Plug-and-Play Networks - Adding Vertices and Connections to Preserve Algebraic Connectivity.

In many networked dynamic systems, algebraic connectivity plays a key role in important system properties such as stability, string stability and rate of convergence. There has therefore been recent interest in classes of networks (e.g. expander networks, random networks) that have good algebraic connectivity properties while maintaining a low nodal degree. In this paper, we give some initial results on methods to allow addition of agents to an existing network. We are particularly interested in methods with minimal disruption to the existing network and which preserve, to the extent possible, algebraic connectivity properties. To this end upon connection of a node any new connections must preserve an upper bound on the degree of all vertices and no existing connections may be severed. We find conditions on the ability to connect nodes and give some indicative studies on the problem of new link selection.