Novel centrality measures and distance-related topological indices in network data mining

Wilczek, P.

Artykuł - szczegóły

Tytuł artykułu

Novel centrality measures and distance-related topological indices in network data mining

Autorzy

Wilczek P.

Treść / Zawartość

Pełne teksty:

wilczek_Silesian_J_Pure_Appl_Math_2017_1.pdf

Pobierz

Identyfikatory

Warianty tytułu

Języki publikacji

Abstrakty

The present work proposes two new Euclidean distance functions, six new centrality measures as well as several new entropies definable on any complex network. It is demonstrated on four spatial and two social real-world datasets that these concepts are applicable in network data mining. Also, several new topological indices are introduced and their basic computational properties are established.

Słowa kluczowe

complex networks centrality measures topological indices chemical graph theory

sieci złożone miary centralności wskaźnik topologiczny chemiczna teoria grafów

Wydawca

Wydawnictwo Politechniki Śląskiej

Czasopismo

Silesian Journal of Pure and Applied Mathematics

Rocznik

2017

Tom

Vol. 7, iss. 1

Strony

21--63

Opis fizyczny

Bibliogr. 45 poz.

Twórcy

autor

Wilczek P.

piotr.wilczek.net@onet.pl

Computer Laboratory, Poznań, Poland

Bibliografia

1. Albert R., Barabási A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002), 47–97.
2. Babić D., Klein D.J., Lukovits I., Nikolić S., Trinajstić N.: Resistance-distance matrix: a computational algorithm and its application. Int. J. Quantum Chem. 90 (2002), 166–176.
3. Barabási A.-L., Albert R.: Emergence of scaling in random networks. Science 286 (1999), 509–512.
4. Barthélemy M.: Spatial networks. Phys. Rep. 499 (2011), 1–101.
5. Batagelj V.: vlado.fmf.uni-lj.si/pub/networks/data/bio/dolphins.net.
6. Bavelas A.: Communication patterns in task-oriented groups. J. Acoust. Soc. Am. 22 (1950), 725–730.
7. Bonchev D.: A simple integrated approach to network complexity and node centrality. In: Analysis of Complex Networks. From Biology to Linguistics. Dehmer M., Emmert-Streib F. (eds.), Wiley-VCH, Weinheim 2009, 47–53.
8. Bonchev D., Balaban A.T., Liu X., Klein D.J.: Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances and reciprocal distances. Int. J. Quantum Chem. 50 (1994), 1–20.
9. Bonchev D., Buck G.A.: Quantitative measures of network complexity. In: Complexity in Chemistry, Biology, and Ecology. Bonchev D., Rouvray D.H. (eds.), Springer, New York 2005, 191–235.
10. Bonchev D., Trinajstić N.: Information theory, distance matrix and molecular branching. J. Chem. Phys. 67 (1977), 4517–4533.
11. Clauset A., Newman M.E.J., Moore C.: Finding community structure in very large networks. Phys. Rev. E 70 (2004), 066111.
12. Csardi G.: igraphdata: A collection of network data sets for the ’igraph’ package. R package version 1.0.1, https://CRAN.R-project.org/package=igraphdata.
13. Csardi G., Nepusz T.: The igraph software package for complex network research. InterJournal Complex Syst. 1695 (2006), http://igraph.org.
14. Dehmer M.: Information theory of networks. Symmetry 3 (2011), 767–779.
15. Dehmer M., Grabner M., Furtula B.: Structural discrimination of networks by using distance, degree and eigenvalue-based measures. PLoS ONE 7 (2012), e38564.
16. Dehmer M., Grabner M., Varmuza K.: Information indices with high discriminative power for graphs. PloS ONE 7 (2012), e31214.
17. Dorogovtsev S.N., Mendes J.F.F.: Evolution of Networks: From Biological Networks to the Internet and WWW. Oxford University Press, Oxford 2003.
18. Dray S., Dufour A.B.: The ade4 package: implementing the duality diagram for ecologists. J. Stat. Soft. 22 (2007), 1–20.
