Assortativity and information in directed biological networks

We analyse the relationship between assortative mixing and information content in biological networks which are typically directed. We develop the theoretical background for analysing mixing patterns in directed networks before applying them to specific biological networks. Two new quantities are introduced, namely the in-assortativity and the out-assortativity, which are shown to be useful in quantifying assortative mixing in directed networks. We also introduce a general measure for information content in directed networks, followed by the 'out-information' and 'in-information' to quantify the information content of out-degree and in-degree mixing patterns respectively. We apply the measures introduced to a range of real world networks, demonstrating that out-degree mixing patterns contain the highest amount of information in most real world biological networks.