  The transport and distribution of organisms like larvae, seeds or litter in
the ocean as well as particles in industrial flows is often approximated by a
transport of tracer particles. We present a theoretical investigation to check
the accuracy of this approximation by studying the transport of inertial
particles between different islands embedded in an open hydrodynamic flow
aiming at the construction of a Lagrangian flow network reflecting the
connectivity between the islands. To this end we formulate a two-dimensional
kinematic flow field which allows the placement of an arbitrary number of
islands at arbitrary locations in a flow of prescribed direction. To account
for the mixing in the flow we include a von K\'arm\'an vortex street in the
wake of each island. We demonstrate that the transport probabilities of
inertial particles making up the links of the Lagrangian flow network depend
essentially on the properties of the particles, i.e. their Stokes number, the
properties of the flow and the geometry of the setup of the islands. We find a
strong segregation between aerosols and bubbles. Upon comparing the mobility of
inertial particles to that of tracers or neutrally buoyant particles, it
becomes apparent that the tracer approximation may not always accurately
predict the probability of movement. This can lead to inconsistent forecasts
regarding the fate of marine organisms, seeds, litter or particles in
industrial flows.
