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References
C. Shannon and W. Weaver, Mathematical Theory of Communications, University of Illinois Press, Urbana, IL (1949).
H. Kastler (ed.), Essays on the Use of Information Theory in Biology, University of Illinois Press, Urbana, IL (1953).
H. Linshitz, The Information Content of a Bacterial Cell, in Essays on the Use of Information Theory in Biology, H. Kastler (ed.), University of Illinois Press, Urbana, IL (1953).
N. Rashevsky, Bull. Math. Biophys. 17, 229–235 (1955).
E. Trucco, Bull. Math. Biophys. 18, 129–135 (1956).
A. Mowshowitz, Bull. Math. Biophys. 30, 175–204 (1968).
D. Minoli, Atti. Acad. Naz. Lincei Rend. 59, 651–661 (1976).
A. N. Kolmogorov, Problem’i Peredachi Informatsii (Russ.) 1, 1–7 (1965).
D. Bonchev, Bulg. Chem. Commun. 28, 567–582 (1995).
D. Bonchev, D. Kamenski, and V. Kamenska, Bull. Math. Biol. 38, 119–133 (1976).
D. Bonchev, and N. Trinajstić, J. Chem. Phys. 67, 4517–4533 (1977).
D. Bonchev and V. Kamenska, Croat. Chem. Acta 51, 19–27 (1978).
D. Bonchev, MATCH-Commun. Math. Comput. Chem. 7, 65–113 (1979).
D. Bonchev, O. Mekenyan, and N. TrinajstiÊ, J. Comput. Chem. 2, 127–148 (1981).
D. Bonchev and N. Trinajstić, Intern. J. Quantum Chem. Symp. 16, 463–480 (1982).
D. Bonchev, InformationTheoretic Indices for Characterization of Chemical Structures. Research Studies Press, Chichester, UK (1983).
D. Bonchev, Shannon’s Information and Complexity in, Mathematical Chemistry Series: Complexity in Chemistry, Vol. 7, D. Bonchev and D. H. Rouvray (eds.), Taylor & Francis, London (2003) pp. 155–187.
S. H. Bertz, J. Am. Chem. Soc. 103, 3599–3601 (1981).
S. H. Bertz, J. Chem. Soc. Chem. Commun. 209 (1981).
D. Bonchev, The Problems of Computing Molecular Complexity, in Computational Chemical Graph Theory, D. H. Rouvray (ed.), Nova Publications, New York (1990) pp. 34–67.
S. Nikolić, N. Trinajstić, M. Tolić, G. Rücker, and C. Rücker, On Molecular Complexity Indices, in Mathematical Chemistry Series: Complexity in Chemistry, Vol. 7, D. Bonchev and D. H. Rouvray (eds.), Taylor & Francis, London (2003) pp. 29–89.
S. H. Bertz, A. Mathematical Model of Molecular Complexity, in Chemical Applications of Topology and Graph Theory, R. B. King (ed.), Elsevier, Amsterdam (1983) pp. 206–221.
D. Bonchev and O. E. Polansky, On the Topological Complexity of Chemical Systems, in Graph Theory and Topology in Chemistry, R. B. King and D. H. Rouvray (eds.), Elsevier, Amsterdam (1987) pp.126–158.
D. Bonchev and W. A. Seitz, The Concept of Complexity in Chemistry. In: Concepts in Chemistry: A Contemporary Challenge, D. H. Rouvray (ed.),Wiley, New York (1997) pp. 353–381.
D. Bonchev, SAR QSAR Environ. Res. 7, 23–43 (1997).
S. H. Bertz and T. J. Sommer, Chem. Commun. 2409–2410 (1997).
S. H. Bertz and W. F. Wright, Graph Theory Notes New York Acad. Sci. 35, 32–48 (1998).
D. Bonchev, Overall Connectivity and Molecular Complexity. in Topological Indices and Related Descriptors, J. Devillers and A. T. Balaban (eds.), Gordon and Breach, Reading, UK (1999) pp. 361–401.
D. Bonchev, J. Chem. Inf. Comput. Sci. 40, 934–941 (2000).
G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 40, 99–106 (2000).
G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 41, 1457–1462 (2001).
D. Bonchev, O. N. Temkin and D. Kamenski, React. Kinet. Catal. Lett. 15, 119–124 (1980).
D. Bonchev, D. Kamensky, and O. N. Temkin, J. Math. Chem. 1, 345–388 (1987).
K. Gordeeva, D. Bonchev, D. Kamenski, and O. N. Temkin, J. Chem. Inf. Comput. Sci. 34, 244–247 (1994).
O. N. Temkin, A. V. Zeigarnik, and D. Bonchev, Chemical Reaction Networks. A Graph Theoretical Approach. CRC Press, Boca Raton, FL (1996).
F. Harary, Graph Theory, Addison-Wesley, Reading, MA (1969).
F. Harary, R. Z. Norman, and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs, Wiley, New York (1965).
N. Trinajstić, Chemical Graph Theory, 2nd ed., CRC Press, Boca Raton, FL (1992).
H. L. Morgan, J. Chem. Docum. 5, 107–113 (1965).
D. Bonchev, A. T. Balaban and O. Mekenyan, J. Chem. Inf. Comput. Sci. 20, 106–113 (1980).
D. Bonchev, Theochem 185, 155–168 (1989).
D. Bonchev, O. Mekenyan and AT Balaban, J. Chem. Inf. Comput. Sci. 29, 91–97 (1989).
M. E. J. Neuman, S. H. Strogatz, and D. J. Watts, Random Graphs With Arbitrary Degree Distribution and Their Applications, Santa Fe Institute (2000) Working Paper 00-07-042.
