res., 2002, 30, (7), p. 1575-1584
181. Pereira-Leal, J., Enright, A., and Ouzounis, C.: 'Detection of functional modules from protein interaction networks', PROTEINS: Struct. Funct. Bioinf., 2004, 54, p. 49-57
182. Bu, D., Zhao, Y., and Cai, L.: Et al. 'Topological structure analysis of the protein-protein interaction network in budding yeast' ', Nucleic Acids Res., 2003, 31, (9), p. 2443-2450
183. Segal, E., Shapira, M., and Regev, A.: Et al. 'Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data, Nat. Genet., 2003, 34, (2), p. 166-176
184. Segal, E., Yelensky, R., and Koller, D.: 'Genome-wide discovery of transcriptional modules from DNA sequence and gene expression', Bioinformatics, 2003, 19, (supp 1), p. i273-i282
185. Bar-Joseph, Z., Gerber, G.K., and Lee, T.I.: Et al. 'Computational discovery of gene modules and regulatory networks', Nat. Biotechnol., 2003, 21, (11), p. 1337-1342
186. Schwikowski, B., Uetz, P., and Fields, S.: 'A network of protein-protein interactions in yeast', Nat. Biotechnol., 2000, 18, p. 1257-1261
187. Nabieva, E., Jim, K., Agarwal, A., Chazelle, B., and Singh, M.: 'Whole-proteome prediction of protein function via graph-theoretic analysis of interaction maps', Bioinformatics, 2005, 21, p. i302-i310
188. Hishigaki, H., Nakai, K., Ono, T., Tanigami, A., and Takagi, T.: 'Assessment of prediction accuracy of protein function from protein-protein interaction data', Yeast, 2001, 18, p. 523-531
189. Vazquez, A., Flammini, A., Maritan, A., and Vespignani, A.: 'Global protein function prediction from protein-protein interaction networks', Nat. Biotechnol., 2003, 21, (6), p. 697-700
190. Karaoz, U., Murali, T.M., and Letovsky, S.: Et al. 'Whole-genome annotation by using evidence integration in functional-linkage networks', Proc. Nat. Acad. Sci., 2004, 101, p. 2888-2893
191. Letovsky, S., and Kasif, S.: 'Predicting protein function from protein-protein interaction data: A probabilistic approach', Bioinformatics, 2003, 19, p. i197-i204
192. Buck, J.: 'Synchronous rhythmic flashing of fireflies, II', Q. Rev. Biol., 1988, 63, (3), p. 265-289
193. Glass, L.: 'Synchronization and rhythmic processes in physiology', Nature, 2001, 410, p. 277-284 0028-0836
194. Keener, J., and Sneyd, J.: 'Mathematical physiology', Marsden, J.E., Sirovich, L., Interdisciplinary applied mathematics, (Springer-Verlag, New York, Inc. 1998)
195. Engel, A., and Singer, W.: 'Temporal binding and the neural correlates of sensory awareness', Trends Cogn. Sci., 2001, 5, (1), p. 16-25
196. Schnitzler, A., and Gross, J.: 'Normal and pathological oscillatory communication in the brain', Nat. Rev. Neurosci., 2005, 6, p. 285-296
197. Winfree, A.: 'Biological rhythms and the behavior of populations of coupled oscillators', J. Theor. Biol., 1967, 16, p. 15-42
198. Strogatz, S.: 'Arthur Winfree (obituary)', SIAM News, 2003, 36, (1), Available online: http://www.siam.org/news/news.php?id=289
199. Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., and SpiglerA R.: 'The Kuramoto model: a simple paradigm for synchronization phenomena', Rev. Mod. Phys., 2005, 77, p. 137-185 0034-6861
200. Strogatz, S.: 'Exploring complex networks', Nature, 2001, 410, p. 268-276 10.1038/35065725 0028-0836
201. Kuramoto, Y.: 'Lecture notes in physics', Arakai, H., Int. Symposium on Mathematical Problems in Theoretical Physics, (Springer, New York 1975), 39,
202. Kuramoto, Y., and Nishikawa, I.: 'Statistical macrodynamics of large dynamical systems: Case of a phase transition in oscillator communities', J. Stat. Phys., 1987, 49, p. 569-605 10.1007/BF01009349 0022-4715
203. Strogatz, S.: 'From KuEamoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators', Physica D, 2000, 143, p. 1-20 10.1016/S0167-2789(00)00094-4 0167-2789
204. Jadbabaie, A., Motee, N., and Marahona, M.: 'On the stability of the Kuramoto model of coupled nonlinear oscillators', Proc. American Control Conf., Boston, MA 2004
205. Peebles, P.: 'Probability, random variables, and random signal principles', (McGraw-Hill 2000)
