Decomposition of flux distributions into metabolic pathways

3-way networks: application of hypergraphs for modelling increased complexity in comparative genomics

We present and develop the theory of 3-way networks, a type of hypergraph in which each edge models relationships between triplets of objects as opposed to pairs of objects as done by standard network models. We explore approaches of how to prune these 3-way networks, illustrate their utility in comparative genomics and demonstrate how they find relationships which would be missed by standard 2-way network models using a phylogenomic dataset of 211 bacterial genomes.

Genomes contain the information underlying the molecular functions of an organism. One way to compare the entire genomes of different organisms is to compare their gene-family content profiles which is effectively a comparison of their functional potential. Standard networks, when used to model phylogenomic similarities, are not capable of capturing some of the underlying complexity of the relationships between genomes. In order to address this, we have developed a new three-way similarity metric and constructed three-way networks modelling the relationships between 211 bacterial genomes. We find that such three-way networks find cross-species genomic similarities that would have been otherwise missed by simpler models such as standard networks.