Essential proteins are critical to the development and survival of cells. Identification of essential proteins is helpful for understanding the minimal set of required genes in a living cell and for designing new drugs. To detect essential proteins, various computational methods have been proposed based on protein-protein interaction (PPI) networks. However, protein interaction data obtained by high-throughput experiments usually contain high false positives, which negatively impacts the accuracy of essential protein detection. Moreover, most existing studies focused on the local information of proteins in PPI networks, while ignoring the influence of indirect protein interactions on essentiality. In this paper, we propose a novel method, called Essentiality Ranking (EssRank in short), to boost the accuracy of essential protein detection. To deal with the inaccuracy of PPI data, confidence scores of interactions are evaluated by integrating various biological information. Weighted edge clustering coefficient (WECC), considering both interaction confidence scores and network topology, is proposed to calculate edge weights in PPI networks. The weight of each node is evaluated by the sum of WECC values of its linking edges. A random walk method, making use of both direct and indirect protein interactions, is then employed to calculate protein essentiality iteratively. Experimental results on the yeast PPI network show that EssRank outperforms most existing methods, including the most commonly-used centrality measures (SC, DC, BC, CC, IC, and EC), topology based methods (DMNC and NC) and the data integrating method IEW.