The aim of this work is to detect spatial clusters based on the number of connected components of a graph. We link Erd\"os graph and Poisson point process. We give the probability distribution function (pdf) of the number of connected component for an Erdos graph and obtain the pdf of the number of clusters for a Poisson process.
We extend our results to the pdf of the number of connected component of size greater than a given threshold as well as for marked point process.
Using this result, we obtain a test for complete spatial randomness and also identify the clusters that violates the CSR hypothesis. Border effects are computed.
We compare this method with classical methods.We illustrate our results on a tropical forest example
This is joint work with Michel Koskas and Nicolas Picard