Topological Characteristics of Molecular Networks



We present currently available computational methods for graph-theoretic analysis, modeling, and comparison of biological networks. Biological network research is still in its infancy, since the current data is of low quality, and since the existing methods for their analyses are relatively crude, owing to the computational intractability of many graph theoretic problems. Nonetheless, the field has already provided valuable insights into biological function, evolution, and disease. Further systems-level analyses of cellular inter-connectedness have an enormous potential to lead to new interesting biological discoveries and give novel insights into organizational principles of life and therapeutics, thus potentially having huge impacts on public health. The impact of the field of biological network research is likely to increase with the growth of available biological network data of high quality, as well as with improvements of network analysis and modeling methods. The field is likely to stay at the forefront of scientific research in the years to come.


Degree Distribution Cluster Coefficient Biological Network Network Motif Network Alignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    W. Aiello, F. Chung, and L. Lu. A random graph model for power law graphs. Experimental Mathematics, 10:53–66, 2001.Google Scholar
  2. 2.
    U. Alon. Network motifs: theory and experimental approaches. Nature Reviews Genetics, 8:450–461, 2007.PubMedCrossRefGoogle Scholar
  3. 3.
    S. F. Altschul, W. Gish, W. Miller, and D. J. Lipman. Basic local alignment search tool. Journal of Molecular Biology, 215:403–410, 1990.PubMedGoogle Scholar
  4. 4.
    R. Aragues, C. Sander, and B. Oliva. Predicting cancer involvement of genes from heterogeneous data. BMC Bioinformatics, 9:172, 2008.PubMedCrossRefGoogle Scholar
  5. 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, 305:1107c, 2004.CrossRefGoogle Scholar
  6. 6.
    G. D. Bader and C. W. V. Hogue. An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics, 4:2, 2003.PubMedCrossRefGoogle Scholar
  7. 7.
    A.-L. Barabási and R. Albert. Emergence of scaling in random networks. Science, 286(5439):509–512, 1999.PubMedCrossRefGoogle Scholar
  8. 8.
    A.-L. Barabási, R. Albert, and H. Jeong. Mean-field theory for scale-free random networks. Physica A, 272:173–197, 1999.CrossRefGoogle Scholar
  9. 9.
    J. Berg and M. Lassig. Local graph alignment and motif search in biological networks. PNAS, 101:14689–14694, 2004.PubMedCrossRefGoogle Scholar
  10. 10.
    J. Berg and M. Lassig. Cross-species analysis of biological networks by Bayesian alignment. Proceedings of the National Academy of Sciences, 103(29):10967–10972, 2006.CrossRefGoogle Scholar
  11. 11.
    S. I. Berger and R. Iyengar. Network analyses in systems pharmacology. Bioinformatics, 25:2466–2472, 2009.PubMedCrossRefGoogle Scholar
  12. 12.
    A. Beyer, S. Bandyopadhyay, and T. Ideker. Integrating physical and genetic maps: from genomes to interaction networks. Nature Reviews Genetics, 8:699–710, 2007.PubMedCrossRefGoogle Scholar
  13. 13.
    B. Bollobas. Random Graphs. Academic, London, 1985.Google Scholar
  14. 14.
    C. Boone, H. Bussey, and B. J. Andrews. Exploring genetic interactions and networks with yeast. Nature Reviews Genetics, 8:437–449, 2007.PubMedCrossRefGoogle Scholar
  15. 15.
    S. Bornholdt and H. Ebel. World-wide web scaling exponent from Simon’s 1955 model. Physical Review E, 64:046401, 2001.Google Scholar
  16. 16.
    A. Brandstadt, L. Van Bang, and J. P. Spinrad. Graph classes: a survey. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, PA 19104-2688, 1999.Google Scholar
  17. 17.
    A Chatr-aryamontri, A Ceol, D Peluso, A Nardozza, S Panni, F Sacco, M Tinti, A Smolyar, L Castagnoli, M Vidal, ME Cusick, and G Cesareni. Virusmint: a viral protein interaction database. Nucleic Acids Res, 37:D669–D673, 2009.Google Scholar
  18. 18.
    HN Chua, WK Sung, and L Wong. Exploiting indirect neighbours and topological weight to predict protein function from protein-protein interactions. Bioinformatics, 22:1623–1630, 2006.Google Scholar
  19. 19.
    S.R. Collins, P. Kemmeren, X.-C. Zhao, J.F. Greenblatt, F. Spencer, F.C.P. Holstege, J.S. Weissman, and N.J. Krogan. Toward a comprehensive atlas of the phyisical interactome of saccharomyces cerevisiae. Mol. Cell Proteomics, 6(3):439–450, 2007.PubMedGoogle Scholar
  20. 20.
    S.R. Collins, M. Schuldiner, N.J. Krogan, and J.S. Weissman. A strategy for extracting and analyzing large-scale quantitative epistatic interaction data. Genome Biology, 7:R63, 2006.PubMedCrossRefGoogle Scholar
  21. 21.
    S. Coulomb, M. Bauer, D. Bernard, and M.-C. Marsolier-Kergoat. Gene essentiality and the topology of protein interaction networks. Proc. Roy. Soc. B., 272:1721–1725, 2005.CrossRefGoogle Scholar
  22. 22.
