The neighbors of a central atom in the supercooled, unit-density Lennard-Jones liquid are sorted by "neighborship" (first neighbor, second neighbor, etc.), and an analysis of static and dynamical properties is presented. A preliminary model is that neighbors n =1-12 fall in the first shell S1, that n = 13,14 are transitional neighbors, and that S2 begins at n = 15. S1 is identified as the cage of the central atom, and S1 plus the central atom is considered as a possible cluster; diffusion is proposed to occur via S1-->S2 transitions. The radial probability distribution functions, P(n,r), for the nth neighbor are calculated. With decreasing T the shells pull away from each other and from the transitional neighbors, and a mean-field theory of P(n,r) breaks down. It is suggested that such behavior correlates with a dynamical slowing down.. Similarly, a diffusive model for the number of original S1 neighbors still in S1 at time r fails fbr (reduced) T less than or equal to 0.80, indicating the onset of collective slow cluster dynamics. Static and dynamic evidence points to T similar to 0.8 as a temperature below which the liquid becomes more complex. The need to separate fast vibrational dynamics from measures of diffusion is discussed; one atom makes a first passage S1-->S2 very quickly. The two-atoms first passage time tau(2) is therefore proposed as an approximate single-atom diffusive time. The rate tau(2)(-1) is in excellent agreement with the barrier hopping rate omega(h) calculated from instantaneous normal mode theory.