19. Estrada E.: The Structure of Complex Networks: Theory and Applications. Oxford University Press, Oxford 2011.
20. Eubank N.: http://github.com/nickeubank/gis in r/blob/master/RGIS6 Data/.
21. Gower J.C., Legendre P.: Metric and Euclidean properties of dissimilarity coefficients. J. Classification 3 (1986), 5–48.
22. Hausser J., Strimmer K.: Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks. J. Mach. Learn. Res. 10 (2009), 1469–1484.
23. International Academy of Mathematical Chemistry: www.moleculardescriptors.eu.
24. Ivanciuc O., Balaban T.S., Balaban A.T.: Design of topological indices. Part 4*. Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 12 (1993), 309–318.
25. Janežič D., Miličević A., Nikolić S., Trinajstić N.: Graph Theoretical Matrices in Chemistry, University of Kragujevac, Kragujevac 2007.
26. Klein D.J.: Graph geometry, graph metrics and Wiener. MATCH Commun. Math. Comput. Chem. 35 (1997), 7–27.
27. Konstantinova E.V., Skorobogatov V.A., Vidyuk M.V.: Applications of information theory in chemical graph theory. Indian J. Chem. Sect. A 42 (2003), 1227–1240.
28. Koschűtzki D., Lehman K.A., Peeters L., Richter S., Tenfelde-Podehl D., Zlotowski O.: Centrality indices. In: Network Analysis: Methodological Foundations. Brandes U., Erlebach T. (eds.), Springer, Berlin 2005.
29. Lusseau D., Schneider K., Boisseau O.J., Haase P., Slooten E., Dawson S.M.: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behav. Ecol. sociobiol. 54 (2003), 396–405.
30. Mallion R.B., Trinajstić N.: Reciprocal spanning-tree density: a new index for characterising the intricacy of a (poly)cyclic molecular-graphs. MATCH Commun. Math. Comput. Chem. 48 (2003), 97–116.
31. Manitz J.: NetOrigin: Origin estimation for propagation processes on complex networks. R package version 1.0-2, https://CRAN.R-project.org/package= NetOrigin.
32. Meghanathan N.: Exploiting the discriminating power of eigenvector centrality measure to detect graph isomorphism. IJFCST 5 (2015), 1–13.
33. Newman M.E.J.: The structure and function of complex networks. SIAM Review 45 (2003), 167–256.
34. Pólya G., Read R.C.: Combinatorial Enumeration of Groups, Graphs and Chemical Compounds, Springer-Verlag, New York 1987.
35. Pons P., Latapy M.: Computing communities in large networks using random walks. J. Graph Algorithms Appl. 10 (2006), 191–218.
36. Randić M.: On characterization of cyclic structures. J. Chem. Inf. Comput. Sci. 37 (1997), 1063–1071.
37. Randić M., Pisanski T., Novič M., Plavšić D.: Novel graph distance matrix. J. Comput. Chem. 31 (2010), 1832–1841.
38. Rappaport D.: research.cs.queensu.ca/˜daver/235/C1352963146/ E20070302133910.
39. Raychaudhury C., Ray S.K., Ghosh J.J., Roy A.B., Basak S.C.: Discrimination of isomeric structures using information theoretic topological indices. J. Comput. Chem. 5 (1984), 581–588.
40. R Core Team: R: a language and environment for statistical computing. R foundation for Statistical Computing, Vienna 2015, http://www.Rproject.org/.
41. Rochat Y.: Closeness Centrality Extended to Unconnected Graphs: the Harmonic Centrality Index, Application of Social Networks Analysis, Zurich 2009.
42. Ronqui J.R.F., Travieso G.: Analyzing complex networks through correlations in centrality measurements. J. Stat. Mech.: Theory Exp. 2015 (2015), P05030.
43. Todeschini R., Consonni V.: Molecular Descriptors for Chemoinformatics. Wiley-VCH, Weinheim 2009.
44. Watts D.J., Strogatz S.H.: Collective dynamics of ’small-world’ networks. Nature 393 (1998), 440–442.
45. Wilczek P.: https://github.com/PiotrWilczeknet/R-functions-1.

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-8b98bb54-80fd-4fe2-894c-16b37da1ab81