A Structural Analysis of Population Graphs

TL;DR

This paper analyzes population graphs constructed from genomic data, proving metric properties of a distance measure, developing a visualization algorithm, and statistically comparing these graphs to other types.

Contribution

It introduces a new algorithm for constructing population graphs and provides a statistical analysis distinguishing them from random and small-world graphs.

Findings

GENPOFAD distance is a metric function.

Population graphs differ significantly from random graphs.

Population graphs also differ from small-world graphs.

Abstract

The format of graphing algorithms for genomic data has been a debate in recent biotechnology. In this paper, we discuss the construction of population graphs using said genomic data. We first examine the GENPOFAD distance measurement, developed by Joly et. al., and prove that this constitutes a metric function. We develop an algorithm to construct graphs to visualize the relationships between individuals in a population. We then provide a statistical analysis of these simulated population graphs, and show that they are distinct from randomly generated graphs, and also show differences from small-world graphs.