Steady and ranging sets in graph persistence

09/15/2020

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by   Mattia G. Bergomi, et al.

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Generalised persistence functions (gp-functions) are defined on (ℝ, ≤)-indexed diagrams in a given category. A sufficient condition for stability is also introduced. In the category of graphs, a standard way of producing gp-functions is proposed: steady and ranging sets for a given feature. The example of steady and ranging hubs is studied in depth; their meaning is investigated in three concrete networks.