A topological approach based on analysis of atomic size distributions has been developed and applied to multicomponent amorphous alloys with different glass-forming ability. The atomic size distributions were obtained by plotting atomic concentrations versus atomic radii of constitutive elements. Ordinary amorphous alloys with high critical cooling rates were found to have single-peak distributions with a concave downward shape. These amorphous systems have at least one alloying element with a smaller radius, and at least one alloying element with a larger radius relative to the base element. The concentration of an alloying element decreases rapidly as the difference in the atomic sizes of the base element and the alloying element increases. Atomic size distributions of Zr, Pd, or Ln-based bulk amorphous alloys, which have a critical cooling rate in the range of 1-100 K/s, have a completely different, concave upward shape with a minimum at an intermediate atomic size. The base alloying element in these alloys has the largest atomic size and the smallest atom often has the next-highest concentration. A model that explains the concave upward shape of atomic size distributions for the bulk amorphous alloys is suggested. This model takes into account that all alloying elements in bulk glass formers are smaller than the matrix element, and some of them are located in interstitial sites while others substitute for matrix atoms in a reference crystalline solid solution. The interstitial and substitutional atoms attract each other and produce short-range ordered atomic configurations that stabilize the amorphous state. According to this model, the critical concentration of an interstitial element required to amorphize the alloy increases with increasing size difference from the matrix atom.