Combinatorial Models for Cooperation Networks

We analyze special random network models - so-called thickened trees which are constructed by random trees where the nodes are replaced by local clusters. These objects serve as models for random real world networks. It is shown that under a symmetry condition for the cluster sets a local-global principle for the degree distribution holds: the degrees given locally through the choice of the cluster sets directly affect the global degree distribution of the network. Furthermore, we show a superposition property when using clusters with different properties while building a thickened tree.