Measuring nodal contribution to global network robustness

Network centrality indices are quantification of the fact that some nodes/edges are more central or more important in a network than others. Different centrality indices are suitable for different applications, but most of them have structural significance and require that the network be connected. Most centrality measures are only definitions and there hasn't been much work done in measuring the effectiveness of the measure in describing a network's performance, robustness and survivability. In this work, we have quantified the importance of a node that its centrality index implicates. We have conducted empirical analysis on different network robustness measures. The contribution of a node to these measures is studied as a function of its centrality index. We also propose a new type of betweenness centrality that is based on the flow circulating in a network. We compare circulation-based betweenness, eigenvector and shortest-path based betweenness centralities using network average clustering and shortest-path based network efficiency.