james-kuo/fitting-network-models

Fitting and model checking a dynamic model for directed scale-free networks on a bitcoin network dataset.

Linear Preferential Attachment models are frequently used to theoretically explain why scale-free networks exist, or networks which have power-law as its degree distribution, but likelihood-based approaches are seldom done to test how well model explains data. I fitted such a model using a novel likelihood-based method developed in the literature on a bit-coin network in R and devised a set of heuristical and predictive checking simulation studies to examine how well model matches up with data. I developed the code from bottom-up for this project.

Final_Project.pdf is the paper. Kuo_Final_Presentation.pdf are the slides for an earlier version of the paper.

Functions.R, Analysis.R, and LinearAP.R are the main R codes which process the data, simulate the network, and estimate the model.

Bit.RData, SampleSim.RData, updated_graphs.RData and dynamics.RData are the processed datasets. soc-sign-bitcoinotc.csv is the raw dataset.

Some Pictures

Degree Distribution

A key aspect of the project is to see if degree distribution of the real network is well-captured by the model. The model hypothesized that both the in-degree and out-degree distributions of the real network will follow power law, meaning there will be a straight line in the log-log plot with a specified slope. Blue dots are what the degree distributions actually look like. Red dots are what the model predicts. A more rigorous statistical test (Kolmogorov-Smirnov test) shows the red and blue dots likely come from different distributions, so the model fails in this aspect.

A Picture of the Network

This is what the model says how the (scaled-down) bitcoin network should look like. Larger nodes have larger degrees (better connected).