An Interdisciplinary Review on Application of Graph Theory
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Abstract
Graph theory is a branch of discrete mathematics that is used to model and analyze interconnected systems. This paper presents a review on application of its concepts and algorithms that support diverse applications in computer science, biology, neuroscience, social sciences, engineering and geosciences. It is also reviewedthat graph theory helped in network optimization, clustering, molecular modelling and brain connectivity, it provides powerful tools for solving complex problems. It is reviewed that spectral methods, probabilistic models and graph neural network let the graph theory to evolve continuously as an essential interdisciplinary framework for understanding and optimizing complex networks in the modern world.
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References
Archdeacon, D.: Topological Graph Theory, A Survey.
Balaban, A. T.: Applications of Graph Theory in Chemistry , J. Chem. InJCompur. Sci. (1985),25, 334-343
Barnes, J.A. and Harary, F.: Graph Theory in Network Analysis , Social Networks, Volume 5, (1983) 235-244.
Bandelt , H.J and Chepoi, V.: Metric Graph Theory and Geometry: A Survey, (1991).
Berge, C.: Two Theorems in Graph Theory, (1957).
Bondy, J. A.: A Method n Graph Theory, North-Holland Publishing Company,15 (1976)
Bunn, A. G., Urban D. L. and Keitt, T. H.: Landscape connectivity: A conservation application of graph theory, Journal of Environmental Management (2000) 59, 265–278,doi:10.1006/jema.2000.0373, available online at http://www.idealibrary.com on
Chung, F.: Graph Theory in the Information Age, AMS-MAA-SIAM Annual Meeting, Volume 57, Number 6,(2009).
Derrible, S. and Kennedy, C.: Applications of Graph Theory and Network Science to Transit Network Design, Transport Reviews: A Transnational Transdisciplinar Journal, 31:4, (2011),495-519, DOI: 10.1080/01441647.2010.543709.
Dobrjansky, L. and Freudenstein, F.: Some Applications of Graph Theory to the Structural Analysis of Mechanisms, Journal of Engineering for Industry, (1 9 6 7)
Erdős, P.: Graph Theory and Probability, Cambridge University Press, (1959). https://doi.org/10.4153/CJM-1959-003-9
Erdős, P.: Graph Theory And Probability II, Cambridge University Press, (1960),https://doi.org/10.4153/CJM-1961-029-9.
Erdős, P.: Problems and Results In Combinatorial Analysis and Graph Theory, Discrete Mathematics (1988) 81-92.
Gao, W., Wu, H. Kamran Siddiqui, M. QudairBaig, A.: Study of Biological Networks Using Graph Theory, Saudi Journal of Biological Sciences (2017), doi:https://doi.org/10.1016/j.sjbs.2017.11.022.
Harary, F. and Norman, R.Z.: Graph Theory as a Mathematical Model in Social Science, University of Michigan, Institute for Social Research, (1953).
Hubert, L. J.: Some Applications Of Graph Theory To Clustering, Psychometrika, Volume 39,No. 3, (1974).
Jacobs, D.J., Rader, A.J. , Kuhn, L. A. and Thorpe, M.F.: Protein Flexibility Predictions Using Graph Theory, Proteins: Structure, Function, and Genetics 44, (2001), 150–165.
Mackaness, W. A. and Beard, M. K.: Use of Graph Theory to Support Map Generalization, Cartography and Geographic Information Systems, 20, (1993) 210 - 221.
Mondal, B.and De, K.: An Overview Applications of Graph Theory in Real Field, IJSRCSEIT,( 2017) Volume 2 Issue 5 | ISSN : 2456-3307
Prathik, A. Uma, K. and Anuradha J.: An Overview of application of Graph Theory, International Journal of Chem Tech Research, Vol.9, No.02,(2016), pp 242-248, ISSN: 0974-4290.
Phillips, J.D., Schwanghart, W. and Heckmann, T.: Graph Theory In The Geosciences, EarthScience Reviews 143 (2015) 147–160
Reijneveld, J.C., Ponten, S. C., Berendse, H. W. and Cornelis J. Stam, C.J.:Invited Review The Application of Graph Theoretical Analysis to Complex Networks in the Brain, Elsevier Ireland Ltd,(2007), doi:10.1016/j.clinph.2007.08.010
Spielman, D. A.: Spectral Graph Theory and its Applications, 48th Annual IEEE Symposium on Foundations of Computer Science,(2007).
Stam, C,.J. and Reijneveld, J. C.: Graph theoretical analysis of complex networks in the brain, Nonlinear Biomedical Physics 2007 Volume 1, No. 3. doi:10.1186/1753-4631-1-3
Swarup, K. Gupta, P.K. & Mohan, M.: Operations Research, 2008.
Taha, H.A: Operations Research An Introduction, Pearson Education, Eigth Edition, 2011
Thomson, R.C & Richardson, D.E.: A Graph Theory Approach to Road Network Generalization, Oral Presentation 354.
Vergniory, M. G., Elcoro, L., Wang, Z., Cano, J., Felser, C., Aroyo M. I., Bernevig, B. A. and Bradlyn, B.: Graph theory data for topological quantum chemistry, APS Physics, (2017) DOI:10.1103/PhysRevE.96.023310.
Wilson, R.C., Hancock, E.R. and Luo, B.: Pattern Vectors from Algebraic Graph Theory, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 27, No. 7, (2005).