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Application of Graph Theory in Social Network Analysis
- 1 1University of California, Santa Barbara, Santa Barbara, USA; 2Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA
* Author to whom correspondence should be addressed.
Abstract
This literature review aims to discuss the application of graph theory in analyzing social and information networks. We first introduce some key network properties, such as clustering coefficient (transitivity), centrality, and diameter, which are crucial for understanding the dynamics of information dissemination within networks. Then, we talk about, based on these properties, how graph theory can be utilized to analyze social and information networks. Lastly, we provide an overview of various fundamental social and information models including the SIR model and the Linear Threshold model. For the SIR model, we go over the definition of the SIR model, explore the mathematical methods applied to analyze the SIR model, provide one example of how the SIR model reflects the nodes’ status in the network, and discuss the application of the SIR model in Covid-19 epidemic. For the Linear Threshold model, we review its basic properties and explain how it can be used to calculate the maximum influence in a network
Keywords
Graph Theory, Social and Information Networks, SIR model, and Linear Threshold model
[1]. Granovetter, M.S. (1973) The Strength of Weak Ties. American Journal of Sociology, 78, 1360-1380.
[2]. Christakis, N.A. and Fowler, J.H. (2007) The Spread of Obesity in a Large Social Network over 32 Years. The New England Journal of Medicine, 357, 370-379.
[3]. Newman, M.E.J. (2003) The Structure and Function of Complex Networks. SIAM Review, 45, 167-256.
[4]. Pastor-Satorras, R., & Vespignani, A. (2001) Epidemic Spreading in Scale-free Networks. Physical Review Letters 86, 3200-3203.
[5]. Watts, D. and Strogatz, S. (1998) Collective dynamics of ‘small-world’ networks. Nature 393, 440–442.
[6]. Newman, M. E. J. (2010) Networks: An Introduction. Oxford University Press.
[7]. Freeman, L. C. (1977) A set of measures of centrality based on betweenness. Sociometry 40, 35-41.
[8]. Evans, T.S. and Chen, B. (2022) Linking the network centrality measures closeness and degree. Commun Phys 5, 172.
[9]. Li M., Wang X., Gao K. and Zhang S. (2017) A survey on information diffusion in online social networks: models and methods. Information 8, 118.
[10]. Kermack W.O. and McKendrick A.G., (1927) A contribution to the mathematical theory of epidemics. The Royal Society 115, 700–721.
[11]. Postnikov, E.B. (2020) “Estimation of COVID-19 dynamics "on a back-of-envelope": Does the simplest SIR model provide quantitative parameters and predictions?”. Chaos, solitons, and fractals vol. 135, 109841.
[12]. Watts D.J., (2002) A simple model of global cascades on random networks, Proc. Natl. Acad. Sci. U.S.A.99, 5766-5771.
[13]. Chen W., Yuan Y. and Zhang L., (2010) "Scalable Influence Maximization in Social Networks under the Linear Threshold Model," 2010 IEEE International Conference on Data Mining, Sydney, NSW, Australia, 88-97.
[14]. Huang, DW. and Yu, ZG. (2017) Dynamic-Sensitive centrality of nodes in temporal networks. Sci Rep7, 41454.
[15]. Turker, M., Bingol, H.O. [2023] Multi-layer network approach in modeling epidemics in an urban town. Eur. Phys. J. B 96, 16.
Cite this article
Wang,S. (2025). Application of Graph Theory in Social Network Analysis. Theoretical and Natural Science,79,173-179.
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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
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