Controlling edge dynamics in complex networks

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at http://github.com/ntamas/netctr

Controlling centrality in complex networks

Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network crucially depends on the entire pattern of connections, so that the usual approach is to compute node centralities once the network structure is assigned. We face here with the inverse problem, that is, we study how to modify the centrality scores of the nodes by acting on the structure of a given network. We show that there exist particular subsets of nodes, called controlling sets, which can assign any prescribed set of centrality values to all the nodes of a graph, by cooperatively tuning the weights of their out-going links. We found that many large networks from the real world have surprisingly small controlling sets, containing even less than 5 – 10% of the nodes

LOCAL CONTROLLABILITY OF BIOLOGICAL NETWORKS

Ph.DDOCTOR OF PHILOSOPH