What determines the stability of networks inferred from dynamical behavior of a system? Internal and external shocks in a system can destabilize the topological properties of comovement networks. In real-world data, this creates a trade-off between identification of turbulent periods and the problem of high dimensionality. Longer time-series reduces the problem of high dimensionality, but suffers from mixing turbulent and non-turbulent periods. Shorter time-series can identify periods of turbulence more accurately, but introduces the problem of high dimensionality, so that the underlying linkages cannot be estimated precisely. In this paper, we exploit high-frequency multivariate financial data to analyze the origin of instability in the inferred networks during periods free from external disturbances. We show that the topological properties captured via centrality ordering is highly unstable even during such non-turbulent periods. Simulation results with multivariate Gaussian and fat-tailed stochastic process calibrated to financial data show that both sampling frequencies and the presence of outliers cause instability in the inferred network. We conclude that instability of network properties do not necessarily indicate systemic instability. Graphical abstract