Spatial age-dependent random graphs

• Applicant: Professor Dr. Peter Mörters
• Subject Area: Mathematics
• Term: from 2019 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 425842117

We investigate a family of growing graphs embedded into a d-dimensional torus where new vertices arrive at constant rate, are randomly placed on the torus and connect to each existing vertex independently with a probability favouring short edges and connections to old vertices. This simple model for a scale-free network with spatially induced clustering is called the age-based spatial preferential attachment model. We are interested in the effect of the spatial correlations on the topology of the graph and study robustness under attack, length of the shortest paths between typical vertices, and spreading of information on the network. In particular, we study metastability of the contact process on the graph and the way information can be transmitted in the case that graph vertices move according to independent Brownian motions.

• DFG Programme: Research Grants