Network Centrality Metrics Based on Unrestricted Paths, Walks and Cycles Compared to Standard Centrality Metrics
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| Format: | Preprint |
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2025
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| _version_ | 1866908817096179712 |
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| author | Luhtala, Juuso Kuikka, Vesa Kaski, Kimmo K. |
| author_facet | Luhtala, Juuso Kuikka, Vesa Kaski, Kimmo K. |
| contents | Traditional measures of closeness and betweenness centrality in networks rely on the shortest paths between nodes. Many standard metrics fail to accurately reflect the physical or probabilistic characteristics of nodal centrality and network flow, often overlooking processes such as cyclic and recurrent spreading. Here, we present new metrics based on our influence spreading model. These probabilistic measures consider all feasible paths, walks, and cycles within the network. We define in-centrality to assess how central a node is as a target of influence, and out-centrality for its role as a source of influence. We compare our metrics with standard ones by analyzing node rankings, using scatter plots, and calculating the Pearson correlation and Spearman's rank correlation coefficients. Our findings show that the betweenness centrality defined by the influence spreading model emphasizes the importance of alternative routes while maintaining similarity to standard betweenness centrality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Network Centrality Metrics Based on Unrestricted Paths, Walks and Cycles Compared to Standard Centrality Metrics Luhtala, Juuso Kuikka, Vesa Kaski, Kimmo K. Social and Information Networks Traditional measures of closeness and betweenness centrality in networks rely on the shortest paths between nodes. Many standard metrics fail to accurately reflect the physical or probabilistic characteristics of nodal centrality and network flow, often overlooking processes such as cyclic and recurrent spreading. Here, we present new metrics based on our influence spreading model. These probabilistic measures consider all feasible paths, walks, and cycles within the network. We define in-centrality to assess how central a node is as a target of influence, and out-centrality for its role as a source of influence. We compare our metrics with standard ones by analyzing node rankings, using scatter plots, and calculating the Pearson correlation and Spearman's rank correlation coefficients. Our findings show that the betweenness centrality defined by the influence spreading model emphasizes the importance of alternative routes while maintaining similarity to standard betweenness centrality. |
| title | Network Centrality Metrics Based on Unrestricted Paths, Walks and Cycles Compared to Standard Centrality Metrics |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2512.11585 |