An Efficient Approximation of Betweenness Centrality for Uncertain Graphs

Betweenness centrality measures the centrality of nodes and edges in a graph based on the concept of shortest paths. However, such a definition is unsuitable for uncertain graphs due to the uncertainty of links. In the possible-world semantics, the Monte Carlo method is proposed to estimate the betweenness centrality of uncertain graphs. However, this method is computationally intensive. To address this challenging issue, in this paper, we propose the concept of possible shortest paths and develop a metric to approximate the betweenness centrality for uncertain graphs. We demonstrate that the new metric of betweenness centrality generalizes the deterministic one. Unfortunately, it is NP-hard to enumerate all possible shortest paths between two nodes exhaustively. To tackle this difficulty, we design a heuristic algorithm to explore the majority of possible shortest paths efficiently. Our method avoids the sampling process in the Monte Carlo method, and thus significantly improves the computational efficiency. We conduct extensive experiments to evaluate the effectiveness and efficiency of our method. The experimental results show that our approach can approximate the centrality of uncertain graphs accurately with high efficiency. Finally, we apply our method to the Internet network to evaluate the importance of autonomous systems.