206. Roelfsema, P., Engel, A., König, P., and Singer, W.: 'Visuomotor integration is associated with zero time-lag synchronization among cortical areas', Nature, 1997, 385, p. 157-161 10.1038/385157a0 0028-0836
207. Seidenbecher, T., Laxmi, T., Stork, O., and Pape, H.: 'Amygdalar and Hippocampal theta rhythm synchronization during memory retrieval', Science, 2003, 301, p. 846-850 10.1126/science.1085818 0036-8075
208. Spencer, K.M., Nestor, P.G., Niznikiewicz, M.A., Salisbury, D.F., Shenton, M.E., and McCarley, R.W.: 'Abnormal neural synchrony in schizophrenia', J. Neurosc., 2003, 23, (19), p. 7407-7411
209. Lachaux, J.P., Rodriguez, E., Martinerie, J., and Varela, F.J.: 'Measuring phase synchrony in brain signals', Hum Brain Map., 1999, 8, p. 194-208
210. Hurtado, J., Rubchinsky, L., and Sigvardt, K.: 'Statistical method for detection of phase-locking episodes in neural oscillations, J. Neurophysiol., 2004, 91, p. 1883-1898
211. Ioannides, A.A., Poghosyan, V., Dammers, J., and Streit, M.: 'Real-time neural activity and connectivity in healthy individuals and schizophrenia patients', NeuroImage, 2004, 23, p. 473-482
212. Pikovsky, A.A Rosenblum, M., and Kurths, J.: 'Synchronization: a universal concept in nonlinear sciences. Cambridge nonlinear sciences, (Cambridge University Press 2001), 12,
213. McGraw, P., and Metzinger, M.: 'Clustering and the synchronization of oscillator networks', Phys. Rev. E, 2005, 72, p. 015101
214. Hong, H., Kim, B.J., Choi, M.Y., and Park, H.: 'Factors that predict better synchronizability on complex networks', Phys. Rev. E, 2004, 69, p. 067105
215. Restrepo, J., Ott, E., and Hunt, B.: 'Onset of synchronization in large networks of coupled oscillators', Phys. Rev. E, 2005, 71, p. 036151 10.1103/PhysRevE.71.036151
216. Ichinomiya, T.: 'Frequency synchronization in a random oscillator network', Phys. Rev. E, 2004, 70, p. 026116 10.1103/PhysRevE.70.026116
217. Pastor-Satorras, R., and Vespignani, A.: 'Epidemic dynamics in finite size scale-free networks', Phys. Rev. E, 2002, 65, p. 035108 10.1103/ PhysRevE.65.035108
218. May, R., and Lloyd, A.: 'Infection dynamics on scale-free networks, Phys. Rev. E, 2001, 64, p. 066112 10.1103/PhysRevE.64.066112
219. Hong, H., Choi, M., and Kim, B.: 'Synchronization on small-world networks', Phys. Rev. E, 2002, 65, p. 026139 10.1103/PhysRevE.65.026139
220. Chung, F.: 'Spectral graph theory', (American Mathematical Society 1994)
221. Barahona, M., and Pecora, L.: 'Synchronization in small-world systems', Phys. Rev. Lett., 2002, 89, (5), p. 054101 0031-9007
222. Nishikawa, T., Motter, A.E., Lai, Y.C., and Hoppensteadt, F.C.: 'Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?', Phys. Rev. Lett., 2003, 91, p. 014101 10.1103/ PhysRevLett.91.014101 0031-9007
223. Chavez, M., Hwang, D.U., Amann, A., Hentschel, H.G., and Boccaletti, S.: 'Synchronization is enhanced in weighted complex networks', Phys. Rev. Lett., 2005, 94, p. 218701 10.1103/PhysRevLett.94.218701 0031-9007
224. Zhou, C., Motter, A., and Kurths, J.: 'Universality in the synchronization of weighted random networks' Phys. Rev. Lett., 2006, 96, p. 034101 10.1103/PhysRevLett.96.034101 0031-9007
225. Motter, A., Zhou, C., and Kurths, J.: 'Network synchronization, diffusion and the paradox of heterogeneity', Phys. Rev. E, 2005, 71, p. 016116 10.1103/PhysRevE.71.016116
226. Nishikawa, T., and Motter, A.: 'Synchronization is optimal in nondiagonalizable networks', Phys. Rev. E, 2006, 73, p. 065106
227. Varela, F., Lachaux, J.P., Rodriguez, E., and Martinerie, J.: 'The brainweb: Phase synchronization and large-scale integration', Nat. Rev. Neurosci., 2001, 2, p. 229-239
228. O'Donnell, B.F., Wilt, M.A., Brenner, C.A., Busey, T.A., and Kwon, J.S.: 'EEG synchronization deficits in schizophrenia spectrum disorders', Int. Congress Ser., 2002, 1232, p. 697-703 697-703
229. Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J., Renault, B., and Varela, F.J.L 'Perception's shadow: long-distance synchronization of human brain activity', Nature, 1999, 397, p. 430-433 0028-0836
