1. A network security management system comprising one or more computing devices including instructions embodied in one or more non-transitory machine-readable storage media, wherein the instructions are executable by the one or more computing devices to cause the one or more computing devices to: determine a current context of a computer network in live operation; generate an interactive visualization of the network for display by a display device, the interactive visualization comprising a plurality of graphical elements arranged to depict the current context of the network, at least one of the graphical elements indicative of a network security event detected on the network; using an interaction model and the interactive visualization of the current context of the network, determine interpretations of gesture-based interactions with a computing system, wherein determine interpretations comprises interpreting at least one of the gesture-based interactions as a network security directive and interpreting at least one of the gesture-based interactions as a network exploration directive and interpreting at least one of the gesture-based interactions as an interaction that should be disregarded as neither a network security directive nor a network exploration directive; when a gesture-based interaction is interpreted as a network security directive, convert the network security directive to a set of instructions executable by one or more switching devices of the computer network; when a gesture-based interaction is interpreted as a network exploration directive, update a displayed view of the interaction visualization; when a gesture-based interaction is interpreted as an interaction that should be disregarded as neither a network security directive nor a network exploration directive, neither convert the network security directive to a set of instructions executable by one or more switching devices of the computer network nor update the displayed view of the interaction visualization.