We would like to invite you to the following talk of the Eindhoven Stochastics Colloquium:

**Jeannette Janssen (Dalhousie University) – Recognizing graphs formed by a spatial random process**

Thursday 17 January, 15.00-16.00, Room MF 11-12 (4th floor, MetaForum Building, TU/e)

ABSTRACT:

It is a safe assumption about social networks that links are more often formed between people that have a lot in common. This can be modelled with a simple spatial model for link formation. Individuals are represented by vertices placed in a virtual space that represents their interests and characteristics. Links are formed stochastically so that most links are local, i.e. links are less likely between vertices that are further apart.

Given a graph, but no information about the spatial embedding, can we measure whether the graph conforms to a spatial model? Focusing on the case where the space is one-dimensional, we introduce a parameter, $\Gamma$, that provide such a measure. We use the theory of graph limits to show that graphs for which $\Gamma$ is small resemble samples from a spatial model. We also show how, given a sample from a (1D) spatial model, essential spatial information about the vertices can be retrieved from the sample. This is joint work with Mahya Ghandehari and Aaron Smith.

Upcoming events of the Eindhoven Stochastics Colloquium: http://www.win.tue.nl/StoSem/