Many real-life processes can be thought of as dynamics on graphs. As a consequence, understanding how network architecture shapes, enhances or facilitates the dynamical function of a system is a major challenge in a multitude of fields, ranging from Neuroscience and Social Science to Production Logistics and Systems Biology. Here I will explore the relationship between structure and dynamics in complex networks using simple models of dynamical processes. As the main example, with Computational Neuroscience in mind, I discuss the relationships between structural connectivity (the network’s adjacency matrix) and functional connectivity (the network derived from similarities in dynamical behavior between nodes) for excitable dynamics on graphs [1,2,3]. Furthermore, I will employ random walks [4] and flow dynamics [5] to analyze, how network architecture influences the organization of dynamical processes on graphs.
[1] Müller-Linow, Hilgetag and Hütt (2008) PLoS Comp. Biol. 4, e1000190.
[2] Messé, Hütt, König and Hilgetag (2015) Sci. Rep. 5:7870.
[3] Garcia, Lesne, Hütt and Hilgetag (2012) Frontiers in Computational Neuroscience 6, 50.
[4] Kosmidis, Beber and Hütt (2015) Advances in Complex Systems, in press.
[5] Beber, Armbruster and Hütt (2013) European Physical Journal B 86, 473.
