Over the past decade, there has been a concerted effort to develop a network science for studying physical, biological, social, and information networks within a common framework.  Of particular interest is the understanding of connectivity, information dynamics, and robustness in large-scale networks with spatial location and mobility.  In this talk, we discuss a number of recent results from the application of network science ideas to mobile wireless communication.

We first study connectivity and information dissemination in large-scale wireless networks modelled by random geometric graphs with dynamic on-off links.   Using a percolation-based perspective, we show that the delay for information dissemination exhibits two behavioral regimes, corresponding to a phase transition of the underlying network connectivity. When the dynamic network is in the subcritical phase, ignoring propagation delays, the dissemination delay scales linearly with the Euclidean distance between the sender and the receiver. When the dynamic network is in the supercritical phase, the delay scales sublinearly with the distance.  More interestingly, by using a new analysis which maps a network of mobile nodes to a network of stationary nodes with dynamic links, we show that the above results can be used to characterize information dissemination in wireless networks with mobile nodes.

Next, we study the resilience of wireless networks to node failures.  In sensor networks exposed to natural hazards and battery constraints, and in military networks exposed to enemy attack, node failure is a common occurrence.  The failure of a node often depends on its degree, which may reflect the amount of traffic load on the node, or the relative importance of the node.  Furthermore, in networks carrying traffic load, the failure of one node can result in redistribution of the load onto other nearby nodes. If these nodes fail due to excessive load, then this process can result in a cascading failure.  From the percolation perspective, the resilience of the network can be characterized in terms of whether correlated node failures lead to a large connected component of failed nodes or not.  Using this approach, we obtain analytic conditions on the existence or non-existence of correlated and cascading failures.

Finally, we discuss potential application of these results to other important problems such as cascading failures in power networks, and the spread of epidemics among humans.