Theoretical Statistics and Mathematics Unit, ISI Delhi
Graphs and networks are ubiquitous in modern science and society, and random graph models play a major role in underpinning the statistical analysis of network data. One such model is the random geometric graph: a large number of vertices are scattered randomly in a spatial region, and two vertices are connected by an edge whenever they are sufficiently close together. This is a very natural model for networks with spatial content and randomness; for example mobile communications networks.
In this talk, we address some of the basic questions one might ask about such a graph, such as the following. Is it connected; that is, are any two vertices connected by a path? If not, how many pieces does the graph split into? How large are these pieces? In particular, does the largest piece contain a significant proportion of the of vertices? How many edges, triangular sub-graphs and so on does the graph have? We shall also explore the relationship with other random graph models, so far as time permits.