    E. de Silva and M.P.H. Stumpf. Complex networks and simple models in biology. Roy. Soc. Interface, 2:419–430, 2005.CrossRefGoogle Scholar
  23. 23.
    E. de Silva, T. Thorne, P. Ingram, I. Agrafioti, J. Swire, C. Wiuf, and M.P.H. Stumpf. The effects of incomplete protein interaction data on structural and evolutionary inferences. BMC Biology, 4(39):1–13, 2006.Google Scholar
  24. 24.
    P. Erdös and A. Rényi. On random graphs. Publicationes Mathematicae, 6:290–297, 1959.Google Scholar
  25. 25.
    E. Estrada and J. A. Rodríguez-Velázquez. Subgraph centrality in complex networks. Phys Rev E Stat Nonlin Soft Matter Phys, 71(5 Pt 2), 2005.Google Scholar
  26. 26.
    C. Guerrero et al. Characterization of the proteasome interaction network using a qtax-based tag-team strategy and protein interaction network analysis. PNAS, 105:13333–13338, 2008.PubMedCrossRefGoogle Scholar
  27. 27.
    J-D J. Han et al. Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature, 430, 2004.Google Scholar
  28. 28.
    K. I. Goh et al. The human disease network. PNAS, 104:8685–8690, 2007.PubMedCrossRefGoogle Scholar
  29. 29.
    K.C. Gunsalus et al. Predictive models of molecular machines involved in caenorhadbitis elegans early embryogenesis. Nature, 436:861–865, 2005.PubMedCrossRefGoogle Scholar
  30. 30.
    L.V. Zhang et al. Motifs, themes and thematic maps of an integrated saccharomyces cerevisiae interaction network. J. Biol., 4(6), 2005.Google Scholar
  31. 31.
    M. A. Yildirim et al. Drug-target network. Nature Biotechnology, 25:1119–1126, 2007.PubMedCrossRefGoogle Scholar
  32. 32.
    M. E. Cusick et al. Literature-curated protein interaction datasets. Nature Methods, 6:39–46, 2009.PubMedCrossRefGoogle Scholar
  33. 33.
    N. Bertin et al. Confirmation of organized modularity in the yeast interactome. PLoS Biology, 5:e153, 2007.PubMedCrossRefGoogle Scholar
  34. 34.
    N. Bertin et al. Still stratus not altocumulus: Further evidence against the date/party hub distinction. PLoS Biology, 5:e154, 2007.CrossRefGoogle Scholar
  35. 35.
    N. N. Batada et al. Stratus not altocumulus: a new view of the yeast protein interaction network. PLoS Biology, 4:e317, 2006.PubMedCrossRefGoogle Scholar
  36. 36.
    P. Kammeren et al. Protein interaction verification and functional annotation by integrated analysis of genome-scale data. Mol. Cell, 9:1133–1143, 2002.CrossRefGoogle Scholar
  37. 37.
    S. L. Wong et al. Combining biological networks to predict genetic interactions. Proc. Natl. Acad. Sci. USA, 101:15682–15687, 2004.PubMedCrossRefGoogle Scholar
  38. 38.
    T. Reguly et al. Comprehensive curation and analysis of global interaction networks in saccharomyces cerevisiae. Journal of Biology, 5:11, 2006.PubMedCrossRefGoogle Scholar
  39. 39.
    S. Fields. High-throughput two-hybrid analysis. the promise and the peril. FEBS J., 272:5391–5399, 2005.Google Scholar
  40. 40.
    J. Flannick, A. Novak, S.S. Balaji, H.M. Harley, and S. Batzglou. Graemlin general and robust alignment of multiple large interaction networks. Genome Res, 16(9):1169–1181, 2006.PubMedCrossRefGoogle Scholar
  41. 41.
    J. Flannick, A. F. Novak, C. B. Do, B. S. Srinivasan, and S. Batzoglou. Automatic parameter learning for multiple network alignment. In RECOMB, pages 214–231, 2008.Google Scholar
  42. 42.
    AK Ganesan, H Ho, B Bodemann, S Petersen, J Aruri, S Koshy, Z Richardson, LQ Le, T Krasieva, MG Roth, P Farmer, and MA White. Genome-wide siRNA-based functional genomics of pigmentation identifies novel genes and pathways that impact melanogenesis in human cells. PLoS Genet, 4(12):e1000298, 2008.Google Scholar
  43. 43.
    M. R. Garey and D. S. Johnson. Computers and Intractability–A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York, 1979.Google Scholar
  44. 44.
    A. C. Gavin, M. Bosche, R. Krause, P. Grandi, M. Marzioch, A. Bauer, J. Schultz, J. M. Rick, A. M. Michon, C. M. Cruciat, M. Remor, C. Hofert, M. Schelder, M. Brajenovic, H. Ruffner, A. Merino, K. Klein, M. Hudak, D. Dickson, T. Rudi, V. Gnau, A. Bauch, S. Bastuck, B. Huhse, C. Leutwein, M. A. Heurtier, R. R. Copley, A. Edelmann, E. Querfurth, V. Rybin, G. Drewes, M. Raida, T. Bouwmeester, P. Bork, B. Seraphin, B. Kuster, G. Neubauer, and G. Superti-Furga. Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature, 415(6868):141–147, 2002.PubMedCrossRefGoogle Scholar
  45. 45.
