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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.03796 |
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| _version_ | 1866915988906180608 |
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| author | Tuzhilin, Mikhail |
| author_facet | Tuzhilin, Mikhail |
| contents | In this article we present a new centrality measure called ksi-centrality. We show that ksi-centrality distinguishes real networks from random ones, similar to degree centrality: the ksi-centrality distribution is right-skewed for real networks and centered for random Erdos-Renyi networks, and has linear pattern with a heavy tail on a log plot. Furthermore, the ksi-centrality distribution is centered for models simulating real networks: Barabasi-Albert, Watts-Strogatz, and Boccaletti-Hwang-Latora. Thus, this centrality distribution is an additional and independent property with respect to scale-freeness. We also introduce a normalized version of ksi-centrality and show that it is related to algebraic connectivity and the Chegeer's value of a network. Moreover, the average value of this normalized centrality is in bijective correspondence with the relative number of edges that a new node connects to others in the Barabasi-Albert preferential attachment model, thus answering the question of how to choose the parameter $m$ to model a given real-world network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Capability centrality: the next step from scale-free property Tuzhilin, Mikhail Social and Information Networks In this article we present a new centrality measure called ksi-centrality. We show that ksi-centrality distinguishes real networks from random ones, similar to degree centrality: the ksi-centrality distribution is right-skewed for real networks and centered for random Erdos-Renyi networks, and has linear pattern with a heavy tail on a log plot. Furthermore, the ksi-centrality distribution is centered for models simulating real networks: Barabasi-Albert, Watts-Strogatz, and Boccaletti-Hwang-Latora. Thus, this centrality distribution is an additional and independent property with respect to scale-freeness. We also introduce a normalized version of ksi-centrality and show that it is related to algebraic connectivity and the Chegeer's value of a network. Moreover, the average value of this normalized centrality is in bijective correspondence with the relative number of edges that a new node connects to others in the Barabasi-Albert preferential attachment model, thus answering the question of how to choose the parameter $m$ to model a given real-world network. |
| title | Capability centrality: the next step from scale-free property |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2605.03796 |