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Dynamic Graphs Generators Analysis: An Illustrative Case Study

Authors Vincent Bridonneau, Frédéric Guinand , Yoann Pigné



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Author Details

Vincent Bridonneau
  • Université Le Havre Normandie, Normandie Univ, LITIS EA 4108, 76600 Le Havre, France
Frédéric Guinand
  • Université Le Havre Normandie, Normandie Univ, LITIS EA 4108, 76600 Le Havre, France
Yoann Pigné
  • Université Le Havre Normandie, Normandie Univ, LITIS EA 4108, 76600 Le Havre, France

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Vincent Bridonneau, Frédéric Guinand, and Yoann Pigné. Dynamic Graphs Generators Analysis: An Illustrative Case Study. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 8:1-8:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SAND.2023.8

Abstract

In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We focus on generated graphs whose orders are neither growing nor constant along time. We introduce a novel concept, called "sustainability," to qualify the long-term evolution of dynamic graphs. A dynamic graph is considered sustainable if its evolution does not result in a static, empty, or periodic graph. To measure the dynamics of the sets of vertices and edges, we propose a metric, named "Nervousness," which is derived from the Jaccard distance. As an illustration of how the analysis can be conducted, we design a parametrized generator, named D3G3 (Degree-Driven Dynamic Geometric Graphs Generator), that generates dynamic graph instances from an initial geometric graph. The evolution of these instances is driven by two rules that operate on the vertices based on their degree. By varying the parameters of the generator, different properties of the dynamic graphs can be produced. Our results show that in order to ascertain the sustainability of the generated dynamic graphs, it is necessary to study both the evolution of the order and the Nervousness for a given set of parameters.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Mathematics of computing → Random graphs
  • Networks → Topology analysis and generation
Keywords
  • Dynamic Graphs
  • Graph Generation
  • Graph Properties
  • Evolutionary models

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