    AC Gavin, P Aloy, P Grandi, R Krause, M Boesche, M Marzioch, C Rau, LJ Jensen, S Bastuck, B Dumpelfeld, A Edelmann, MA Heurtier, V Hoffman, C Hoefert, K Klein, M Hudak, AM Michon, M Schelder, M Schirle, M Remor, T Rudi, S Hooper, A Bauer, T Bouwmeester, G Casari, G Drewes, G Neubauer, JM Rick, B Kuster, P Bork, RB Russell, and G Superti-Furga. Proteome survey reveals modularity of the yeast cell machinery. Nature, 440(7084):631–636, 2006.PubMedCrossRefGoogle Scholar
  46. 46.
    L Giot, JS Bader, C Brouwer, A Chaudhuri, B Kuang, Y Li, YL Hao, CE Ooi, B Godwin, E Vitols, G Vijayadamodar, P Pochart, H Machineni, M Welsh, Y Kong, B Zerhusen, R Malcolm, Z Varrone, A Collis, M Minto, S. Burgess, L McDaniel, E Stimpson, F Spriggs, J Williams, K. Neurath, N Ioime, M Agee, E Voss, K Furtak, R Renzulli, N Aanensen, S Carrolla, E Bickelhaupt, Y Lazovatsky, A DaSilva, J Zhong, CA Stanyon, RL Jr Finley, KP White, M Braverman, T Jarvie, S Gold, M Leach, J Knight, RA Shimkets, MP McKenna, J Chant, and JM Rothberg. A protein interaction map of drosophila melanogaster. Science, 302(5651):1727–1736, 2003.Google Scholar
  47. 47.
    K.-I. Goh, B. Kahng, and D. Kim. Hybrid network model: the protein and the protein family interaction networks. arXiv:q-bio.MN/0312009 v2, 28 March 2004, 2004.Google Scholar
  48. 48.
    L. Hakes, J.W. Pinney, D. L. Robertson, and S. C. Lovell. Protein-protein interaction networks and biology–what’s the connection? Nature Biotechnology, 26(1):69–72, 2008.PubMedCrossRefGoogle Scholar
  49. 49.
    J. D. H. Han, D. Dupuy, N. Bertin, M. E. Cusick, and Vidal. M. Effect of sampling on topology predictions of protein-protein interaction networks. Nature Biotechnology, 23:839–844, 2005.Google Scholar
  50. 50.
    Christopher T. Harbison, D. Benjamin Gordon, Tong I. Lee, Nicola J. Rinaldi, Kenzie D. Macisaac, Timothy W. Danford, Nancy M. Hannett, Jean-Bosco Tagne, David B. Reynolds, Jane Yoo, Ezra G. Jennings, Julia Zeitlinger, Dmitry K. Pokholok, Manolis Kellis, P. Alex Rolfe, Ken T. Takusagawa, Eric S. Lander, David K. Gifford, Ernest Fraenkel, and Richard A. Young. Transcriptional regulatory code of a eukaryotic genome. Nature, 431(7004):99–104, 2004.Google Scholar
  51. 51.
    D.J. Higham, M. Rašajski, and N. Pržulj. Fitting a geometric graph to a protein-protein interaction network. Bioinformatics, 24(8):1093–1099, 2008.PubMedCrossRefGoogle Scholar
  52. 52.
    H. Hishigaki, K. Nakai, T. Ono, A. Tanigami, and T. Takagi. Assessment of prediction accuracy of protein function from protein-protein interaction data. Yeast, 18:523–531, 2001.PubMedCrossRefGoogle Scholar
  53. 53.
    Y. Ho, A. Gruhler, A. Heilbut, G. D. Bader, L. Moore, S. L. Adams, A. Millar, P. Taylor, K. Bennett, K. Boutilier, L. Yang, C. Wolting, I. Donaldson, S. Schandorff, J. Shewnarane, M. Vo, J. Taggart, M. Goudreault, B. Muskat, C. Alfarano, D. Dewar, Z. Lin, K. Michalickova, A. R. Willems, H. Sassi, P. A. Nielsen, K. J. Rasmussen, J. R. Andersen, L. E. Johansen, L. H. Hansen, H. Jespersen, A. Podtelejnikov, E. Nielsen, J. Crawford, V. Poulsen, B. D. Sorensen, J. Matthiesen, R. C. Hendrickson, F. Gleeson, T. Pawson, M. F. Moran, D. Durocher, M. Mann, C. W. Hogue, D. Figeys, and M. Tyers. Systematic identification of protein complexes in saccharomyces cerevisiae by mass spectrometry. Nature, 415(6868):180–183, 2002.PubMedCrossRefGoogle Scholar
  54. 54.
    A. L. Hopkins and C. R. Groom. The druggable genome. Nature Reviews Drug Discovery, 1:727–730, 2002.PubMedCrossRefGoogle Scholar
  55. 55.
