This paper connects variance-covariance estimation methods, Gaussian graphical models, and the growing literature on economic and nancial networks. We construct the network using the concept of partial correlations which captures direct linear dependence between any two entities, conditional on dependence between all other entities. We relate the centrality measures of this network to shock propagation. The methodology is applied to construct the perceived network of the publicly traded Australian banks and their connections to the domestic nancial sector, real economy, and international markets. We find strong links between the big four Australian banks, the financial services sector and the other sectors of the economy and determine which entities play a central role in transmitting and absorbing the shocks.