Expansion and flooding in dynamic random networks with node churn

We study expansion and flooding in evolving graphs, when nodes and edges are continuously created and removed. We consider a model with Poisson node inter-arrival and exponential node survival times. Upon joining the network, a node connects to d = O(1) random nodes, while an edge disappears whenever one of its endpoints leaves the network. For this model, we show that, although the graph has Omega(d)(n) isolated nodes with large, constant probability, flooding still informs a fraction 1 - exp(-Omega(d)) of the nodes in time O(log n). Moreover, at any given time, the graph exhibits a "large-set expansion" property. We further consider a model in which each edge leaving the network is replaced by a fresh, random one. In this second case, we prove that flooding informs all nodes in time O(log n), with high probability. Moreover, the graph is a vertex expander with high probability.