  We aim to generate virtual commuting networks in the French rural regions in
order to study the dynamics of their municipalities. Since we have to model
small commuting flows between municipalities with a few hundreds or thousands
inhabitants, we opt for a stochastic model presented by Gargiulo et al. 2012.
It reproduces the various possible complete networks using an iterative
process, stochastically choosing a workplace in the region for each commuter
living in the municipality of a region. The choice is made considering the job
offers in each municipality of the region and the distance to all the possible
destinations. This paper presents how to adapt and implement this model to
generate French regions commuting networks between municipalities. We address
three different questions: How to generate a reliable virtual commuting network
for a region highly dependant of other regions for the satisfaction of its
resident's demand for employment? What about a convenient deterrence function?
How to calibrate the model when detailed data is not available? We answer
proposing an extended job search geographical base for commuters living in the
municipalities, we compare two different deterrence functions and we show that
the parameter is a constant for network linking French municipalities.
