Modeling message propagation in random graph networks

Message propagation is used in a wide range of applications, such as search in unstructured P2P overlays, modeling infection spread in epidemiology, and modeling the spread of gossip in social networks. For example, in a P2P network that has an unstructured overlay, search for a piece of information is conducted by propagating the query message within the network, usually with the desire that as many nodes as possible are covered with as few message forwardings as possible. In this paper, we study the behavior of the message propagation process in random graph networks and give a simple model to describe this process. When applied to a large network with random graph topology, the message propagation process can usually be modeled as a random pick process or the coupon collection problem. We show that these models are less accurate when the number of covered nodes becomes large. We investigate the inaccuracy and then propose refined models which remedy the factors that cause the error. The refined models have been confirmed by our simulations to effectively compensate for the errors, especially under high coverage conditions. Thus, when a large number of messages is expected to be used in the message propagation process, the refined models of higher orders are essential.