Dynamic state determination of a software-defined network via dual basis representation

To maximize the performance of a software-defined network, a network observer must develop a state that can be tracked and controlled. We propose a novel method that uses the entire eigenspace of the Laplacian matrix to determine the state of a SDN. Our approach exploits the double orthogonality of the Laplacian matrix in order to define the dual basis. Each basis uses the entire reachability space with the objective of fully describing the centrality of each node over time. The reachability space is defined by the dual basis once the null space has been removed. The definition of the dual basis allows the network controller to observe the network state to determine which areas are most utilized and least utilized. Once the state has been estimated, the controller may choose to correct the network state by rerouting flows or preventing additional flows.