We introduce a novel measure that captures the influences among variables in a network and introduce a new type of graphical model, influence structural graph, to visualize the dependencies. Our new measure captures the influence of a variable (potential cause) on another variable (effect) in the network by assigning different values to the potential cause, while other variables’ effects are removed, and observing the behavior of the effect variable. We show that influence structural graphs admit global Markov property that can be used for structural learning and establish a connection between our measure and the integral probability metric that has been studied extensively in the literature. This allows us to efficiently estimate the new measure using kernel methods.