Entropy bounds for hierarchical molecular networks

PLoS ONE

Volumn 3, Issue 8, 2008, Pages

  Dehmer, Matthias ^a,d   Borgert, Stephan ^b,e   Emmert Streib, Frank ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF SIEGEN   (Germany)

^c QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

^d UNIVERSITY OF COIMBRA   (Portugal)

^e DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOCHEMISTRY; ENTROPY; FEASIBILITY STUDY; GENERALIZED TREE; INFORMATION PROCESSING; INFORMATION RETRIEVAL; MACHINE LEARNING; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; QUANTITATIVE STRUCTURE PROPERTY RELATION; ROOTED TREE; STATISTICAL ANALYSIS; THEORY; ALGORITHM; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BIOLOGY; CHEMICAL STRUCTURE; COMPUTER SIMULATION; METHODOLOGY; PROBABILITY; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; ENTROPY; MODELS, MOLECULAR; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED; PROBABILITY;

EID: 52649173207     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0003079     Document Type: Article

References (75)

1. Bonchev D, Rouvray DH (1991) Chemical Graph Theory. Introduction and Fundamentals Abacus Press.
2. Diudea MV, Gutman I, Jäntschi L (2001) Molecular Topology Nova Publishing.
3. Gutman I, Polansky OE (1986) Mathematical Concepts in Organic Chemistry Springer.
4. Trinajstić N (1992) Chemical Graph Theory CRC Press.
5. Batagelj V (1988) Similarity measures between structured objects. In: Graovac A, ed. Dubrovnik/Yugoslavia: Proceedings of an International Course and Conference on the Interfaces between Mathematics, Chemistry and Computer Sciences. pp 25-40.
6. Bonchev D, Trinajstić N (1977) Information theory, distance matrix and molecular branching. Journal of Chemical Physics 67: 4397-4533.
7. Bonchev D (1983) Information Theoretic Indices for Characterization of Chemical Structures. Chichester: Research Studies Press.
8. Rupp M, Proschak E, Schneider G (2007) Kernel approach to molecular similarity based on iterative graph similarity. J Chem Inf Comput Sci 47: 2280-2286.
9. Skvortsova MI, Baskin H, Stankevich IV, Palyulin VA, Zefirov NS (1998) Molecular similarity. I. Analytical description of the set of graph similarity measures. J Chem Inf Comput Sci 38: 785-790.
10. Benigni R (2003) Quantitative Structure-Activity Relationship (QSAR) Models of Mutagens and Carcinogens. CRC Press.
11. Devillers J, Balaban AT (2000) Topological Indices and Related Descriptors in QSAR and QSPAR. CRC Press.
12. Diudea MV (2001) QSPR/QSAR Studies by Molecular Descriptors. Nova Publishing.
13. Bonchev D (2000) Overall connectivities and topological complexities: A new powerful tool for QSPR/QSAR. J Chem Inf Comput Sci 40(4): 934-941.
14. Bonchev D (2003) Complexity in Chemistry. Introduction and Fundamentals. Taylor and Francis.
15. Bunke H (1983) What is the distance between graphs? Bulletin of the EATCS 20: 35-39.
16. Bunke H (2000) Recent developments in graph matching. In: 15-th International Conference on Pattern Recognition 2. pp 117-124.
17. Bunke H, Neuhaus M (2007) Graph matching. Exact and error-tolerant methods and the automatic learning of edit costs. In: Cook D, Holder LB, eds. Mining Graph Data Wiley-Interscience. pp 17-32.
18. Sobik F (1982) Graphmetriken und Klassifikation strukturierter Objekte. ZKI-Informationen, Akad Wiss DDR 2(82): 63-122.
19. Sobik F (1986) Modellierung von Vergleichsprozessen auf der Grundlage von Ähnlichkeitsmaßen fur Graphen. ZKI-Informationen, Akad Wiss DDR 4: 104-144.
20. Kaden F. Graphmetriken und Distanzgraphen. ZKI-Informationen, Akad Wiss DDR 2(82): 1-63.
21. Zelinka B (1975) On a certain distance between isomorphism classes of graphs. Časopis pro pest. Mathematiky 100: 371-373.
