Exploring statistical and population aspects of network complexity

PLoS ONE

Volumn 7, Issue 5, 2012, Pages

  Emmert Streib, Frank ^a,b   Dehmer, Matthias ^c  

^a QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

^c UNIVERSITY FOR HEALTH SCIENCES   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CLASSIFICATION; CONTROLLED STUDY; INTERMETHOD COMPARISON; MATHEMATICAL MODEL; NETWORK DIVERSITY SCORE; NETWORK LEARNING; POPULATION DYNAMICS; PROBABILITY; PROCESS DEVELOPMENT; QUANTITATIVE ANALYSIS; SCORING SYSTEM; STRUCTURE ANALYSIS; VALIDATION PROCESS; THEORETICAL MODEL;

MODELS, THEORETICAL;

EID: 84860700562     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0034523     Document Type: Article

References (98)

1. Bar-Yam Y, (1997) Dynamics of Complex Systems. Perseus Books.
2. Chaitin G, (1966) On the length of programs for computing finite binary sequences. Journal of the ACM pp. 547-569.
3. Kolmogorov AN, (1965) Three approaches to the quantitative definition of 'information'. Problems of Information Transmission 1: 1-7.
4. López-Ruiza R, Mancinib H, Calbet X, (1995) A statistical measure of complexity. Physics Letters A 209: 321-326.
5. Nicolis G, Prigogine I, (1989) Exploring Complexity. Freeman.
6. Prokopenko M, Boschetti F, Ryan A, (2009) An information-theoretic primer on complexity, selforganization, and emergence. Complexity 15: 11-28.
7. Schuster H, (2002) Complex Adaptive Systems. Scator Verlag.
8. Solomonoff R, (1960) A preliminary report on a general theory of inductive inference. Technical Report V-131, Zator Co., Cambridge, Ma.
9. Wolfram S, (1983) Statistical mechanics of cellular automata. Phys Rev E 55: 601-644.
10. Badii R, Politi A, (1997) Complexity: Hierarchical Structures and Scaling in Physics. Cambridge University Press, Cambridge.
11. Bennett C, (1988) Logical depth and physical complexity. Herken R, editor, The Universal Turing Machine- a Half-Century Survey, Oxford University Press pp. 227-257.
12. Crutchfield JP, Young K, (1989) Inferring statistical complexity. Phys Rev Lett 63: 105-108.
13. Emmert-Streib F, (2010) Exploratory analysis of spatiotemporal patterns of cellular automata by clustering compressibility. Physical Review E 81: 026103.
14. Emmert-Streib F, (2010) Statistic Complexity: Combining Kolmogorov Complexity with an Ensemble Approach. PLoS ONE 5: e12256.
15. Gell-Mann M, Lloyd S, (1998) Information measures, effective complexity, and total information. Complexity 2: 44-52.
16. Grassberger P, (1986) Toward a quantitative theory of self-generated complexity. Int J Theor Phys 25: 907-938.
17. Lloyd S, Pagels H, (1988) Complexity as thermodynamic depth. Annals of Physics 188: 186-213.
18. Zurek W, eds. (1990) Complexity, Entropy and the Physics of Information. Addison-Wesley, Redwood City.
19. Grassberger P, (1989) Problems in quantifying self-generated complexity. Helvetica Physica Acta 62: 489-511.
20. Li M, Vitányi P, (1997) An Introduction to Kolmogorov Complexity and Its Applications. Springer.
21. Crutchfield J, Packard N, (1983) Symbolic dynamics of noisy chaos. Physica D 7: 201-223.
22. Bialek W, Nemenman I, Tishby N, (2001) Predictability, complexity, and learning. Neural Computation 13: 2409-2463.
23. Bonchev D, (1983) Information Theoretic Indices for Characterization of Chemical Structures. Research Studies Press, Chichester.
24. Bonchev D, Rouvray DH, (2005) Complexity in Chemistry, Biology, and Ecology. Mathematical and Computational Chemistry. Springer. New York, NY, USA.
25. Janežić D, Miležević A, Nikolić S, Trinajstić N, (2009) Topological complexity of molecules. Meyers R, editor, Encyclopedia of Complexity and System Science, Springer, volume 5 pp. 9210-9224.
26. Bertz SH, (1983) On the complexity of graphs and molecules. Bull Math Biol 45: 849-855.
27. Bonchev D, Polansky OE, (1987) On the topological complexity of chemical systems. King RB, Rouvray DH, editors, Graph Theory and Topology, Elsevier pp 125-158. Amsterdam, The Netherlands.
28. Kim J, Wilhelm T, (2008) What is a complex graph? Physica A 387: 2637-2652.
29. Dancoff SM, Quastler H, (1953) Information content and error rate of living things. Quastler H, editor, Essays on the Use of Information Theory in Biology, University of Illinois Press pp. 263-274.
