On the complexity of directed biological networks

Recently, there was an increased interest towards network approach to biology and environmental sciences. Networks are believed to be the key to the understanding of the work of biological machine in cells, organs, organisms, and ecosystems. While complexity of undirected networks has been recently analyzed, the assessment of complexity in directed networks has specificity that has not been explored so far. The present paper aims to address the existing gap by discussing the applicability of the available complexity descriptors. New specific measures (vertex accessibility, accessible connectedness, and adjusted average distance) are introduced based on assessment of the reduced accessibility of nodes in directed networks.