  We consider Markov jump processes on a graph described by a rate matrix that
depends on various control parameters. We derive explicit expressions for the
static responses of edge currents and steady-state probabilities. We show that
they are constrained by the graph topology (i.e. the incidence matrix) by
deriving response relations (i.e. linear constraints linking the different
responses) and topology-dependent bounds. For unicyclic networks, all scaled
current sensitivities are between zero and one and must sum to one. Applying
these results to stochastic thermodynamics, we derive explicit expressions for
the static response of fundamental currents (which carry the full dissipation)
to fundamental thermodynamic forces (which drive the system away from
equilibrium).
