Analysis of exponential trees via contraction method

The exponential trees model certain aspects of fast-growing social networks. In exponentially growing trees, each node independently attracts a new node with probability p, or not to attract with probability 1 − p. Recently, the size of these trees, number of leaves, profile and total path length are investigated. Here, we study the asymptotic behavior of the number of protected nodes, nodes that are not leaf and not all of their children are leaves. We also give some characterizations of the limit law of the total path length of protected nodes via contraction method.