The motion of the Center of Mass (CM) of the Earth system with respect to the Center of Figure (CF) of the Earth surface, called the geocenter motion, plays an important role in space geodesy, as it connects the satellite orbits to the point positions of stations on the ground. However, the measurement of the geocenter motion is complicated by the finite and uneven coverage of the Earth surface by geodetic networks, resulting in a discrepancy between the theoretical CF and the more accessible Center of Network (CN). Here, we develop a method to estimate the error introduced by this “network effect”, using statistical and numerical methods, for a network of a given finite size. Also, we find that the network effect may be comparable in magnitude with the geocenter motion itself for some geophysical processes, for example, co-seismic displacements and elastic deformation due to hydrological loading. Therefore, we find that the measurement of the geocenter motion is severely constrained by the network effect. Finally, we present an alternative definition of the CN that reduces the network effect by up to 50% for realistic networks such as the core site network of the International Terrestrial Reference Frame (ITRF).