Described herein is a magnetoresistive network responsive to a magnetic field of the type comprising a plurality of magnetoresistive elements. According to the invention, the one or more magnetoresistive elements comprise at least one magnetoresistive element in the form of nanoconstriction, the nanoconstriction comprising at least two pads made of magnetic material, associated to which are respective magnetizations oriented in directions substantially opposite to one another and connected through a nanochannel, the nanochannel being able to set up a domain wall that determines an electrical resistance of the nanoconstriction as a function of the position, with respect to said nanochannel, of said domain wall formed in said sensor device.