We propose a framework for estimation of spillovers between funding costs of individual banks. The estimation proceeds in three steps: First, using data from liquidity auctions of the European Central Bank, we estimate the funding costs in a given week for each individual bank. In the second step, we apply the adaptive elastic net (a LASSO type estimator) to this panel to estimate the financial network. Finally, using the estimated network we propose new measures of the systemicness and vulnerability of each bank. Our measure of systemicness has quite a natural interpretation, since it can roughly be viewed as the total externality a bank would impose on the funding costs of all other banks in the system. We estimate that most of the banks have fairly weak links and, therefore, if one were to suffer an adverse shock there would likely be a rather limited effect on the other ones. On the other hand, there are a few banks that are quite central: an increase in their funding costs would result in a very significant increase (up to 95 bp per 100 bp shock) in the funding costs of the other banks. Our vulnerability scores estimated using data from 2007-2008 are positively correlated with the probability of a bank being bailed out later.