Cancer is a complex disease caused by mutations accumulated over a lifetime. Albeit cancer cells harbor many mutations, only a small fraction, called driver mutations, are responsible for the emergence and maintenance of the disease. Pathway networks are subsets from the whole cell interactome and represent meaningful biological functions. In this study, we explore the topological complexity of pathway sub-networks using the persistence homology theory, observing driver genes' role. Results show drivers are associated with higher-order structures, and their removal is more impactful than non-drivers in the network complexity. These findings increase our understanding of drivers and can be used to discover new driver genes.