A Neighbor List, or Verlet List, is a technique for speeding up the evaluation of short-range interactions in a system of particles. Given that (1) each particle has a cutoff radius rc beyond which it does not interact with other particles, (2) the cutoff distance is smaller than the the simulation box, then it is calculationally advantageous to exclude from energy and force calculations particle pairs that are not interacting.
For a given particle p, its neighbor list will consist of all particles within a distance rv where rv > rc. If no particle has moved a distance greater than rv − rc, then all the neighbor lists are still accurate and it is sufficient to use the lists to calculate all interactions (Order N calculation). As soon as a particle in the system moves a distance greater than rv − rc then there is the possibility that some subset of particles have had their neighbor lists affected and the lists are recalculated (Order N2 calculation).
By the above definition, if particle p is in particle q 's neigbor list, then particle q is in particle p 's neigbor list. However, for Molecular Dynamic simulations, this redundancy is not necessary. It is preferrable to store only one of the two relationships, as long as every neighbor-neighbor relationship is stored once and only once.