A comprehensive statistical study of metabolic and protein-protein interaction network properties

Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs representing metabolic and proteinprotein interaction (PPI) networks. The focus of the analysis is, apart from the description of the main properties of the graphs, to identify those properties that deviate from the expected values had the networks been build by randomly linking nodes with the same degree distribution. This survey identifies the properties of biological networks which are not solely the result of the degree distribution of the networks, but emerge from the evolutionary pressures under which the network evolves. The findings suggest that, while PPI networks have properties that differ from their expected values in their randomized versions with great statistical significance, the differences for metabolic networks have a smaller statistical significance, though it is possible to identify some drift. We also investigate the quality of fits obtained for the nodes degree distributions to power-law functions. The fits for the metabolic networks do describe the distributions if one disregards nodes with degree equal to one, but in the case of PPI networks the power-law distribution poorly describes the data except for the far right tail covering around half or less of the total distribution.