A computational approach to construct a multivariate complete graph invariant

Information Sciences

Volumn 260, Issue , 2014, Pages 200-208

  Dehmer, Matthias ^a   Emmert Streib, Frank ^b   Grabner, Martin ^a  

^a Institute for Bioinformatics and Translational Research   (Austria)

^b QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

Information inequality; Quantitative graph theory; Random network model; Statistics

Indexed keywords

COMPLETE GRAPHS; COMPUTATIONAL APPROACH; GRAPH INVARIANT; INFORMATION INEQUALITY; ITERATIVE APPROACH; NUMERICAL RESULTS; POLYNOMIAL TIME COMPLEXITY; RANDOM NETWORK MODELS;

COMPUTATIONAL METHODS; POLYNOMIAL APPROXIMATION; STATISTICS;

GRAPH THEORY;

EID: 84891738883     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2013.11.008     Document Type: Article

References (60)

1. M. Abdulrahim, and M. Misra A graph isomorphism algorithm for object recognition Pattern Anal. Appl. 1 1998 189 201
2. A.V. Aho, J.E. Hopcroft, and J.D. Ullman The Design and Analysis of Computer Algorithms 1974 Addison-Wesley
3. V. Arvind, B. Das, and J. Köbler The space complexity of k-tree isomorphism Proceedings of the 18th International Symposium on Algorithms and Computation (ISAAC) LNCS 4835 2007 Springer 822 833
4. V. Arvind, B. Das, and J. Köbler A logspace algorithm for partial 2-tree canonization Proceedings of the 3rd International Computer Science Symposium in Russia (CSR) LNCS 5010 2008 Springer 40 51
5. L. Babai, and E.M. Luks Canonical labeling of graphs In STOC'83: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing 1983 ACM Press NY, USA
6. A.T. Balaban Highly discriminating distance-based topological index Chem. Phys. Lett. 89 1982 399 404
7. A.T. Balaban, and T.S. Balaban New vertex invariants and topological indices of chemical graphs based on information on distances J. Math. Chem. 8 1991 383 397
8. A.T. Balaban, and F. Harary The characteristic polynomial does not uniquely determine the topology of a molecule J. Chem. Document. 11 1971 258 259
9. S.C. Basak Information-theoretic indices of neighborhood complexity and their applications J. Devillers, A.T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPAR 1999 Gordon and Breach Science Publishers Amsterdam, The Netherlands 563 595
10. S.C. Basak, and V.R. Magnuson Molecular topology and narcosis Arzeim.-Forsch./Drug Des. 33 I 1983 501 503
11. D. Bonchev Information Theoretic Indices for Characterization of Chemical Structures 1983 Research Studies Press Chichester
12. D. Bonchev, O. Mekenyan, and N. Trinajstić Isomer discrimination by topological information approach J. Comput. Chem. 2 2 1981 127 148
13. M. Borgwardt, Graph Kernels. Ph.D. Thesis, Ludwig-Maximilians- Universität München, Fakultät für Mathematik, Informatik und Statistik, 2007.
14. D. Conte, F. Foggia, C. Sansone, and M. Vento Thirty years of graph matching in pattern recognition Int. J. Pattern Recog. Artif. Intell. 18 2004 265 298
15. T.H. Cormen, C.E. Leiserson, and R.L. Rivest Introduction to Algorithms 1990 MIT Press
16. D.G. Corneil, and C.C. Gotlieb An efficient algorithm for graph isomorphism J. ACM 17 1970 51 64
17. L.daF. Costa, F. Rodrigues, and G. Travieso Characterization of complex networks: a survey of measurements Adv. Phys. 56 2007 167 242
18. M. Dehmer Structural Analysis of Complex Networks 2010 Birkhäuser Publishing
19. M. Dehmer, F. Emmert-Streib, Y. Tsoy, and K. Varmuza Quantifying structural complexity of graphs: information measures in mathematical chemistry M. Putz, Quantum Frontiers of Atoms and Molecules 2011 Nova Publishing 479 498
20. M. Dehmer, M. Grabner, and B. Furtula Structural discrimination of networks by using distance, degree and eigenvalue-based measures PLoS ONE 7 2012 e38564
21. M. Dehmer, M. Grabner, and K. Varmuza Information indices with high discriminative power for graphs PLoS ONE 7 2012 e31214
22. M. Dehmer, and V. Kraus On extremal properties of graph entropies MATCH Commun. Math. Comput. Chem. 68 2012 889 912
23. M. Dehmer, and A. Mowshowitz A history of graph entropy measures Inform. Sci. 1 2011 57 78
24. J. Devillers, and A.T. Balaban Topological Indices and Related Descriptors in QSAR and QSPR 1999 Gordon and Breach Science Publishers Amsterdam, The Netherlands
25. M.V. Diudea, I. Gutman, and L. Jäntschi Molecular Topology 2001 Nova Publishing New York, NY, USA
26. J.L. Faulon Isomorphism, automorphism partitioning, and canonical labeling can be solved in polynomial-time for molecular graphs J. Chem. Inform. Comput. Sci. 38 3 1998 432 444
