A connector has a socket contact to be electrically connected to a counter-connector contact, the socket contact including: one or more pairs of conduction contact points disposed respectively on both sides of a fitting plane in an elastically displaceable manner; and one or more pairs of displacement regulator contact points disposed respectively on both sides of the fitting plane and coming into contact with the counter-connector contact when the counter-connector contact shifts, the one or more pairs of conduction contact points and the one or more pairs of displacement regulator contact points are disposed side by side in a direction along the fitting plane at a substantially same depth in a fitting direction, each of the pairs of displacement regulator contact points having a gap therebetween larger than that in each of the pairs of conduction contact points.