30. Linshitz H, (1953) The information content of a battery cell. Quastler H, editor, Essays on the Use of Information Theory in Biology, University of Illinois Press Urbana, IL, USA.
31. Morowitz H, (1953) Some order-disorder considerations in living systems. Bull Math Biophys 17: 81-86.
32. Minoli D, (1975) Combinatorial graph complexity. Atti Accad Naz Lincei, VIII Ser, Rend, Cl Sci Fis Mat Nat 59: 651-661.
33. Bonchev D, (2003) Complexity in Chemistry. Introduction and Fundamentals. Taylor and Francis. Boca Raton, FL, USA.
34. Constantine G, (1990) Graph complexity and the laplacian matrix in blocked experiments. Linear and Multilinear Algebra 28: 49-56.
35. Jukna S, (2006) On graph complexity. Comb Probab Comput 15: 855-876.
36. Li M, Vitányi P, (1997) An Introduction to Kolmogorov Complexity and Its Applications. Springer.
37. Bonchev D, (1995) Kolmogorov's information, shannon's entropy, and topological complexity of molecules. Bulg Chem Commun 28: 567-582.
38. Dehmer M, Mowshowitz A, (2011) A history of graph entropy measures. Information Sciences 1: 57-78.
39. Dehmer M, (2008) Information processing in complex networks: Graph entropy and information functionals. Appl Math Comput 201: 82-94.
40. Skorobogatov VA, Dobrynin AA, (1988) Metrical analysis of graphs. Commun Math Comp Chem 23: 105-155.
41. Diudea MV, Gutman I, J̈antschi L, (2001) Molecular Topology. Nova Publishing. New York, NY, USA.
42. Todeschini R, Consonni V, Mannhold R, (2002) Handbook of Molecular Descriptors. Weinheim Wiley-VCH.
43. Adami C, (2002) What is complexity? BioEssays 24: 1085-1094.
44. Langton C, (1990) Computation at the edge of choas: phase transitions and emergent computation. Physica D 42: 12-37.
45. Ribeiro AS, Kauffman SA, Lloyd-Price J, Samuelsson B, Socolar JES, (2008) Mutual information in random boolean models of regulatory networks. Phys Rev E 77: 011901.
46. Newman M, (2010) Networks: An Introduction. Oxford Oxford University Press.
47. Balaban AT, (1982) Highly discriminating distance-based topological index. ChemPhysLett 89: 399-404.
48. Bonchev D, Trinajstić N, (1977) Information theory, distance matrix and molecular branching. J Chem Phys 67: 4517-4533.
49. Latora V, Marchiori M, (2001) Efficient behavior of small-world networks. Phys Rev Lett 87: 198701.
50. Latora V, MarchioriM, (2003) Economic small-world behavior in weighted networks. The European Physical Journal B Condensed Matter 32: 249-263.
51. Gutman I, (1991) Polynomials in graph theory. Bonchev D, Rouvray DH, editors, Chemical Graph Theory Introduction and Fundamentals, Abacus Press. pp133-176. New York, NY, USA.
52. Dehmer M, Emmert-Streib F, Tsoy Y, Varmuza K, (2011) Quantifying structural complexity of graphs: Information measures in mathematical chemistry. Putz M, editor, Quantum Frontiers of Atoms and Molecules, Nova Publishing pp. 479-498.
53. Gutman I, Zhou B, (2006) Laplacian energy of a graph. Linear Algebra and its Applications 414: 29-37.
54. Claussen JC, (2007) Characterization of networks by the offdiagonal complexity. Physica A 365-373: 321-354.
55. Randić M, (1975) On characterization of molecular branching. J Amer Chem Soc 97: 6609-6615.
56. Mowshowitz A, (1968) Entropy and the complexity of the graphs I: An index of the relative complexity of a graph. Bull Math Biophys 30: 175-204.
57. Wiener H, (1947) Structural determination of paraffin boiling points. Journal of the American Chemical Society 69: 17-20.
58. Rashevsky N, (1955) Life, information theory, and topology. Bull Math Biophys 17: 229-235.
59. Trucco E, (1956) A note on the information content of graphs. Bull Math Biol 18: 129-135.
60. Mowshowitz A, (1968) Entropy and the complexity of graphs II: The information content of digraphs and infinite graphs. Bull Math Biophys 30: 225-240.
61. Mowshowitz A, (1968) Entropy and the complexity of graphs III: Graphs with prescribed information content. Bull Math Biophys 30: 387-414.
62. Cormen TH, Leiserson CE, Rivest RL, (1990) Introduction to Algorithms. MIT Press.
63. Dijkstra E, (1959) A note on two problems in connection with graphs. Numerische Math 1: 269-271.
64. Balaban AT, Balaban TS, (1991) New vertex invariants and topological indices of chemical graphs based on information on distances. J Math Chem 8: 383-397.
65. Buckley F, Harary F, (1990) Distance in Graphs. Addison Wesley Publishing Company.
