Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems - delay-tolerant networks, opportunistic-mobility networks, social networks - obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts can be viewed as fragments of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Besides this definitional work, we articulate both existing works and original suggestions around three main federative motifs. They are, a hierarchy of classes of TVGs defined with respects to properties that showed algorithmic significance in distributed computing; the problem of analyzing complex dynamic networks, in particular recognizing properties on the network dynamics and capturing emerging phenomena; and finally, the description of some techniques to study dynamic networks from a stochastic, yet analytical, perspective.