    T. Ito, K. Tashiro, S. Muta, R. Ozawa, T. Chiba, M. Nishizawa, K. Yamamoto, S. Kuhara, and Y. Sakaki. Toward a protein-protein interaction map of the budding yeast: A comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. Proc Natl Acad Sci U S A, 97(3):1143–1147, 2000.PubMedCrossRefGoogle Scholar
  56. 56.
    S. Itzkovitz, R. Levitt, N. Kashtan, R. Milo, M. Itzkovitz, and U. Alon. Coarse graining and self-dissimilarity of complex networks. Physical Review E, 71:016127, 2005.CrossRefGoogle Scholar
  57. 57.
    H. Jeong, S. P. Mason, A.-L. Barabási, and Z. N. Oltvai. Lethality and centrality in protein networks. Nature, 411(6833):41–42, 2001.PubMedCrossRefGoogle Scholar
  58. 58.
    H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási. The large-scale organization of metabolic networks. Nature, 407(6804):651–654, 2000.PubMedCrossRefGoogle Scholar
  59. 59.
    P. F. Jonsson and P. A. Bates. Lobal topological features of cancer proteins in the human interactome. Bioinformatics, 22:2291–2297, 2006.PubMedCrossRefGoogle Scholar
  60. 60.
    S. Kaplan, A. Bren, E. Dekel, and U Alon. The incoherent feed-forward loop can generate non-monotonic input functions for genes. Molecular Systems Biology, 4:203, 2008.Google Scholar
  61. 61.
    S. Kaplan, A. Bren, A. Zaslaver, E. Dekel, and U. Alon. Diverse two-dimensional input functions control bacterial sugar genes. Molecular Cell, 29:786–792, 2008.PubMedCrossRefGoogle Scholar
  62. 62.
    E. F. Keller. Revisiting scale-free networks. BioEssays, 27:11060–11068, 2005.Google Scholar
  63. 63.
    B. P. Kelley, Y. Bingbing, F. Lewitter, R. Sharan, B. R. Stockwell, and T. Ideker. PathBLAST: a tool for alignment of protein interaction networks. Nucl. Acids Res., 32:83–88, 2004.CrossRefGoogle Scholar
  64. 64.
    R. Kelley and T. Ideker. Systematic interpretation of genetic interactions using protein networks. Nature Biotechnology, 23:561–566, 2005.PubMedCrossRefGoogle Scholar
  65. 65.
    A. D. King, Pržulj, N., and I. Jurisica. Protein complex prediction via cost-based clustering. Bioinformatics, 20(17):3013–3020, 2004.Google Scholar
  66. 66.
    M. Koyutürk, Y. Kim, U. Topkara, S. Subramaniam, W. Szpankowski, and A. Grama. Pairwise alignment of protein interaction networks, 2006.Google Scholar
  67. 67.
    NJ Krogan, G Cagney, H Yu, G Zhong, X Guo, A Ignatchenko, J Li, S Pu, N Datta, AP Tikuisis, T Punna, JM Peregrn-Alvarez, M Shales, X Zhang, M Davey, MD Robinson, A Paccanaro, JE Bray, A Sheung, B Beattie, DP Richards, V Canadien, A Lalev, F Mena, P Wong, A Starostine, MM Canete, J Vlasblom, S Wu, C Orsi, SR Collins, S Chandran, R Haw, JJ Rilstone, K Gandi, NJ Thompson, G Musso, P St Onge, S Ghanny, MH Lam, G Butland, AM Altaf-Ul, S Kanaya, A Shilatifard, E O’Shea, JS Weissman, CJ Ingles, TR Hughes, J Parkinson, M Gerstein, SJ Wodak, A Emili, and JF Greenblatt. Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature, 440:637–643, 2006.Google Scholar
  68. 68.
    O. Kuchaiev, T. Milenkovic, V. Memisevic, W. Hayes, and N. Pržulj. Topological network alignment uncovers biological function and phylogeny. Journal of the Royal Society Interface, 2010.Google Scholar
  69. 69.
    O. Kuchaiev and N. Pržulj. Learning the structure of protein-protein interaction networks. 2009 Pacific Symposium on Biocomputing (PSB), 2009.Google Scholar
  70. 70.
    O. Kuchaiev, M. Rasajski, D. Higham, and N. Pržulj. Geometric de-noising of protein-protein interaction networks. PLoS Computational Biology, 5:e1000454, 2009.PubMedCrossRefGoogle Scholar
  71. 71.
    Harold W. Kuhn. The hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2:83–97, 1955.CrossRefGoogle Scholar
  72. 72.
    Douglas J. LaCount, Marissa Vignali, Rakesh Chettier, Amit Phansalkar, Russell Bell, Jay R. Hesselberth, Lori W. Schoenfeld, Irene Ota, Sudhir Sahasrabudhe, Cornelia Kurschner, Stanley Fields, and Robert E. Hughes. A protein interaction network of the malaria parasite plasmodium falciparum. Nature, 438:103–107, 2005.PubMedCrossRefGoogle Scholar
  73. 73.
    M. Lappe and L. Holm. Unraveling protein interaction networks with near-optimal efficiency. Nature Biotechnology, 22(1):98–103, 2004.PubMedCrossRefGoogle Scholar
  74. 74.
