#### Project Title

### A Random Graph Algorithm for Modeling Social Networks

#### Disciplines

Applied Statistics | Data Science | Discrete Mathematics and Combinatorics | Numerical Analysis and Computation | Probability | Statistical Models | Theory and Algorithms

#### Abstract (300 words maximum)

A common goal in the network analysis community is the modeling of social network graphs, which tend to exhibit low average path length, high clustering, and a power law degree distribution. However, most existing attempts to do so fall short on one or more of these properties. Here, a novel approach is utilized, which uses an older algorithm over many iterations to generate the bulk of the nodes, as well as a modified version for the highly connected ‘influencer’ nodes. Several statistical expectations of the model were derived and compared to values calculated from simulations. The model, when tuned correctly, reasonably mimics the properties displayed by social network graphs. This algorithm not only provides a quick-performing method to model social network graphs, but also a possible alternative for modeling other types of graphs, given proper appropriate hyperparameter tuning.

#### Academic department under which the project should be listed

CCSE - Data Science and Analytics

#### Primary Investigator (PI) Name

Andrew Wilson

A Random Graph Algorithm for Modeling Social Networks

A common goal in the network analysis community is the modeling of social network graphs, which tend to exhibit low average path length, high clustering, and a power law degree distribution. However, most existing attempts to do so fall short on one or more of these properties. Here, a novel approach is utilized, which uses an older algorithm over many iterations to generate the bulk of the nodes, as well as a modified version for the highly connected ‘influencer’ nodes. Several statistical expectations of the model were derived and compared to values calculated from simulations. The model, when tuned correctly, reasonably mimics the properties displayed by social network graphs. This algorithm not only provides a quick-performing method to model social network graphs, but also a possible alternative for modeling other types of graphs, given proper appropriate hyperparameter tuning.