Málstofa: Szabolcs Horvát

Ágrip: Network science has developed many methods for the characterization of networks, most being designed for generic sparse graphs. However, the nodes of many real-world networks exist in physical space, with only nearby nodes being connected. This strongly constrains their possible connectivity structures, rendering many classic graph measures uninformative, and of limited use for classification. This is even more true in networks where only direct spatial neighbours are connected, and long-range connections are completely missing. Examples include various transport networks in biological organisms (such as vasculature), networks of streets, fungal networks, etc. In all these cases, node locations almost completely determine connectivity.

We propose a novel approach to characterizing such networks through the concept of β-skeletons, a family of parametrized proximity graphs that naturally capture spatial neighbour relations. Despite its great potential, this concept has so far been mostly ignored within the field of spatial network analysis. We study the statistical properties of β-skeletons using both exact and numerical approaches, then building on these results, we introduce an innovative way of characterizing spatial point patterns by analysing their skeletons. Finally, we use three-dimensional biological network datasets to demonstrate that β-skeletons accurately capture the structure of most direct-neighbour spatial networks based on their node locations, and can thus be used to gain insight into their local network structure.

Based on joint work with Carl Modes.