How Global Directionality and Hierarchy shape the Structure and Function of Directed Complex Networks

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My PhD concerned the study of directed complex networks and the application of a method known as Trophic Analysis to study these systems which can be as diverse as food webs, neural networks, social networks, the internet or economies. Trophic Analysis measures the global directional organisation of these systems as well as providing a local ranking of the nodes by their place in the hierarchical structure. Throughout my PhD I have been applying these methods to study various facets of directed complex systems. I have published work on a variety of topics. We studied how in directed Hopfield Neural Networks the global directionality and hierarchy can influence the ability to store and recover patterns as well as the fact that the location in the hierarchy of information presentation can affect the ability of networks to recall the pattern. We also showed some analytical results which show how emergence of strong connectivity in real directed networks can be predicted using Trophic Analysis and by using percolation theory on the edges which break the global directionality and incite the strongly connected component. We also have worked on the notion of influence and influenceability in a directed systems and showed the correlation between dynamical and structural notions of network influence and the directed ordering of the system as measured by Trophic Analysis. We are also working on notions to explain how ordered structures arise in directed systems by working on network generative models based on node fitness difference distributions.