Topology tracking of static and dynamic networks based on structural equation models

Abstract

Most of the complex networks have hidden topologies, therefore, their structures must first be modeled in order to conduct meaningful network analytics. Structural equation models (SEMs) are from prominent network models and they often express the relationship between exogenous inputs of the network and outputs linearly. In this paper, based on SEMs, we propose a method to track the topology of static and dynamic networks over time. The static networks have fixed topologies while the topology of the dynamic networks changes over time. The proposed tracking algorithm will improve the topology estimation in static networks, and trace the changes of topology in dynamic networks. The important advantage of the proposed method is about exogenous inputs. Ordinary SEMs assume full knowledge of the exogenous inputs, which may not always be a correct hypothesis. We assume that the exogenous inputs are piecewise stationary and in each piece, the correlation matrix of the exogenous inputs is known, which is a more practical assumption than given exogenous inputs. Numerical tests demonstrate the effectiveness of the proposed algorithm in tracking the topology of static and dynamic networks.