Systemic risk quantification in the current literature is concentrated on market-based methods such as CoVaR(Adrian and Brunnermeier (2016)). Although it is easily implemented, the interactions among the variables of interest and their joint distribution are less addressed. To quantify systemic risk in a system-wide perspective, we propose a network-based factor copula approach to study systemic risk in a network of systemically important financial institutions (SIFIs). The factor copula model offers a variety of dependencies/tail dependencies conditional on the chosen factor; thus constructing conditional network. Given the network, we identify the most 'connected' SIFI as the central SIFI, and demonstrate that its systemic risk exceeds that of non-central SIFIs. Our identification of central SIFIs shows a coincidence with the bucket approach proposed by the Basel Committee on Banking Supervision, but places more emphasis on modeling the interplay among SIFIs in order to generate systemwide quantifications. The network defined by the tail dependence matrix is preferable to that defined by the Pearson correlation matrix since it confirms that the identified central SIFI through it severely impacts the system. This study contributes to quantifying and ranking the systemic importance of SIFIs.