    L. Li, D. Alderson, R. Tanaka, J. C. Doyle, and W. Willinger. Towards a theory of scale-free graphs: definition, properties, and implications (extended version). arXiv:cond-mat/0501169, 2005.Google Scholar
  75. 75.
    S Li, CM Armstrong, N Bertin, H Ge, S Milstein, M Boxem, P-O Vidalain, J-DJ Han, A Chesneau, T Hao, N Goldberg, DS Li, M Martinez, J-F Rual, P Lamesch, L Xu, M Tewari, SL Wong, LV Zhang, GF Berriz, L Jacotot, P Vaglio, J Reboul, T Hirozane-Kishikawa, Q Li, HW Gabel, A Elewa, B Baumgartner, DJ Rose, H Yu, S Bosak, R Sequerra, A Fraser, SE Mango, WM Saxton, S Strome, S van den Heuvel, F Piano, J Vandenhaute, C Sardet, M Gerstein, L Doucette-Stamm, KC Gunsalus, JW Harper, ME Cusick, FP Roth, DE Hill, and M Vidal. A map of the interactome network of the metazoan c. elegans. Science, 303: 540–543, 2004.Google Scholar
  76. 76.
    Zhi Liang, Meng Xu, Maikun Teng, and Liwen Niu. NetAlign: a web-based tool for comparison of protein interaction networks. Bioinformatics, 22(17):2175–2177, 2006.PubMedCrossRefGoogle Scholar
  77. 77.
    Chung-Shou Liao, Kanghao Lu, Michael Baym, Rohit Singh, and Bonnie Berger. Isorankn: spectral methods for global alignment of multiple protein networks. Bioinformatics, 25(12):i253–258, 2009.PubMedCrossRefGoogle Scholar
  78. 78.
    L.J. Lu, Y. Xia, A. Paccanaro, H. Yu, and M. Gerstein. Assessing the limits of genomic data integration for predicting protein networks. Genome Res., 15:945–953, 2005.PubMedCrossRefGoogle Scholar
  79. 79.
    V. Memisević, T. Milenković, and N. Pržulj. Complementarity of network and sequence information in homologous proteins. Journal of Integrative Bioinformatics, 7(3):135, 2010.Google Scholar
  80. 80.
    V. Memisević, T. Milenković, and N. Pržulj. An integrative approach to modeling biological networks. Journal of Integrative Bioinformatics, 7(3):120, 2010.Google Scholar
  81. 81.
    T. Milenković, J. Lai, and N. Pržulj. Graphcrunch: a tool for large network analyses. BMC Bioinformatics, 9(70), 2008.Google Scholar
  82. 82.
    T. Milenković, V. Memisević, A. K. Ganesan, and N. Pržulj. Systems-level cancer gene identification from protein interaction network topology applied to melanogenesis-related interaction networks. Journal of the Royal Society Interface, doi:10.1098/rsif.2009.0192, 2009.Google Scholar
  83. 83.
    T. Milenković and N. Pržulj. Uncovering biological network function via graphlet degree signatures. Cancer Informatics, 6:257–273, 2008.PubMedGoogle Scholar
  84. 84.
    Tijana Milenkovic, Weng Leong Ng, Wayne Hayes, and Nataša Pržulj. Optimal network alignment with graphlet degree vectors. Cancer Informatics, 9:121–137, 2010.Google Scholar
  85. 85.
    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, 303:1538–1542, 2004.PubMedCrossRefGoogle Scholar
  86. 86.
    R. Milo, S. 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.PubMedCrossRefGoogle Scholar
  87. 87.
    M. Molloy and B. Reed. A critical point of random graphs with a given degree sequence. Random Structures and Algorithms, 6:161–180, 1995.CrossRefGoogle Scholar
  88. 88.
    M. Molloy and B. Reed. The size of the largest component of a random graph on a fixed degree sequence. Combinatorics, Probability and Computing, 7:295–306, 1998.Google Scholar
  89. 89.
    E Nabieva, K Jim, A Agarwal, B Chazelle, and M Singh. Whole-proteome prediction of protein function via graph-theoretic analysis of interaction maps. Bioinformatics, 21: i302–i310, 2005.Google Scholar
  90. 90.
    M. E. J. Newman. The structure and function of complex networks. SIAM Review, 45(2): 167–256, 2003.CrossRefGoogle Scholar
  91. 91.
    M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64:026118–1, 2001.CrossRefGoogle Scholar
  92. 92.
    M. E. J. Newman and D. J. Watts. Renormalization group analysis in the small-world network model. Physics Letters A, 263:341–346, 1999.CrossRefGoogle Scholar
  93. 93.
    M. E. J. Newman and D. J. Watts. Scaling and percolation in the small-world network model. Physical Review E, 60:7332–7342, 1999.CrossRefGoogle Scholar
  94. 94.
    S.R. Paladugu, S. Zhao, A. Ray, and A. Raval. Mining protein networks for synthetic genetic interactions. BMC Bioinformatics, 9(426), 2008.Google Scholar
  95. 95.
    Jodi R Parrish, Jingkai Yu, Guozhen Liu, Julie A Hines, Jason E Chan, Bernie A Mangiola, Huamei Zhang, Svetlana Pacifico, Farshad Fotouhi, Victor J DiRita, Trey Ideker, Phillip Andrews, and Russell L Finley Jr. A proteome-wide protein interaction map for campylobacter jejuni. Genome Biology, 8:R130, 2007.Google Scholar
  96. 96.
