Maximum Likelihood Estimation for ErdsRnyi Graphs: Applications and Limitations in Social Network Analysis

This study explores the use of Maximum Likelihood Estimation (MLE) to infer the edge probability parameter, p, in ErdsRnyi (ER) graphs, which are foundational in the analysis of social networks. MLE is meticulously applied to derive p, with its accuracy validated through a series of simulations that demonstrate the methods efficacy in both synthetic and real-world settings. The research highlights that MLE achieves lower percentage errors as the network size increases, confirming its scalability. A case study focusing on a high school friendship network further underscores the practicality of MLE in operational settings such as friend recommendation systems, enhancing its relevance to everyday applications. However, the study also points out the limitations due to the assumption of uniform edge probability within the ER model, which may not hold in more complex, heterogeneous network structures often observed in real-world social systems. These findings prompt a call for the development of more robust models that can handle diverse network scenarios, suggesting a potential direction for future research to expand the applicability of MLE in network analysis.