Centrality and Composition of Four-node Motifs in Metabolic Networks

Analysing subgraph patterns and recurring motifs in networks is a useful way to understand their local topology and func- tion. Motifs have been considered useful in analysing design patterns of networks as well. Three-node patterns (triads) in metabolic networks have been studied to some extent producing classification of organisms based on triads, but their network placement was not analysed. We obtain the frequencies of all four-node subgraphs in a wide range of metabolic networks. We construct significance profiles of subgraphs and employ correlation analysis to compare and contrast these profiles, highlight- ing four-node motifs. We then compute specific centrality measures of nodes involved in each subgraph, namely betweenness centrality and closeness centrality. We observe that multiple four-node motifs exist in metabolic networks. The correlation analysis shows that the significance profiles of Eukaryotic networks are highly correlated across organisms, whereas those of the Prokaryotic networks are correlated less so. The centrality indices of nodes that participate in identified network motifs are shown to be quite high. The analysis provides a tool to pinpoint the transition between evolution stages of Prokaryotic and Eukaryotic metabolic networks.