| F. Sofoulis, K. Theodoropoulos, G. Drakopoulos, C. Troussas, and Ph. Mylonas |
| Approximating Power Series Centrality With The Katz Metric: Matching The Vertex Gap In Julia |
| 22nd International Conference on Artificial Intelligence Applications and Innovations (AIAI 2026), 16 - 19 July 2026, Chania, Greece |
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ABSTRACT
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| Vertex centrality metrics are crucial in evaluating the role a single vertex or even a group of vertices play in structural terms as, for instance, in the the overall graph resilience. Such metrics being of higher order they reveal significant information. However, many of these metrics such as the total communicability are defined as a power series of the underlying graph adjacency matrix making their computation difficult from a computational, algorithmic, and numerical perspective. Therefore, it makes perfect sense to explore whether they can be approximated by centrality metrics which are less challenging. One such metric is Katz centrality which in its core relies on solving a special linear system involving said adjacency matrix. In order to assess the approximation quality, statistical measures including Kendall¢s tau and Spearman¢s rho are computed for two power series centrality metrics, namely the exponential and the Mercator series, for a number of benchmark graphs including ca-CondMat and ca-AstroPh and for a number of Katz parameters determined by linear algebraic criteria. The results indicate that the proposed approximation is feasible.
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| 17 April , 2026 |
| F. Sofoulis, K. Theodoropoulos, G. Drakopoulos, C. Troussas, and Ph. Mylonas, "Approximating Power Series Centrality With The Katz Metric: Matching The Vertex Gap In Julia", 22nd International Conference on Artificial Intelligence Applications and Innovations (AIAI 2026), 16 - 19 July 2026, Chania, Greece |
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