Ephemeral networks with random availability of links: The case of fast networks

• We define the Temporal Diameter (TD) and the expected TD of temporal networks with random availabilities of links.
• We define fast and slow random temporal networks, according to their expected TD.
• Random temporal networks on instances of dense (directed) random graphs Gn,pGn,p are fast.
• We introduce the critical availability as a measure of periodic availability of links.
• We give a lower and an upper bound on the critical availability.

We consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We then provide a partial characterization of fast random temporal networks. We also define the critical availability as a measure of periodic random availability of the links of a network, required to make the network fast. We finally give a lower bound as well as an upper bound on the (critical) availability.