    R. Pastor-Satorras, E. Smith, and R. V. Sole. Evolving protein interaction networks through gene duplication. Journal of Theoretical Biology, 222:199–210, 2003.PubMedCrossRefGoogle Scholar
  97. 97.
    M. Penrose. Geometric Random Graphs. Oxford Univeristy Press, 2003.Google Scholar
  98. 98.
    Dmitry K. Pokholok, Christopher T. Harbison, Stuart Levine, Megan Cole, Nancy M. Hannett, Tong Ihn Lee, George W. Bell, Kimberly Walker, P. Alex Rolfe, Elizabeth Herbolsheimer, Julia Zeitlinger, Fran Lewitter, David K. Gifford, and Richard A. Young. Geome-wide map of nucleosome acetylation and metylation in yeast. Cell, 122:517–527, 2005.Google Scholar
  99. 99.
    N. Pržulj. Biological network comparison using graphlet degree distribution. Bioinformatics, 23:e177–e183, 2007.PubMedCrossRefGoogle Scholar
  100. 100.
    N. Pržulj, D. G. Corneil, and I. Jurisica. Modeling interactome: Scale-free or geometric? Bioinformatics, 20(18):3508–3515, 2004.PubMedCrossRefGoogle Scholar
  101. 101.
    N. Pržulj, D. G. Corneil, and I. Jurisica. Efficient estimation of graphlet frequency distributions in protein-protein interaction networks. Bioinformatics, 22(8):974–980, 2006. doi:10.1093/bioinformatics/btl030.PubMedCrossRefGoogle Scholar
  102. 102.
    N. Pržulj and D. J. Higham. Modelling protein-protein interaction networks via a stickiness index. Journal of the Royal Society Interface, 3(10):711–716, 2006.CrossRefGoogle Scholar
  103. 103.
    N. Pržulj, O. Kuchaiev, A. Stevanovic, and W. Hayes. Geometric evolutionary dynamics of protein interaction networks. 2010 Pacific Symposium on Biocomputing (PSB), 2010.Google Scholar
  104. 104.
    N. Pržulj, D. Wigle, and I. Jurisica. Functional topology in a network of protein interactions. Bioinformatics, 20(3):340–348, 2004.PubMedCrossRefGoogle Scholar
  105. 105.
    P. Radivojac, K. Peng, W. T. Clark, B. J. Peters, A. Mohan, S. M. Boyle, and Mooney S. D. An integrated approach to inferring gene-disease associations in humans. Proteins, 72(3):1030–1037, 2008.Google Scholar
  106. 106.
    J.-D. Rain, L. Selig, H. De Reuse, V. Battaglia, C. Reverdy, S. Simon, G. Lenzen, F. Petel, J. Wojcik, V. Schachter, Y. Chemama, A. Labigne, and P. Legrain. The protein-protein interaction map of helicobacter pylori. Nature, 409:211–215, 2001.PubMedCrossRefGoogle Scholar
  107. 107.
    O. Ratmann, C. Wiuf, and J. W. Pinney. From evidence to inference: probing the evolution of protein interaction networks. HFSP Journal, 2009. Published online 19 October 2009.Google Scholar
  108. 108.
    J.-F. Rual, K. Venkatesan, T. Hao, T. Hirozane-Kishikawa, A. Dricot, N. Li, G. F. Berriz, F. D. Gibbons, M. Dreze, N. Ayivi-Guedehoussou, N. Klitgord, C. Simon, M. Boxem, S. Milstein, J. Rosenberg, D. S. Goldberg, L. V. Zhang, S. L. Wong, G. Franklin, S. Li, J. S. Albala, J. Lim, C. Fraughton, E. Llamosas, S. Cevik, C. Bex, P. Lamesch, R. S. Sikorski, J. Vandenhaute, H. Y. Zoghbi, A. Smolyar, S. Bosak, R. Sequerra, L. Doucette-Stamm, M. E. Cusick, D. E. Hill, F. P. Roth, and M. Vidal. Towards a proteome-scale map of the human protein-protein interaction network. Nature, 437:1173–78, 2005.PubMedCrossRefGoogle Scholar
  109. 109.
    M.P. Samanta and S. Liang. Predicting protein functions from redundancies in large-scale protein interaction networks. PNAS, 100:12579–12583, 2003.PubMedCrossRefGoogle Scholar
  110. 110.
    A.S. Schwartz, J. Yu, K.R. Gardenour, Finley R.L. Jr., and T. Ideker. Cost-effective strategies for completing the interactome. Nature Methods, 6(1):55–61, 2009.Google Scholar
  111. 111.
    B. Schwikowski, P. Uetz, and A. Fields. A network of protein-protein interactions in yeast. Nature Biotechnology, 18:1257–1261, 2000.PubMedCrossRefGoogle Scholar
  112. 112.
    R. Sharan, T. Ideker, B. P. Kelley, R. Shamir, and R. M. Karp. Identification of protein complexes by comparative analysis of yeast and bacterial protein interaction data. In Proceedings of the eighth annual international conference on Computational molecular biology (RECOMB’04), 2004.Google Scholar
  113. 113.
