On the shape of Gaussian scale-free polymer networks

We consider the model of complex hyperbranched polymer structures formed on the basis of scale-free graphs, where functionalities (degrees)kof nodes obey a power-law decaying probabilityp(k)∼k-α. Such polymer topologies can be considered as generalization of regular hierarchical dendrimer structures with fixed functionalities. The conformational size and shape characteristics, such as averaged asphericity⟨A3⟩and size ratiogof such polymer networks are obtained numerically by application of Wei's method, which defines the configurations of any complex Gaussian network in terms of eigenvalue spectra of the corresponding Kirchhoff matrix. Our quantitative results indicate, in particular, an increase of compactness and symmetry of network structures with the decrease of parameterα.