66. Li X, Gutman I, (2006) Mathematical Aspects of Randić-Type Molecular Structure Descriptors. Mathematical Chemistry Monographs. University of Kragujevac and Faculty of Science Kragujevac.
67. Dehmer M, Müller L, Graber A, (2010) New polynomial-based molecular descriptors with low degeneracy. PLoS ONE 5.
68. Garey MR, Johnson DS, (1979) Computers and Intractability: A Guide to the Theory of NPCompleteness. Series of Books in the Mathematical Sciences. W. H. Freeman.
69. Mowshowitz A, Mitsou V, (2009) Entropy, orbits and spectra of graphs. Dehmer M, Emmert-Streib F, editors, Analysis of Complex Networks: From Biology to Linguistics, Wiley-VCH pp. 1-22.
70. Devillers J, Balaban AT, (1999) Topological Indices and Related Descriptors in QSAR and QSPR. Gordon and Breach Science Publishers. Amsterdam, The Netherlands.
71. Sagan H, (1989) Boundary and Eigenvalue Problems in Mathematical Physics. Dover Publications.
72. Pons P, LatapyM, (2005) Computing communities in large networks using random walks. Yolum p, Güngör T, Gürgen F, Özturan C, editors, Computer and Information Sciences- ISCIS 2005, Springer Berlin/Heidelberg, volume 3733 of Lecture Notes in Computer Science pp. 284-293.
73. Van Dongen S, (2000) Graph clustering by flow simulation. Ph.D. thesis, Centers for mathematics and computer science (CWI), University of Utrecht.
74. Ziv E, Middendorf M, Wiggins CH, (2005) Information-theoretic approach to network modularity. Phys Rev E 71: 046117.
75. Chung FRK, (1997) Spectral Graph Theory. American Mathematical Society.
76. Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, et al. (2002) Network motifs: simple building blocks of complex networks. Science 298: 824-7.
77. Erdös P, Rényi A, (1959) On random graphs. I. Publicationes Mathematicae 6: 290-297.
78. Gilbert EN, (1959) Random graphs. Annals of Mathematical Statistics 20: 1141-1144.
79. Albert R, Barabasi A, (2002) Statistical mechanics of complex networks. Rev of Modern Physics 74: 47.
80. Barabási AL, Albert R, (1999) Emergence of scaling in random networks. Science 206: 509-512.
81. Feller W, (1968) An Introduction to Probability Theory and Its Applications Vol. 1. John Wiley & Sons.
82. Watts D, Strogatz S, (1998) Collective dynamics of 'small-world' networks. Nature 393: 440-442.
83. Lehman E, Casella G, (1999) Theory of point estimation. New York Springer.
84. NewmanMEJ, (2001) The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences of the United States of America 98: 404-409.
85. Newman MEJ, (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74: 036104.
86. Xenarios I, Rice DW, Salwinski L, Baron MK, Marcotte EM, et al. (2000) DIP: the Database of Interacting Proteins. Nucl Acids Res 28: 289-291.
87. Ceccatto HA, Huberman BA, (1988) The complexity of hierarchical systems. Physica Scripta 37: 145.
88. Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi AL, (2002) Hierarchical organization of modularity in metabolic networks. Science 297: 1551-1555.
89. Emmert-Streib F, (2007) The chronic fatigue syndrome: A comparative pathway analysis. Journal of Computational Biology 14: 961-972.
90. Emmert-Streib F, Glazko G, (2011) Pathway analysis of expression data: deciphering functional building blocks of complex diseases. PLoS Computational Biology 7: e1002053.
91. Schadt E, (2009) Molecular networks as sensors and drivers of common human diseases. Nature 461: 218-223.
92. Boginski V, Butenko S, Pardalos P, (2005) Statistical analysis of financial networks. Computational Statistics and Data Analysis 48: 431-443.
93. Emmert-Streib F, Dehmer M, (2010) Identifying Critical Financial Networks of the DJIA: Towards a Network-based Index. Complexity 16: 24-33.
94. Emmert-Streib F, Dehmer M, (2010) Influence of the Time Scale on the Construction of Financial Networks. PLoS ONE 5: e12884.
95. Kaiser M, Hilgetag CC, Kötter R, (2010) Hierarchy and dynamics of neural networks. Frontiers in Neuroinformatics 4.
96. Sporns O, (2011) Networks of the brain. Cambridge, Mass MIT Press.
97. R Development Core Team (2008) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
98. Mueller LA, Kugler KG, Dander A, Graber A, Dehmer M, (2010) QuACN- An R Package for Analyzing Complex Biological Networks Quantitatively. Bioinformatics.