Interrelations of graph distance measures based on topological indices

PLoS ONE

Volumn 9, Issue 4, 2014, Pages

  Dehmer, Matthias ^a,b   Emmert Streib, Frank ^c   Shi, Yongtang ^d  

^a BUNDESWEHR UNIVERSITY MUNICH   (Germany)

^b UNIVERSITY FOR HEALTH SCIENCES   (Austria)

^c QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

^d NANKAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOINFORMATICS; COMPUTER PROGRAM; EIGENVALUE BASED MEASURE; GRAPH DISTANCE MEASURE; GRAPH ENTROPHY; MATHEMATICAL PHENOMENA; RANDIC INDEX; SCORING SYSTEM; TOPOLOGICAL INDEX; WIENER INDEX; BIOLOGY; COMPUTER GRAPHICS; PROCEDURES; THEORETICAL MODEL;

COMPUTATIONAL BIOLOGY; COMPUTER GRAPHICS; MODELS, THEORETICAL;

EID: 84899705018     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0094985     Document Type: Article

References (58)

1. Dehmer M, Mehler A (2007) A new method of measuring similarity for a special class of directed graphs. Tatra Mountains Mathematical Publications 36: 39-59.
2. Sobik F (1982) Graphmetriken und klassifikation strukturierter objekte, ZKI-informationen. Akad Wiss DDR 2: 63-122.
3. Zelinka B (1975) On a certain distance between isomorphism classes of graphs. Časopis propest Mathematiky 100: 371-373.
4. Emmert-Streib F (2007) The chronic fatigue syndrome: A comparative pathway analysis. J Comput Biology 14: 961-972.
5. Junker B, Schreiber F (2008) Analysis of Biological Networks. Wiley-Interscience. Berlin.
6. Kier L, Hall L (2002) The meaning of molecular connectivity: A bimolecular accessibility model. Croat Chem Acta 75: 371-382.
7. Bonchev D, Trinajstić N (1977) Information theory, distance matrix and molecular branching. J Chem Phys 67: 4517-4533.
8. Skvortsova M, Baskin I, Stankevich I, Palyulin V, Zefirov N (1998) Molecular similarity. 1. analytical description of the set of graph similarity measures. J Chem Inf Comput Sci 38: 785-790. (Pubitemid 128610990)
9. Varmuza K, Scsibrany H (2000) Substructure isomorphism matrix. J Chem Inf Comput Sci 40: 308-313.
10. Mehler A, Weiß P, Lücking A (2010) A network model of interpersonal alignment. Entropy 12: 1440-1483.
11. Hsieh S, Hsu C (2008) Graph-based representation for similarity retrieval of symbolic images. Data Knowl Eng 65: 401-418. (Pubitemid 351626194)
12. Dehmer M, Mehler A (2007) A new method of measuring similarity for a special class of directed graphs. Tatra Mountains Mathematical Publications 36: 39-59.
13. Bunke H (2000) Recent developments in graph matching. In: 15-th International Conference on Pattern Recognition. pp. 117-124.
14. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP Completeness. Series of Books in the Mathematical Sciences. W. H. Freeman.
15. Bunke H (1983) What is the distance between graphs? Bulletin of the EATCS 20: 35-39.
16. Robles-Kelly A, Hancock R (2003) Edit distance from graph spectra. In: Proceedings of the IEEE International Conference on Computer Vision. pp. 234-241.
17. Dehmer M (2008) Information processing in complex networks: Graph entropy and information functionals. Appl Math Comput 201: 82-94.
18. Dehmer M, Mowshowitz A, Emmert-Streib F (2011) Connections between classical and parametric network entropies. PLoS ONE 6: e15733.
19. Polansky OE, Bonchev D (1986) The Wiener number of graphs. I. General theory and changes due to graph operations. MATCH Communications in Mathematical and in Computer Chemistry 21: 133-186.
20. Polansky OE, Bonchev D (1990) Theory of the wiener number of graphs. II. Transfer graphs and some of their metric properties. MATCH Communications in Mathematical and in Computer Chemistry 25: 3-40.
21. Schädler C (1999) Die Ermittlung struktureller Ähnlichkeit und struktureller Merkmale bei komplexen Objekten: Ein konnektionistischer Ansatz und seine Anwendungen. Ph.D. thesis, Technische Universität Berlin.
22. Li X, Shi Y, Wang L (2008) An updated survey on the randić index. In: I Gutman BF, editor, Recent Results in the Theory of Randic Index, University of Kragujevac and Faculty of Science Kragujevac. pp. 9-47.
23. Todeschini R, Consonni V, Mannhold R (2002) Handbook of Molecular Descriptors. Wiley-VCH. Berlin.
24. Gutman I, Li X, Zhang J (2009) Graph energy. In: Dehmer M, Emmert-Streib F, editors, Analysis of Complex Networks. From Biology to Linguistics, Wiley-VCH. pp. 145-174. Weinheim.