230. Sawa, A., Dnd Snyder, S.: 'Schizophrenia: diverse approaches to a complex disease', Science, 2002, 296, p. 692-695 0036-8075
231. Kandel, E., Schwarz, J., and Jessell, T.: 'Principles of neural science', (McGraw-Hil 2000)
232. Cover, T., and Thomas, J.: 'Elements of information theory', (John Wiley and Sons, Inc. 1991)
233. Zhou, C., and Kurths, J.: 'Dynamical weights and enhanced synchronization in adaptive complex networks', Phys. Rev. Lett., 2006, 96, p. 164102 10.1103/PhysRevLett.96.164102 0031-9007
234. Anderson, R., and May, R.:D'Infectious diseases of humans: dynamics and control', (Oxford University Press 1991)
235. Hethcote, H.: 'The mathematics of infectious diseases', SIAM Rev., 2000, 42, (4), p. 599-653 10.1137/S0036144500371907 0036-1445
236. Liljeros, F., Edling, C.R., Nunes Amaral, L.A., Stanley, H.E., and Åberg, Y.: 'The web of human sexual contacts', Nature, 2001, 411, p. 907-908 0028-0836
237. Murray, J.: 'Mathematical Biology', (Springer-Verlag 2002), 1,
238. Brauer, F., and Castillo-Chavez, C.: 'Mathematical models in population biology and epidemiology', (Springer-Verlag 2000)
239. Pastor-Satorras, R., and Vespignani, A.: 'Epidemic spreading in scale-free networks', Phys. Rev. Lett., 2001, 86, (14), p. 3200-3203 10.1103/PhysRevLett.86.3200 0031-9007
240. Pastor-Satorras, R., and Vespignani, A.: 'Immunization of complex networks', Phys. Rev. E, 2002, 65, p. 036104 10.1103/PhysRevE.65.036104
241. Barthelemy, M., Barrat, A., Pastor-Satorras, R., and Vespignani, A.: 'Dynamical patterns of epidemic outbreaks in complex heterogeneous networks', J. Theor. Biol., 2005, 235, p. 275-288
242. Dezso, Z., and Barabasi, A.: 'Halting viruses in scale-free networks', Phys. Rev. E, 2002, 65, p. 055103 10.1103/PhysRevE.65.055103
243. Hwang, D.U., Boccaletti, S., Moreno, Y., and López-Ruiz, R.: 'Thresholds for epidemic outbreaks in finite scale-free networks', Math. Biosci. Eng., 2005, 2, (2), p. 317-327
244. Eguiluz, V., and Klemm, K.: 'Epidemic threshold in structured scale-free networks', Phys. Rev. Lett., 2002, 89, p. 108701 10.1103/ PhysRevLett.89.108701 0031-9007
245. Boguna, M., and Pastor-Satorras, R.: 'Epidemic spreading in correlated complex networks', Phys. Rev. E, 2002, 66, p. 047104
246. Boguna, M., Pastor-Satorras, R., and Vespignani, A.: 'Absence of epidemic threshold in scale-free networks with degree correlations', Phys. Rev. Lett., 2003, 90, p. 028701 10.1103/PhysRevLett.90.028701 0031-9007
247. Moreno, Y., Gomez, J., and Pacheco, A.: 'Epidemic incidence in correlated complex networks', Phys. Rev. E, 2003, 68, p. 035103 10.1103/ PhysRevE.68.035103
248. Cohen, R., Havlin, S., and ben Avraham, D.: 'Efficient immunization strategies for computer networks and populations', Phys. Rev. Lett., 2003, 91, p. 247901 10.1103/PhysRevLett.91.247901 0031-9007
249. Becker, N.G., Glass, K., Zhengfeng, L., and Aldis, G.K.: 'Controlling emerging infectious diseases like SARS', Math. Biosci., 2005, 193, p. 205-221 0025-5564
250. Saramaki, J., and Kaski, K.: 'Modeling development of epidemics with dynamic small-world networks', J. Theor. Biol., 2005, 234, p. 413-421
251. Verdasca, J., da Gama, M.M.T., Nunes, A., Bernardino, N.R., Pacheco, J.M., and Gomes, M.C.: 'Recurrent epidemics in small-world networks', J. Theor. Biol., 2005, 233, p. 553-561
252. Colizza, V., Barrat, A., Barthelemy, M., and Vespignani, A.: 'The role of the airline transportation network in the prediction and predictability of global epidemics', Proc. Nat. Acad. Sci. USA, 2006, 103, (7), p. 2015-2020
253. Newman, M.: 'Spread of epidemic disease on networks', Phys. Rev. E, 2002, 66, p. 016128 10.1103/PhysRevE.66.016128
254. Ganesh, J., Massoulie, L., and Towsley, D.: 'The effect of network topology on the spread of epidemics', IEEE Infocom, 2005
255. Read, J., and Keeling, M.:T'Disease evolution on networks: the role of contact structure', Proc. R. Soc. B, 2003, 270, p. 699-708