Analysis of the Robustness Dynamics of Wireless Mobile Ad Hoc Networks via Time Varying Dual Basis Representation

Many network models are too complex to readily identify which structural aspects of a network are most influential on robustness. To analyze the dynamics and robustness of a network, many of the protocol details can be reduced to a graph theory representation of nodes, links and link weights. Our method uses the spectral analysis of the Laplacian matrix to decouple the interactions between nodes to analyze the robustness of a wireless mobile ad hoc network (MANET) with a time-varying wireless channel. This spectral analysis and the resulting algebraic connectivity can be used to determine how robust a network is, where the weak links are, and how to best increase overall performance of a network. Using a simulation of wireless devices in a MANET with a time-varying channel, we show that robustness is a function of time, that nodes become coupled and decoupled as the structure of the network changes and that any robustness analysis is more complete when more than a single Eigen value is evaluated.