M. Gell-Mann, The Quark and the Jaguar, Freeman, New York (1994) p.31.
D. Bonchev, SAR QSAR Envir. Sci. 14, 199–214 (2003).
D. Bonchev, Complexity of Protein-Protein Interaction Networks, Complexes and Pathways, in Handbook of Proteomics Methods, M. Conn (ed.), Humana, New York (2003) pp. 451–462.
D. Bonchev, Chem. and Biodiversity, 1, 312–332 (2004).
D. Bonchev and D. H. Rouvray (eds.), Mathematical Chemistry Series: Complexity in Chemistry, Vol. 7, Taylor & Francis, London (2003).
S. Nicolić, I. M. Tolić, N. Trinajstić, and I. Baučić, Croat. Chem. Acta 73, 909–921 (2000).
M. Randić and D. Plavšsić, Croat. Chem. Acta 75, 107–116 (2002).
J. R. Platt, J. Phys. Chem. 56, 328–336 (1952).
D. Bonchev, Croat. Chem. Acta 77, 167–173 (2004).
M. Gordon and G. R. Scantleburry, Trans. Faraday Soc. 60, 604–621 (1964).
S. H. Bertz and W. C. Herndon, The Similarity of Graphs and Molecules, in Artificial Intelligence Applications to Chemistry, T. H. Pierce and B. A. Hohne (eds.), ACS, Washington, DC (1986), pp.169–175.
G. Rücker and C. Rücker, MATCH—Commun. Math. Comput. Chem. 41, 145–149 (2000).
D. Bonchev and N. Trinajstić, SAR QSAR Environ. Res. 12, 213–235 (2001).
D. Bonchev, J. Mol. Graphics Model. 20, 55–65 (2001).
H. Wiener, J. Am. Chem. Soc. 69, 17–20 (1947).
H. Wiener, J. Phys. Chem. 52, 1082–1089 (1948).
D. Bonchev, J. Chem. Inf. Comput. Sci. 41, 582–592 (2001).
I. Gutman, B. Rušsćić, N. Trinajstić, and C.W. Wilcox, Jr, J. Chem. Phys. 62, 3399–3405 (1975).
S. Nicolić, G. Kovacevic, A. Milicevic, and N. Trinajstić, Croat. Chem. Acta 76, 113–124 (2003).
D. J. Watts and S. H. Strogatz, Nature 393, 440–442 (1998).
A. L. Barabási, Linked. The NewScience of Networks. Perseus, Cambridge, MA, (2002).
A. L. Barabási and R. Albert, Science 286, 509–512 (1999).
S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079–1187 (2002).
http://www.santafe.edu/sfi/publications/working-papers.html.
T. Ito, T. Chiba, R. Ozava, M. Yoshida, M. Hattori, and Y. Sasaki, Proc. Natl. Acad. Sci. USA 98, 4569–4574 (2001).
G. Weng, U. S. Bhala, and R. Yyengar, Science 284, 92–96 (1999).
A. Wagner, Mol. Biol. Evol. 18, 1283–1292 (2001).
L. Giot, et al., Science 302, 1727–1736 (2003).
A. C. Gavin, et al., Nature 415,141–147 (2002).
T. I. Lee, et al., Science, 298, 799–804 (2002).
N. Friedman, Science, 303, 799–805 (2004).
A. H. Y. Tong, et al., Science, 303, 606–813 (2004).
H. Jeong, B. Tombor, Z. Albert, and A. L. Barabási, Nature 407, 651–654 (2000).
A. Wagner and D. A. Fell, Proc. Roy. Soc. London B 268, 1803–1810 (2001).
H. Ma and A. P. Zengl, Bioinformatics 19, 270–277 (2003).
C. Koch and G. Laurent, Science 284, 96–98 (1999).
S. Karabunarliev and D. Bonchev, Grafman software package, unpublished.
S. N. Dorogovtzev, J. F. F. Mendes, and A. N. Samukhin, Giant Strongly Connected Component of Directed Graphs, arXiv I cond-mat/0103629 v1 Mar 2001.
S. H. Yook, H. Jeong and A. L. Barabási, Proc. Natl. Acad. Sci. 99, 13382–13386, (2002).
J. A. Dunne, R. J. Williams and N. D. Martinez, Networks Topology and Biodiversity Loss in Food Webs: Robustness Increases With Connectance, Santa Fe Institute Working Paper 02-03-013 (2002).
R. Albert, H. Jeong, and A. L. Barabáasi, Nature 406, 378–382 (2000).
S. Maslov and K. Sneppen, Science 296, 309–313 (2002).
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Bonchev, D., Buck, G.A. (2005). Quantitative Measures of Network Complexity. In: Bonchev, D., Rouvray, D.H. (eds) Complexity in Chemistry, Biology, and Ecology. Springer, Boston, MA. https://doi.org/10.1007/0-387-25871-X_5
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