This paper investigates consensus of flocks consisting of n autonomous agents in the plane,where each agent has the same constant moving speed vn and updates its heading by the average value of the kn nearest agents from it,with vn and kn being two prescribed parameters depending on n.Such a topological interaction rule is referred to as kn-nearest-neighbors rule,which has been validated for a class of birds by biologists and verified to be robust with respect to disturbances.A theoretical analysis will be presented for this flocking model under a random framework with large population,but without imposing any a priori connectivity assumptions.We will show that the minimum number of kn needed for consensus is of the order O(log n) in a certain sense.To be precise,there exist two constants C1 ＞ C2 ＞ 0 such that,if kn ＞ C1 logn,then the flocking model will achieve consensus for any initial headings with high probability,provided that the speed vn is suitably small.On the other hand,if kn ＜ C2 log n,then for large n,with probability 1,there exist some initial headings such that consensus cannot be achieved,regardless of the value of vn.