Time-varying graphs and dynamic networks

The past decade has seen intensive research efforts on highly dynamic wireless and mobile networks (variously called delay-tolerant, disruptivetolerant, challenged, opportunistic, etc) whose essential feature is a possible absence of end-to-end communication routes at any instant. As part of these efforts, a number of important concepts have been identified, based on new meanings of distance and connectivity. The main contribution of this paper is to review and integrate the collection of these concepts, formalisms, and related results found in the literature into a unified coherent framework, called TVG (for timevarying graphs). Besides this definitional work, we connect the various assumptions through a hierarchy of classes of TVGs defined with respect to properties with algorithmic significance in distributed computing. One of these classes coincides with the family of dynamic graphs over which population protocols are defined. We examine the (strict) inclusion hierarchy among the classes. The paper also provides a quick review of recent stochastic models for dynamic networks that aim to enable analytical investigation of the dynamics.