    R. Sharan, I. Ulitsky, and R. Shamir. Network-based prediction of protein function. Molecular Systems Biology, 3(88):1–13, 2007.Google Scholar
  114. 114.
    Roded Sharan and Trey Ideker. Modeling cellular machinery through biological network comparison. Nature Biotechnology, 24(4):427–433, Apr 2006.PubMedCrossRefGoogle Scholar
  115. 115.
    Roded Sharan and Trey Ideker. Protein networks in disease. Genome Research, 18:644–652, 2008.PubMedCrossRefGoogle Scholar
  116. 116.
    Roded Sharan, Silpa Suthram, Ryan M. Kelley, Tanja Kuhn, Scott McCuine, Peter Uetz, Taylor Sittler, Richard M. Karp, and Trey Ideker. Conserved patterns of protein interaction in multiple species. Proceedings of the National Academy of Sciences of the United States of America, 102(6):1974–1979, 2005.PubMedCrossRefGoogle Scholar
  117. 117.
    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.PubMedCrossRefGoogle Scholar
  118. 118.
    H. A. Simon. On a class of skew distribution functions. Biometrika, 42:425–440, 1955.Google Scholar
  119. 119.
    Nicolas Simonis, Jean-Francois Rual, Anne-Ruxandra Carvunis, Murat Tasan, Irma Lemmens, Tomoko Hirozane-Kishikawa, Tong Hao, Julie M. Sahalie, Kavitha Venkatesan, Fana Gebreab, Sebiha Cevik, Niels Klitgord, Changyu Fan, Pascal Braun, Ning Li, Nono Ayivi-Guedehoussou, Elizabeth Dann, Nicolas Bertin, David Szeto, Ameli Dricot, Muhammed A. Yildirim, Chenwei Lin, Anne-Sophie De Smet, Huey-Ling Kao, Christophe Simon, Alex Smolyar, Jin Sook Ahn, Muneesh Tewari, Mike Boxem amd Stuart Milstein, Haiyuan Yu, Matija Dreze, Jean Vandenhaute, Kristin C. Gunsalus, Michael E. Cusick, David E. Hill, Jan Tavernier, Frederick P. Roth, and Marc Vidal. Empirically controlled mapping of the caenorhabditis elegans protein-protein interactome network. Nature Methods, 6(1):47–54, 2009.Google Scholar
  120. 120.
    R. Singh, J. Xu, and B. Berger. Pairwise global alignment of protein interaction networks by matching neighborhood topology. In Research in Computational Molecular Biology, pages 16–31. Springer, 2007.Google Scholar
  121. 121.
    R. Singh, J. Xu, and B. Berger. Global alignment of multiple protein interaction networks. Proceedings of Pacific Symposium on Biocomputing 13, pages 303–314, 2008.Google Scholar
  122. 122.
    C. Song, S. Havlin, and H. A. Makse. Self-similarity of complex networks. Nature, 433: 392–395, 2005.PubMedCrossRefGoogle Scholar
  123. 123.
    U. Stelzl, U. Worm, M. Lalowski, C. Haenig, F.H. Brembeck, H. Goehler, M. Stroedicke, M. Zenkner, A. Schoenherr, S. Koeppen, J. Timm, S. Mintzlaff, C. Abraham, N. Bock, S. Kietzmann, A. Goedde, E. Toksoz, A. Droege, S. Krobitsch, B. Korn, W. Birchmeier, H. Lehrach, and E.E. Wanker. A human protein-protein interaction network: A resource for annotating the proteome. Cell, 122:957–968, 2005.PubMedCrossRefGoogle Scholar
  124. 124.
    M. P. H. Stumpf, C. Wiuf, and R. M. May. Subnets of scale-free networks are not scale-free: Sampling properties of networks. Proceedings of the National Academy of Sciences, 102:4221–4224, 2005.CrossRefGoogle Scholar
  125. 125.
    S. Suthram, T. Sittler, and T. Ideker. The plasmodium protein network diverges from those of other eukaryotes. Nature, 438:108112, 2005.CrossRefGoogle Scholar
  126. 126.
    R. Tanaka. Scale-rich metabolic networks. Physical Review Letters, 94:168101, 2005.PubMedCrossRefGoogle Scholar
  127. 127.
    A. H. Y. Tong, G. Lesage, G. D. Bader, H. Ding, H. Xu, X. Xin, J. Young, G. F. Berriz, R. L. Brost, M. Chang, Y. Chen, X. Cheng, G. Chua, H. Friesen, D. S. Goldberg, J. Haynes, C. Humphries, G. He, S. Hussein, L. Ke, N. Krogan, Z. Li, J. N. Levinson, H. Lu, P. Menard, C. Munyana, A. B. Parsons, O. Ryan, R. Tonikian, T. Roberts, A.-M. Sdicu, J. Shapiro, B. Sheikh, B. Suter, S. L. Wong, L. V. Zhang, H. Zhu, C. G. Burd, S. Munro, C. Sander, J. Rine, J. Greenblatt, M. Peter, A. Bretscher, G. Bell, F. P. Roth, G. W. Brown, B. Andrews, H. Bussey, and Charles Boone. Global mapping of the yeast genetic interaction network. Science, 303:808–813, 2004.Google Scholar
  128. 128.
