#### Title

The Mathematical Foundations of Epistemic Network Analysis

#### Abstract

Epistemic network analysis (ENA) has been used in more than 300 published studies to date. However, there is no work in publication that describes the transformations that constitute ENA in formal mathematical terms. This paper provides such a description, focusing on the mathematical formulations that lead to two key affordances of ENA that are not present in other network analysis tools or multivariate analyses: (1) summary statistics that can be used to compare the differences in the content rather than the structure of networks and (2) network visualizations that provide information that is mathematically consistent with those statistics. Specifically, we describe the mathematical transformations by which ENA constructs matrix representations of discourse data, uses those representations to generate networks for units of analysis, places those networks into a metric space, identifies meaningful dimensions in the space, and positions the nodes of network graphs within that space so as to enable interpretation of those dimensions in terms of the content of the networks. We conclude with a discussion of how the mathematical formalisms of ENA can be used to model networks more generally.

#### Publication Title

Communications in Computer and Information Science

#### Recommended Citation

Bowman, D., Swiecki, Z., Cai, Z., Wang, Y., Eagan, B., & Linderoth, J.
(2021). The Mathematical Foundations of Epistemic Network Analysis.* Communications in Computer and Information Science**, 1312*, 91-105.
https://doi.org/10.1007/978-3-030-67788-6_7