Interpersonal power describes this aspect. Power, in general, is the ability to alter the state of another person's thoughts, actions, or beliefs. When the power has the "interpersonal" modifier attached, it shows that there is a relationship attached to the two people involved due to this power not being a one-off, transient concept. When the power is "interpersonal," the change is liable to be more gradual and more long-term than with other types.
