Dynamic Graphs Generators Analysis : an Illustrative Case Study

TL;DR

This paper introduces new concepts and metrics for analyzing the long-term evolution of dynamic graphs, including a novel generator, to better understand their sustainability and behavior over time.

Contribution

It proposes the concepts of 'sustainability' and 'Nervousness' for dynamic graph analysis and presents a parametrized generator, D3G3, to study their properties.

Findings

Sustainability depends on vertex and edge evolution.

Nervousness effectively measures graph dynamics.

Generator parameters influence graph properties.

Abstract

In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over 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), which 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.