Interpolating and Extrapolating Node Counts in Colored Compacted de Bruijn Graphs for Pangenome Diversity

A pangenome is a collection of taxonomically related genomes, often from the same species, serving as a representation of their genomic diversity. The study of pangenomes, or pangenomics, aims to quantify and compare this diversity, which has significant relevance in fields such as medicine and biology. Originally conceptualized as sets of genes, pangenomes are now commonly represented as pangenome graphs. These graphs consist of nodes representing genomic sequences and edges connecting consecutive sequences within a genome. Among possible pangenome graphs, a common option is the compacted de Bruijn graph (cdBG). In our work, we focus on the colored cdBG (ccdBG), where each node is associated with a set of colors that indicate the genomes traversing it. In response to the evolution of pangenome representation, we introduce a novel method for comparing pangenomes by their node counts, addressing two main challenges: the variability in node counts arising from graphs constructed with different numbers of genomes and the large influence of rare genomic sequences. We propose an approach for interpolating and extrapolating node counts in ccdBGs, adjusting for the number of genomes. To tackle the influence of rare genomic sequences, we apply Hill numbers, a well-established diversity index previously utilized in ecology and metagenomics for similar purposes, to proportionally weight both rare and common nodes according to the frequency of genomes traversing them.