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Optimal Inference of Social Network Structure: A Maximum Likelihood Framework for Erdős–Rényi Models
- 1 Nanjing Foreign Language School, Nanjing, China
* Author to whom correspondence should be addressed.
Abstract
In contemporary society, social networks have played a conspicuous role in people’s life, yet accurately analyzing them is still challenging. This paper applies maximum likelihood estimation for Erdős–Rényi graph in social network analysis. It begins with interpreting the significance of social network analysis and the objective of the research. Subsequently, theoretical knowledge of Erdős–Rényi graph and Maximum Likelihood Estimation are presented, including definitions, properties, and the derivation of Maximum Likelihood Estimation calculation formula for estimating the probability of connection in Erdős–Rényi graph. After that, a real-world example is involved in order to thoroughly comprehend the mechanism of this model. Through multiple trials of simulations, the accuracy of Maximum Likelihood Estimation is explored by illustrating a graph about the relationship between the number of nodes and percentage error with the help of python program, revealing the trend that a larger network size contributes to a more accurate estimation. The advantages, including simplicity and statistical rigor and disadvantages that contain the uniform assumption of connection probability and limitations are comprehensively analyzed as well, followed by a proposal of future research directions related to a more sophisticate model added by functions in order to be applied to friendship social networks, aiming to offer insights to further studies.
Keywords
Erdős–Rényi Graph, Maximum Likelihood Estimation, Social Network Analysis, Adjacency Matrix
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Cite this article
Tao,C. (2025). Optimal Inference of Social Network Structure: A Maximum Likelihood Framework for Erdős–Rényi Models. Theoretical and Natural Science,100,165-171.
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Volume title: Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation
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