22. Zhu P, Wilson RC (2005) A study of graph spectra for comparing graphs. In: 16-th British Machine Vision Conference, Oxford Brookes University.
23. Brinkmeier M, Schank T (2005) Network statistics. In: Brandes U, Erlebach T, eds. Network Analysis, Lecture Notes of Computer Science. Springer. pp 293-317.
24. Dorogovtsev SN, Mendes JFF (2003) Evolution of Networks. From Biological Networks to the Internet and WWW: Oxford University Press.
25. Barabási AL (2003) How Everything Is Connected to Everything Else and What It Means: Plume, Reissue edition.
26. Mason O, Verwoerd M (2007) Graph theory and networks in biology. IET Systems Biology 1(2): 89-119.
27. Bonchev D, Rouvray DH (2005) Complexity in Chemistry, Biology, and Ecology Mathematical and Computational Chemistry, Springer.
28. Dehmer M, Emmert-Streib F (2008) Structural information content of networks: Graph entropy based on local vertex functionals. Computational Biology and Chemistry 32: 131-138.
29. Sahu PK, Lee SL (2008) Net-sign identity information index: A novel approach towards numerical characterization of chemical signed graph theory. Chemical Physics Letters, In press.
30. Morowitz H (1953) Some order-disorder considerations in living systems. Bull Math Biophys 17: 81-86.
31. Quastler H (1953) Information Theory in Biology. University of Illinois Press.
32. Dancoff S, Quastler H (1953) Information content and error rate of living things. In: Quastler H, ed. Essays on the Use of Information Theory in Biology University of Illinois Press. pp 263-274.
33. Linshitz H (1953) The information content of a battery cell. In: Quastler H, ed. Essays on the Use of Information Theory in Biology University of Illinois Press. pp 14-15.
34. Rashewsky N (1955) Life, information theory, and topology. Bull Math Biophys 17: 229-235.
35. Trucco E (1956) A note on the information content of graphs. Bulletin of Mathematical Biology 18(2): 129-135.
36. Shannon CE, Weaver W (1997). The Mathematical Theory of Communication: University of Illinois Press.
37. Brillouin L (1956) Science and Information Theory. New York: Academic Press.
38. 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.
39. Mowshowitz A (1968) Entropy and the complexity of graphs II: The information content of digraphs and infinite graphs. Bull Math Biophys 30: 225-240.
40. Mowshowitz A (1968) Entropy and the complexity of graphs III: Graphs with prescribed information content. Bull Math Biophys 30: 387-414.
41. Mowshowitz A (1968) Entropy and the complexity of graphs IV: Entropy measures and graphical structure. Bull Math Biophys 30: 533-546.
42. Fujii JI, Yuki S (1997) Entropy and coding for graphs. Int J Math Stat Sci 6(1): 63-77.
43. Kieffer J, Yang E (1997) Ergodic behavior of graph entropy. Electronic Research Announcements of the American Mathematical Society 3: 11-16.
44. Körner J (1973) Coding of an information source having ambiguous alphabet and the entropy of graphs. Transactions of the 6-th Prague Conference on Information Theory. pp 411-425.
45. Simonyi G (2001) Perfect graphs and graph entropy. An updated survey. In: Ramirez-Alfonsin J, Reed B, eds. Perfect Graphs John Wiley & Sons. pp 293-328.
46. Harary F (1969) Graph Theory. Addison Wesley Publishing Company.
47. Mehler A, Dehmer M, Gleim R (2004) Towards logical hypertext structure - A graph-theoretic perspective. In: Böhme T, Heyer G, eds. Proceedings of the Fourth International Workshop on Innovative Internet Computing Systems (I2CS '04), Lecture Notes in Computer Science 3473. pp 136-150.
48. Aringhieri R, Hansen P, Malucelli F (2001) A linear algorithm for the hyperwiener index of chemical trees. J Chem Inf Comput Sci 41(4): 958-963.
49. Aringhieri R, Hansen P, Malucelli F (2003) Chemical trees enumeration algorithms. 4OR, A Quarterly Journal of Operations Research 1(1): 67-83.
