This paper investigates the effects of contagion in interbank lending networks. I introduce a new measure based on the harmonic distance of Acemoglu et al. (2015b) and, motivated by their theoretical results, compare it to well-known centrality measures already applied in the systemic risk literature which do not take into account the structure of a contagion mechanism. I derive an explicit formula of size-adjusted harmonic distances and extend it with the usage of liquid assets for a heterogeneous banking system. The simulation results on scale-free and complete networks do not confirm that this new distance would perform better than "off-the-shelf" measures but its performance becomes similar to the best known measures in case of averaged networks which are applied in central banking analysis. This new measure is capable of identifying systemically important institutions and its time variation is also presented in an interbank network. I also test for the scale-free property of the Hungarian interbank lending network and besides, network measures as systemic risk indicators are analyzed on Hungarian data.