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 model 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.