A Note on Computing Betweenness Centrality from the 2-core
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913456314122240 |
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| author | Tsourakakis, Charalampos E. |
| author_facet | Tsourakakis, Charalampos E. |
| contents | A central task in network analysis is to identify important nodes in a graph. Betweenness centrality (BC) is a popular centrality measure that captures the significance of nodes based on the number of shortest paths each node intersects with. In this note, we derive a recursive formula to compute the betweenness centralities of a graph from the betweenness centralities of its 2-core.Furthermore, we analyze mathematically the significant impact of removing degree-one nodes on the estimation of betweenness centrality within the context of the popular pivot sampling scheme for Single-Source Shortest Path (SSSP) computations, as described in the Brandes-Pich approach and implemented in widely used software such as NetworkX. We demonstrate both theoretically and empirically that removing degree-1 nodes can reduce the sample complexity needed to achieve better accuracy, thereby decreasing the overall runtime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Computing Betweenness Centrality from the 2-core Tsourakakis, Charalampos E. Social and Information Networks A central task in network analysis is to identify important nodes in a graph. Betweenness centrality (BC) is a popular centrality measure that captures the significance of nodes based on the number of shortest paths each node intersects with. In this note, we derive a recursive formula to compute the betweenness centralities of a graph from the betweenness centralities of its 2-core.Furthermore, we analyze mathematically the significant impact of removing degree-one nodes on the estimation of betweenness centrality within the context of the popular pivot sampling scheme for Single-Source Shortest Path (SSSP) computations, as described in the Brandes-Pich approach and implemented in widely used software such as NetworkX. We demonstrate both theoretically and empirically that removing degree-1 nodes can reduce the sample complexity needed to achieve better accuracy, thereby decreasing the overall runtime. |
| title | A Note on Computing Betweenness Centrality from the 2-core |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2408.01157 |