50. Müller WR, Szymanski K, Knop JV, Trinajstić N (1995) A comparison between the matula numbers and bit-tuple notation for rooted trees. J Chem Inf Comput Sci 35(2): 211-213.
51. Matula DW (1968) A natural rooted tree enumeration by prime factorization. SIAM Review 10: 273.
52. Elk SB (1990) A canonical ordering of polybenzenes and polyadamantanes using a prime factorization technique. J Math Chem 4: 55-68.
53. Visco DP, Pophale RS, Rintoul MD, Faulon JL (2002) Developing a methodology for an inverse quantitative structure-activity relationship using the signature molecular descriptor. Journal of Molecular Graphics and Modelling 20: 429-438.
54. Zmazeka B, Žerovnik J (2007) The hosoya-wiener polynomial of weighted trees. Croatica Chemica Acta 80(1): 75-80.
55. Bohanec, S, Perdih M (1993) Symmetry of chemical structures: A novel method of graph automorpbism group determination. J Chem Inf Comput Sci 33: 719-726.
56. Chepoi V (1996) On distances in benzenoid systems. J Chem Inf Comput Sci 36: 1169-1172.
57. Liu SC, Tong LD, Yeh JY (2000) Trees with the minimum wiener number. International Journal of Quantum Chemistry 78(5): 331-340.
58. Skorobogatov VA, Dobrynin AA (1988) Metrical analysis of graphs. MATCH 23: 105-155.
59. Semple C, Steel M (2000) A supertree method for rooted trees. Discrete Applied Mathematics 105(1-3): 147-158.
60. Felsenstein J (2003) Inferring Phylogenies. Sinauer Associates.
61. Foulds LR (1992) Graph Theory Applications. Springer.
62. Steel M, Dress A, Boker S (2000) Simple but fundamental limitations on supertree and consensus tree methods. Systematic Biology 49: 363-368.
63. Semple C, Steel M (2003) Phylogenetics. Graduate Series Mathematics and its Applications. Oxford University Press.
64. Höchstmann M, Möller T, Giegerich R, Kurtz S (2003) Local similarity in RNA secondary structures. In: Proceedings of the IEEE Computational Systems Bioinformatics Conference (CSB'03). pp 159-168.
65. Shapiro BA, Zhang K (1990) Comparing multiple RNA secondary structures using tree comparisons. Comp Appl Biosci 6(4): 309-318.
66. Emmert-Streib F, Dehmer M, Kilian J (2005) Classification of large graphs by a local tree decomposition. In: Arabnia HR, Scime A, eds. Proceedings of DMIN'05, International Conference on Data Mining, Las Vegas, June 20-23. pp 200-207.
67. Horváth T, Gärtner T, Wrobel S (2005) Cyclic pattern kernels for predictive graph mining. In: Proceedings of the 2004 ACM SIGKDD, International Conference on Knowledge Discovery and Data Mining. pp 158-167.
68. Gambin A, Slonimski PP (2005) Hierarchical clustering based upon contextual alignment of proteins: A different way to approach phylogeny. Comptes Rendus Biologies 328(1): 1-22.
69. Morihiro H, Tatsuya A, Hitoshi N (2006) A novel clustering method for analysis of biological networks using maximal components of graphs. IPSJ SIG Technical Reports 99: 1-8.
70. Bonchev D (1989) The concept for the center of a chemical structure and its applications. Journal of Molecular Structure: Theochem 185: 155-168.
71. Bang-Jensen J, Gutin G (2002) Digraphs. Theory, Algorithms and Applications. London, Berlin, Heidelberg: Springer.
72. Halin R (1989) Graphentheorie. Akademie Verlag.
73. Dehmer M, Emmert-Streib F, Mehler A, Kilian J (2006) Measuring the structural similarity of web-based documents: A novel approach. International Journal of Computalional Intelligence 3(1): 1-7.
74. Emmert-Streib F, Dehmer M, Liu J, Mühlhäuser M (2006) Ranking genes from DNA microarray data of cervical cancer by a local tree comparison. International Journal of Biomedical Science 1(1): 17-22.
75. Dehmer M (2008) Information processing in complex networks: Graph entropy and information functionals. Applied Mathematics and Computation 201: 82-94.