Large-scale social networks often show regular common structures despite coming from independent individuals’ behaviors. One of the most important frameworks for understanding these networks is the small-world framework, originally introduced by Watts and Strogatz [1], which qualifies networks that simultaneously show high local clustering, and short global path lengths. The small world structure has been seen in various contexts, including neural networks, power grids, and online social platforms. The degree to which real-world social networks conform to these idealized small-world models, however, and which parameters best reproduce the observed structures remains a practically relevant question.
Online social networks, such as Twitter (now known as X), provide a relevant testing ground for investigating small-world network properties. Twitter combines cataloged individual social connections with large-scale networks, making its structural organization important to social measurements ranging from the speed of spread of a viral post to group opinion formation. Many previous analyses rely on either simplified metrics or models that do not directly compare empirical data to synthetic networks constructed under controlled parameters.
Therefore the central question of this report is: To what extent does a Twitter ego network exhibit small-world properties, and can these properties be quantitatively reproduced by a Watts-Strogatz type small-world model?
To answer this question, the clustering coefficient and average shortest path length of the combined ego networks are compared to those of several different synthetic network types. These types are a regular lattice, a random graph, and small-world networks which are generated by varying the rewiring probability coefficient. By normalizing the Twitter data relative to a regular lattice baseline graph, this study shows these Twitter networks within the larger space defined by network models. It shows both whether Twitter shows small-world behavior, and how strongly it does so compared to relative benchmarks.
To run the Jupyter Notebook for this project, first download the notebook file from this repository and the Twitter ego network dataset from the SNAP website: https://snap.stanford.edu/data/ego-Twitter.html
Unzip the dataset and ensure the data files are placed in the expected directory structure referenced by the notebook.
To Run the set, ensure all dependencies are installed and then run the cells sequentially.
This project requires Python 3.8+ and the following Python libraries:
numpy scipy pandas networkx matplotlib seaborn jupyter