CASUS Institute Seminar, Dr. Szabolcs Horvát, ELBE postdoctoral fellow at the Center for Systems Biology Dresden, a joint initiative of the Max Planck Institute for Cell Biology and Genetics, and the Max Planck Institute for the Physics of Complex Systems (all Dresden, Germany)

In the past 20 years, network science has introduced many techniques to characterize and model systems with a connectivity structure. However, many of the networks we encounter in the real world, in particular in biology and ecology, exist in physical space. Examples include neuronal connectivity, transportation networks, epidemic spreading contact networks, vascular systems, etc. The connectivity patterns of such networks are strongly constrained by their spatial nature: usually only nearby nodes are linked. Therefore, the generic analysis techniques of classical network science often prove unproductive, affirming the need for a principled mathematical toolset specific to spatial network analysis.

In this talk, Szabolcs Horvát will show a project that represents one step towards such an analysis toolset. So-called “proximity graphs” of spatial point sets are constructed by connecting neighboring points. β-skeletons are a parametrized family of such graphs with many convenient mathematical properties, such as certain guarantees on connectedness and planarity (in the two-dimensional case). He will show that spatial point patterns can be characterized effectively by first constructing their β-skeleton, then describing its network properties. This technique can reveal features that common established point pattern analysis methods are not sensitive to. Finally, he demonstrates the use of proximity graphs as a spatial network null model for a biological dataset.