25. Dehmer M, Mowshowitz A (2011) A history of graph entropy measures. Inform Sciences 181: 57-78.
26. Harary F (1969) Graph Theory. Addison Wesley Publishing Company. Reading, MA, USA.
27. Dehmer M, Varmuza K, Bonchev D, editors (2012) Statistical Modelling of Molecular Descriptors in QSAR/QSPR. Quantitative and Network Biology. Wiley-Blackwell.
28. Ulanowicz RE (2001) Information theory in ecology. Computers and Chemistry 25: 393-399.
29. Emmert-Streib F, Dehmer M (2011) Networks for systems biology: Conceptual connection of data and function. IET Systems Biology 5: 185-207.
30. Wilhelm T, Hollunder J (2007) Information theoretic description of networks. Physica A 388: 385-396. (Pubitemid 47381413)
31. Solé RV, Valverde S (2004) Information theory of complex networks: On evolution and architectural constraints. In: Lecture Notes in Physics. volume 650, pp. 189-207.
32. Bonchev D, Mekenyan O, Trinajstić N (1981) Isomer discrimination by topological information approach. J Comp Chem 2: 127-148.
33. Dehmer M, Emmert-Streib F, Tripathi S (2013) Large-scale evaluation of molecular descriptors by means of clustering. PLoS ONE 8: e83956.
34. Wiener H (1947) Structural determination of paran boiling points. J Amer Chem Soc 69: 17-20.
35. Dobrynin A, Entringer R, Gutman I (2001) Wiener index of trees: theory and application. Acta Appl Math 66: 211-249. (Pubitemid 32658997)
36. Randić M (1975) On characterization of molecular branching. J Amer Chem Soc 97: 6609-6615.
37. Bollobás B, Erdös P (1998) Graphs of extremal weights. Ars Combin 50: 225-233.
38. Li X, Gutman I (2006) Mathematical Aspects of Randić-Type Molecular Structure Descriptors. University of Kragujevac and Faculty of Science Kragujevac.
39. Li X, Shi Y (2008) A survey on the randić index. MATCH Commun Math Comput Chem 59: 127-156.
40. Gutman I (1977) Acylclic systems with extremal hückel π-electron energy. Theor Chim Acta 45: 79-87.
41. Gutman I (2001) The energy of a graph: old and new results. In: Betten A, Kohnert A, Laue R, Wassermann A, editors, Algebraic Combinatorics and Applications, Springer-Verlag. pp. 196-211.
42. Li X, Shi Y, Gutman I (2012) Graph Energy. Springer. New York.
43. Shannon C, Weaver W (1949) The Mathematical Theory of Communication. University of Illinois Press. Urbana, USA.
44. Dehmer M, Mowshowitz A (2011) Generalized graph entropies. Complexity 17: 45-50.
45. Read R, Wilson R (19988) An Atlas of Graphs. Clarendon Press. Oxford.
46. Hosoya H (1971) Topological index. a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull Chem Soc Jpn 4: 2332-2339.
47. Wagner S, Gutman I (2010) Maxima and minima of the hosoya index and the merrifield-simmons index: A survey of results and techniques. Acta Appl Math 112: 323-346.
48. Merrifield R, Simmons H (1980) The structure of molecular topological spaces. Theor Chim Acta 55: 55-75.
49. Merrifield R, Simmons H (1989) Topological Methods in Chemistry. Wiley. New York.
50. Estrada E (2000) Characterization of 3d molecular structure. Chem Phys Lett 319: 713-718.
51. Deng H, Radenković S, Gutman I (2009) The estrada index. In: Cvetković D, Gutman I, editors, Applications of Graph Spectra, Math. Inst. pp. 123-140. Belgrade.
52. Gutman I, Deng H, Radenković S (2011) The estrada index: An updated survey. In: Cvetković D, Gutman I, editors (2011) Selected Topics on Applications of Graph Spectra, Math. Inst. pp. 155-174.
53. Gutman I (1994) A formula for the wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes of New York 27: 9-15.
54. Simić S, Gutman I, Baltić V (2000) Some graphs with extremal szeged index. Math Slovaca 50: 1-15.
55. Dehmer M, Emmert-Streib F (2014) Quantitative Graph Theory. Theory and Applications. CRC Press. In press.
56. Furtula B, Gutman I, Dehmer M (2013) On structure-sensitivity of degree-based topological indices. Applied Mathematics and Computation 219: 8973-8978.
57. Perc M, Wang Z (2010) Heterogeneous aspirations promote cooperation in the prisoner's dilemma game. PLOS ONE 5: e15117.
58. Jin Q, Wang L, Xia C, Wang Z (2014) Spontaneous symmetry breaking in interdependent networked game. Scientific Reports 4: 4095.