Abstract
In this paper, we briefly present a classification scheme of information-based network complexity measures. We will see that existing as well as novel measures can be divided into four major categories: (i) partition-based measures, (ii) non partition-based measures, (iii) non-parametric local measures and (iv) parametric local measures. In particular, it turns out that (ii)-(iv) can be obtained in polynomial time complexity because we use simple graph invariants, e.g., metrical properties of graphs. Finally, we present a generalization of existing local graph complexity measures to obtain parametric complexity measures.
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References
Bonchev, D.: Information indices for atoms and molecules. MATCH 7, 65–113 (1979)
Bonchev, D.: Information Theoretic Indices for Characterization of Chemical Structures. Research Studies Press, Chichester (1983)
Bonchev, D., Rouvray, D.H.: Complexity in Chemistry, Biology, and Ecology. In: Mathematical and Computational Chemistry. Springer, Heidelberg (2005)
Brillouin, L.: Science and Information Theory. Academic Press, New York (1956)
Constantine, G.: Graph complexity and the laplacian matrix in blocked experiments. Linear and Multilinear Algebra 28, 49–56 (1990)
Dehmer, M.: Information processing in complex networks: Graph entropy and information functionals. Applied Mathematics and Computation 201, 82–94 (2008)
Dehmer, M.: Information-theoretic concepts for the analysis of complex networks. Applied Artificial Intelligence (in press) (2008)
Dehmer, M.: A novel method for measuring the structural information content of networks. In: Cybernetics and Systems (in press) (2008)
Halin, R.: Graphentheorie. Akademie Verlag (1989)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
Konstantinova, E.V., Skorobogatov, V.A., Vidyuk, M.V.: Applications of information theory in chemical graph theory. Indian Journal of Chemistry 42, 1227–1240 (2002)
McKay, B.D.: Graph isomorphisms. Congressus Numerantium 730, 45–87 (1981)
Minoli, D.: Combinatorial graph complexity. Atti. Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 59, 651–661 (1975)
Mowshowitz, A.: Entropy and the complexity of the graphs I: An index of the relative complexity of a graph. Bull. Math. Biophys. 30, 175–204 (1968)
Neel, D.L., Orrison, M.E.: The linear complexity of a graph. The Electronic Journal of Combinatorics 13 (2006)
Rashevsky, N.: Life, information theory, and topology. Bull. Math. Biophys. 17, 229–235 (1955)
Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press (1997)
Skorobogatov, V.A., Dobrynin, A.A.: Metrical analysis of graphs. MATCH 23, 105–155 (1988)
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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Dehmer, M., Emmert-Streib, F. (2009). Towards Network Complexity. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_68
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DOI: https://doi.org/10.1007/978-3-642-02466-5_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02465-8
Online ISBN: 978-3-642-02466-5
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