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We investigate the evolution of the force network in experimental systems oftwo-dimensional granular materials under impact. We use the first Betti number,$\beta_1$, and persistence diagrams, as measures of the topological propertiesof the force network. We show that the structure of the network has a complex,hysteretic dependence on both the intruder acceleration and the total forceresponse of the granular material. $\beta_1$ can also distinguish between thenonlinear formation and relaxation of the force network. In addition, using thepersistence diagram of the force network, we show that the size of the loops inthe force network has a Poisson-like distribution, the characteristic size ofwhich changes over the course of the impact.

Topology of Force Networks in Granular Media under Impact