modeling and analysis of composite network embeddings
In a composite network, a piece of information traveling through links in a social network may have to travel over multiple links in an associated communication network. In this paper, we propose a model of composite networks that consists of two networks and an embedding between them, and several composite metrics that characterize information flow under a particular type of embedding. We present analytic results for the scaling behavior of "constrained composite stretch" of a path, "constrained composite diameter" of a graph, and "constrained composite broadcast time" of a tree, under random uniform embeddings onto various communication network structures. We validate our analytical results on composite stretch using two data sets consisting of a friendship social network geographically spread across Western Europe and a historical deployment of a military chain of command. We also present a randomized model of field deployment consistent with real-world data, and use simulations over this model to explore the distribution of constrained composite broadcast time. Finally, we show that our analytical bounds for composite broadcast time agree well with the simulation results.
composite networks broadcast time simulation command and control path stretch composite graphs