Spectral identification of networks using sparse measurements
For researchers studying large-scale networks, this provides a way to infer global network properties without full topology identification, though the method is limited to diffusively-coupled networks with stable equilibria.
The paper introduces spectral network identification, a method to recover global spectral properties of a network from sparse local measurements (possibly one node). Numerical simulations demonstrate detecting the mean number of connections or the addition of a new vertex using measurements from a single node.
We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph topology, we focus on the identification of the spectral graph-theoretic properties of the network, a framework that we call spectral network identification. The main theoretical results connect the spectral properties of the network to the spectral properties of the dynamics, which are well-defined in the context of the so-called Koopman operator and can be extracted from data through the Dynamic Mode Decomposition algorithm. These results are obtained for networks of diffusively-coupled units that admit a stable equilibrium state. For large networks, a statistical approach is considered, which focuses on spectral moments of the network and is well-suited to the case of heterogeneous populations. Our framework provides efficient numerical methods to infer global information on the network from sparse local measurements at a few nodes. Numerical simulations show for instance the possibility of detecting the mean number of connections or the addition of a new vertex using measurements made at one single node, that need not be representative of the other nodes' properties.