Populations genetics and dynamics of bacteria on a Graph
I assume you are simulating a null distribution. Are you investigation recombination??
My main advice is to use population genetic terminology rather than geomometry to describe your simulation (e.g. vertex is a migration event between allopatric populations). Migration is investigated between populations investigated via $F_{ST}$. You appear to be assuming clonality, and population movement appear to follow a 'stepping stone model' (I might have misunderstand the question).
Mutation rate ... I'll have a guess at $10^5$ per site per year. Migration rate depends on the bacterial species being modeled, eg. MRSA spread in a very similiar fashion to that described in your model (along a moterway), in contrast soil bacteria don't adhere to allopatry at all (when I looked at them).
Fixing one parameter (population size) whilst investigation a second (migration) would be normal to assess the parameter space initially. Bacterial populations do undergo selective sweeps and using an appropriate growth model I would look at a standard population growth model (e.g. the one Bob May investigated in chaotic interactions within a differential equation). There are several population growth models and fixing migration whilst assessing the model would seem sensible. The parameter space in the combined model of migration, space and population size becomes complex.

Okay I get your model now. Its fine, the thing I'd be cautious about is the population density of the bacterial host because this would skew migration across the nodes of your graph. A quick literature review will demonstrate the importance,  double paeroto log normal distribution and its cousin (the name escapes me .... ) are sort of key words that might flag up. Bacteria are not my active thing so I'm rusty.