Emergence and complex systems have been the topic of many papers and are still disputed concepts in many fields. This lack of consensus hinders the use of these concepts in practice, particularly in modelling. All definitions of emergence imply the existence of a hierarchical system: a system that can be observed, measured and analysed at both macroscopic and microscopic levels. We argue that such systems are well described by mathematical graphs and, using graph theory, we propose an ontology of dynamic hierarchical systems capable of displaying emergence.

The team of the ERC Grant GeoDiverCity is pleased to announce the publication of the book "Urban dynamics and simulation models" coordinated by Denise Pumain and Romain Reuillon.