This paper introduces a new algorithm for computing betweenness centrality, a crucial measure in social network analysis. The traditional algorithms require Θ(n³) time and Θ(n²) space, making them impractical for large, sparse networks. The proposed algorithm reduces the time complexity to O(nm) for unweighted networks and O(nm + n² log n) for weighted networks, where n is the number of actors and m is the number of links. This improvement significantly extends the feasibility of centrality analysis on large networks. The algorithm leverages a new accumulation technique that integrates well with single-source shortest-paths algorithms, exploiting the sparsity of typical network instances. Experimental results on real and synthetic data demonstrate the effectiveness of the algorithm, showing substantial speedup compared to existing methods. The paper also discusses the practical implications of the algorithm, including its application in analyzing large social networks and web page centrality.This paper introduces a new algorithm for computing betweenness centrality, a crucial measure in social network analysis. The traditional algorithms require Θ(n³) time and Θ(n²) space, making them impractical for large, sparse networks. The proposed algorithm reduces the time complexity to O(nm) for unweighted networks and O(nm + n² log n) for weighted networks, where n is the number of actors and m is the number of links. This improvement significantly extends the feasibility of centrality analysis on large networks. The algorithm leverages a new accumulation technique that integrates well with single-source shortest-paths algorithms, exploiting the sparsity of typical network instances. Experimental results on real and synthetic data demonstrate the effectiveness of the algorithm, showing substantial speedup compared to existing methods. The paper also discusses the practical implications of the algorithm, including its application in analyzing large social networks and web page centrality.