Evolving mortal networks

We discuss a class of models for the evolution of tree networks in which new nodes are recruited into the network at random times, and nodes already in the network may die at random times. Stochastic mechanisms for growth and death of the network that are either sensitive or insensitive to the coordination number or degree of nodes are studied using simulations and mean-field approximations. Critical behavior is observed in the long-time coordination number distribution of the system; associated exponents are universal in one part of parameter space, but depend on the ratio of birth and death parameters elsewhere.