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We propose methods to estimate centrality in Smart-Grid Networks (SGNs) from the view of a flow-based approach. In several network categories, centrality metrics, such as degree, closeness and betweenness, have provided ways to investigate the importance or weakness of components. These well-known metrics utilize either non-global or shortest-path information. We mention several observations which try to use these metrics into a vulnerability measure of SGNs. For this, we stress that using a proper metric, which captures the core network characteristic, is important to induce a correct network analysis. This proper metric changes with network categories. In contrast to data networks, SGNs possess a fundamentally different property that comes from electricity distributions and this requires us to include a multi-path consideration. About this issue, we explain the feasibility of flow-based analysis and suggest to utilize an effective resistance as a distance measure. This allows us to propose new centrality metrics utilizable in SGNs. In several power grid test-beds, our metrics are tested and the differences from using current centrality metrics are compared. These results indicate that SGNs are more scale-free than the estimation from currently used metrics and provide the reason for cascading failure phenomena observed in SGNs. Additionally, we show that the multi-path effect becomes more severe with a network size increment.