Let P be a Poisson process of intensity one in a square Sn of area n. We construct a random geometric graph G n,k by joining each point of P to its k nearest neighbours. For many applications it is desirable that G n,k is highly connected, that is, it remains connected even after the removal of a small number of its vertices. In this paper we relate the study of the s-connectivity of G n,k to our previous work on the connectivity of G n,k . Roughly speaking, we show that for s = o(log n), the threshold (in k) for s-connectivity is asymptotically the same as that for connectivity, so that, as we increase k, G n,k becomes s-connected very shortly after it becomes connected.
Reference REF shows that, in k-nearest neighbor model by increasing , network becomes s-connected very shortly after it becomes connected, where = (log ).
Highly connected random geometric graphs
Discret. Appl. Math.
Discret. Appl. Math.
Computer Science Mathematics