Flooding in dynamic graphs with arbitrary degree sequence

This paper addresses the flooding problem in dynamic graphs, where flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t'> t. In particular, we show that a technique developed in a previous paper, for analyzing flooding in a Markovian sequence of Erdos-Renyi graphs, is robust enough to be used also in different contexts. We establish this by analyzing flooding in a sequence of graphs drawn independently at random according to a model of random graphs with given expected degree sequence. In the prominent case of power-law degree distributions, we prove that flooding takes almost surely O(log n) steps even if, almost surely, none of the graphs in the sequence is connected. In the general case of graphs with an arbitrary degree sequence, we prove several upper bounds on the flooding time, which depend on specific properties of the degree sequence. We believe that these results provide an interesting first step towards the complete analysis of the flooding completion time in the case of more realistic evolving graph models.