  We construct a data-driven model of flows in graphs that captures the
essential elements of the movement of workers between jobs in the companies
(firms) of entire economic systems such as countries. The model is based on the
observation that certain job transitions between firms are often repeated over
time, showing persistent behavior, and suggesting the construction of static
graphs to act as the scaffolding for job mobility. Individuals in the job
market (the workforce) are modelled by a discrete-time random walk on graphs,
where each individual at a node can possess two states: employed or unemployed,
and the rates of becoming unemployed and of finding a new job are node
dependent parameters. We calculate the steady state solution of the model and
compare it to extensive micro-datasets for Mexico and Finland, comprised of
hundreds of thousands of firms and individuals. We find that our model
possesses the correct behavior for the numbers of employed and unemployed
individuals in these countries down to the level of individual firms. Our
framework opens the door to a new approach to the analysis of labor mobility at
high resolution, with the tantalizing potential for the development of full
forecasting methods in the future.
