Vincent Bridonneau (Université de Le Havre Normandie)
Title: Generation and analysis of dynamic graphs
Abstract:
This work investigates iterative processes that generate sequences of graphs, with applications spanning complex network analysis and temporal graph theory. Given a seed configuration, such processes yield a continuous flow of graphs whose structural evolution raises fundamental questions. When no size constraints are imposed, under what conditions can we guarantee non-trivial long-term behavior? How do we rigorously characterize structural transitions between consecutive states? We address the first question by introducing the notion of sustainability, a framework for determining whether an iterative process admits periodic graph sequences. We propose and analyze a graph generator that illustrates the theoretical challenges inherent to this concept. For the second question, we develop a metric quantifying structural change across successive iterations. Together, these contributions open new avenues of inquiry and reinforce the interplay between complex network analysis and temporal graph theory.