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DNA rearrangement processes recombine gene segments that are organized on thechromosome in a variety of ways. The segments can overlap, interleave or onemay be a subsegment of another. We use directed graphs to represent segmentorganizations on a given locus where contigs containing rearranged segmentsrepresent vertices and the edges correspond to the segment relationships. Usinggraph properties we associate a point in a higher dimensional Euclidean spaceto each graph such that cluster formations and analysis can be performed withmethods from topological data analysis. The method is applied to a recentlysequenced model organism \textit{Oxytricha trifallax}, a species of ciliatewith highly scrambled genome that undergoes massive rearrangement process afterconjugation. The analysis shows some emerging star-like graph structuresindicating that segments of a single gene can interleave, or even contain allof the segments from fifteen or more other genes in between its segments. Wealso observe that as many as six genes can have their segments mutuallyinterleaving or overlapping.

Graph Based Analysis for Gene Segment Organization In a Scrambled Genome