    P. Uetz, L. Giot, G. Cagney, T. A. Mansfield, R. S. Judson, J. R. Knight, E. Lockshon, V. Narayan, M. Srinivasan, P. Pochart, A. Qureshi-Emili, Y. Li, B. Godwin, D. Conover, T. Kalbfleish, G. Vijayadamodar, M. Yang, M. Johnston, S. Fields, and J. M. Rothberg. A comprehensive analysis of protein-protein interactions in saccharomyces cerevisiae. Nature, 403:623–627, 2000.PubMedCrossRefGoogle Scholar
  129. 129.
    Peter Uetz, Yu-An Dong, Christine Zeretzke, Christine Atzler, Armin Baiker, Bonnie Berger, Seesandra Rajagopala, Maria Roupelieva, Dietlind Rose, Even Fossum, and Jrgen Haas. Herpesviral protein networks and their interaction with the human proteome. Science, 311:239–242, 2006.PubMedCrossRefGoogle Scholar
  130. 130.
    O. Vanunu, O. Magger, E. Ruppin, T. Shlomi, and R. Sharan. Associating genes and protein complexes with disease via network propagation. PLoS Computational Biology, 6:e1000641, 2010.PubMedCrossRefGoogle Scholar
  131. 131.
    A. Vazquez, A. Flammini, A. Maritan, and A. Vespignani. Modeling of protein interaction networks. ComPlexUs, 1:38–44, 2001.Google Scholar
  132. 132.
    A. Vazquez, A. Flammini, A. Maritan, and A. Vespignani. Global protein function prediction from protein-protein interacton networks. Nature Biotechnology, 21:697–700, 2003.PubMedCrossRefGoogle Scholar
  133. 133.
    K. et al. Venkatesan. An empirical framework for binary interactome mapping. Nature Methods, 6(1):83–90, 2009.Google Scholar
  134. 134.
    Albrecht von Brunn1, Carola Teepe, Jeremy C. Simpson, Rainer Pepperkok, Caroline C. Friedel, Ralf Zimmer, Rhonda Roberts, Ralph Baric, and Jurgen Haas. Analysis of intraviral protein-protein interactions of the sars coronavirus orfeome. PLoS ONE, 2:e459, 2007.Google Scholar
  135. 135.
    C. von Mering, R. Krause, B. Snel, M. Cornell, S. G. Oliver, S. Fields, and P. Bork. Comparative assessment of large-scale data sets of protein-protein interactions. Nature, 417(6887):399–403, 2002.CrossRefGoogle Scholar
  136. 136.
    S. Wachi, K. Yoneda, and R. Wu. Interactome-transcriptome analysis reveals the high centrality of genes differentially expressed in lung cancer tissues. Bioinformatics, 21: 4205–4208, 2005.PubMedCrossRefGoogle Scholar
  137. 137.
    A. Wagner. How the global structure of protein interaction networks evolves. Proceedings of The Royal Society of London. Series B, Biological Sciences, 270:457–466, 2003.Google Scholar
  138. 138.
    D. J. Watts and S. H. Strogatz. Collective dynamics of ‘small-world’ networks. Nature, 393:440–442, 1998.PubMedCrossRefGoogle Scholar
  139. 139.
    D. B. West. Introduction to Graph Theory. Prentice Hall, Upper Saddle River, NJ., 2nd edition, 2001.Google Scholar
  140. 140.
    D. S. Wishart, C. Knox, A. C. Guo, S. Shrivastava, M. Hassanali, P. Stothard, Z. Chang, and J. Woolsey. Drugbank: a comprehensive resource for in silico drug discovery and exploration. Nucleic Acids Research, 34:D668–D672, 2006.PubMedCrossRefGoogle Scholar
  141. 141.
    SJ Wodak, S Pu, J Vlasblom, and B Seraphin. Challenges and rewards of interaction proteomics. Mol. Cell Proteomics, 8(1):3–18, 2009.PubMedCrossRefGoogle Scholar
  142. 142.
    I. Xenarios, L. Salwinski, X. J. Duan, P. Higney, S. M. Kim, and Eisenberg D. DIP, the Database of Interacting Proteins: a research tool for studying cellular networks of protein interactions. Nucleic Acids Research, 30(1):303–305, 2002.Google Scholar
  143. 143.
    E Yeger-Lotem, S Sattath, N Kashtan, S Itzkovitz, R Milo, RY Pinter, U Alon, and H Margalit. Network motifs in integrated cellular networks of transcription-regulation and protein-protein interaction. Proc Natl Acad Sci U S A, 101(16):5934–5939, April 2004.PubMedCrossRefGoogle Scholar
  144. 144.
    H. et al. Yu. High-quality binary protein interaction map of the yeast interactome networks. Science, 322:104–110, 2008.Google Scholar
  145. 145.
    M. Zaslavskiy, F. Bach, and J. P. Vert. Global alignment of protein-protein interaction networks by graph matching methods. Bioinformatics, 25(12):i259–i267, 2009.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Imperial College LondonLondonUK

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