27. I. Gutman, X. Li, and J. Zhang Graph energy M. Dehmer, F. Emmert-Streib, Analysis of Complex Networks: From Biology to Linguistics 2009 Wiley-VCH 145 174
28. R. Halin Graphentheorie 1989 Akademie Verlag Berlin, Germany
29. N.R. Hall, and S. Preiser Combined network complexity measures IBM J. Res. Develop. 28 1984 15 27
30. F. Harary Graph Theory 1969 Addison Wesley Publishing Company Reading, MA, USA
31. W.-D. Ihlenfeldt, and J. Gasteiger Hash codes for the indentification and classification of molecular structure elements J. Comput. Chem. 15 8 1994 793 813
32. D. Janežić, A. Miležević, S. Nikolić, N. Trinajstić, Graph-Theoretical Matrices in Chemistry. Mathematical Chemistry Monographs, University of Kragujevac and Faculty of Science Kragujevac, 2007.
33. T. Junttila, and P. Kaski Engineering an efficient canonical labeling tool for large and sparse graphs D. Applegate, G. Stolting Brodat, D. Panario, R. Sedgewick, Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithms and Combinatorics 2007 SIAM
34. E.V. Konstantinova The discrimination ability of some topological and information distance indices for graphs of unbranched hexagonal systems J. Chem. Inform. Comput. Sci. 36 1996 54 57
35. E.V. Konstantinova On some applications of information indices in chemical graph theory R. Ahlswede, L. Bäumer, N. Cai, H. Aydinian, V. Blinovsky, C. Deppe, H. Mashurian, General Theory of Information Transfer and Combinatorics Lecture Notes of Computer Science 2006 Springer 831 852
36. E.V. Konstantinova, and A.A. Paleev Sensitivity of topological indices of polycyclic graphs Vychisl. Sistemy 136 1990 38 48 (in Russian)
37. F. Li, H. Shang, and P.Y. Woo Determination of isomorphism and its applications for arbitrary graphs based on circuit simulation Circuits Syst. Signal Process. 27 5 2008 749 761
38. J. Liu, and B. Liu A laplacian-energy-like invariant of a graph MATCH Commun. Math. Comput. Chem. 2 2008 355 372
39. X. Liu, and D.J. Klein The graph isomorphism problem J. Comput. Chem. 12 10 1991 1243 1251
40. E.M. Luks Isomorphism of graphs of bounded valence can be tested in polynomial time J. Comput. Syst. Sci. 25 1982 42 49
41. B.D. McKay Graph isomorphisms Congr. Numer. 730 1981 45 87
42. B.D. McKay. Nauty, 2010. < http://cs.anu.edu.au/∼bdm/nauty/ >.
43. A. Mehler, P. Weiß, and A. Lücking A network model of interpersonal alignment Entropy 12 6 2010 1440 1483
44. A. Mowshowitz Entropy and the complexity of the graphs I: an index of the relative complexity of a graph Bull. Math. Biophys. 30 1968 175 204
45. L.A.J. Müller, M. Schutte, K. G. Kugler, and M. Dehmer. QuACN: Quantitative Analyze of Complex Networks, 2012. R Package Version 1.6.
46. M. Noy Graphs determined by polynomial invariants Theor. Comput. Sci. 307 2 2003 365 384
47. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2008. ISBN 3-900051-07-0.
48. C. Raychaudhury, S.K. Ray, J.J. Ghosh, A.B. Roy, and S.C. Basak Discrimination of isomeric structures using information theoretic topological indices J. Comput. Chem. 5 1984 581 588
49. R. Read, and D. Corneil The graph isomorphism disease J. Graph Theory 1 1977 339 363
50. H. Sagan Boundary and Eigenvalue Problems in Mathematical Physics 1989 Dover Publications
51. S. Skiena Graph isomorphism S. Pemmaraju, S. Skiena, Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica 1990 Reading, Addison-Wesley MA, USA 181 187
52. L. Spialter The atom connectivity matrix (ACM) and its characteristic polynomial (ACMCP): a new computer-oriented chemical nomenclature J. Am. Chem. Soc. 85 1963 2012 2013
53. S. Toda Graph isomorphism: its complexity and algorithms (abstract) C.P. Rangan, V. Raman, R. Ramanujam, FSTTCS, Foundations of Software Technology and Theoretical Computer Science, 19th Conference, Chennai, India, December 13-15, 1999, Proceedings, Lecture Notes in Computer Science vol. 1738 1999 Springer 341
54. R. Todeschini, V. Consonni, and R. Mannhold Handbook of Molecular Descriptors 2002 Wiley-VCH Weinheim, Germany
55. R.E. Ulanowicz Information theory in ecology Comput. Chem. 25 2001 393 399
56. R.E. Ulanowicz Quantitative methods for ecological network analysis Comput. Biol. Chem. 28 2004 321 339
57. W. Wang, and Y. Luo On laplacian-energy-like invariant of a graph Linear Algebra Appl. 437 2012 713 721
58. T. Wilhelm, and J. Hollunder Information theoretic description of networks Physica A 388 2007 385 396
59. C.W. Wu On graphs whose laplacian matrix's multipartite separability is invariant under graph isomorphism Discr. Mathem. 310 2010 2811 2814
60. V.N. Zemlyachenko, N.M. Korneenko, and R.I. Tyshkevich Graph isomorphism problem J. Math. Sci. 29 1985 1426 1481