Our simulations show that the network arrangement, i.e. its rich-club organisation, plays an important role in the transition of the areas from desynchronous to synchronous behaviours.

Scale-free networks are structures, whose nodes have degree distributions that follow a power law. Here we focus on the dynamics of semiflexible scale-free polymer networks. The semiflexibility is modeled in the framework of [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], which allows for tree-like networks with arbitrary architectures to include local constrains on bond orientations. From the wealth of dynamical quantities we choose the mechanical relaxation moduli (the loss modulus) and the static behavior is studied by looking at the radius of gyration. First we study the influence of the network size and of the stiffness parameter on the dynamical quantities, keeping constant γ, a parameter that measures the connectivity of the scale-free network. Then we vary the parameter γ and we keep constant the size of the structures. This fact allows us to study in detail the crossover behavior from a simple linear semiflexible chain to a star-like structure. We show that the semiflexibility of the scale-free networks clearly manifests itself by displaying macroscopically distinguishable behaviors.

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Small-world structures are often used to describe structural connections in the brain. In this work, we compare the strucutural connection of cortical areas of a healthy brain and a brain affected by Alzheimer's disease with artificial small-world networks. Based on statistics analysis, we demonstrate that similar smallworld networks can be constructed using Newman-Watts procedure. The network quantifiers of both structural matrices are identified inside the probabilistic valley. Despite of similarities between strcutural connection matrices and sampled small-world networks, increased assortivity can be found in the Alzheimer brain. Our results indicate that network quantifiers can be helpful to identify abnormalities in real structural connection matrices.

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