A note on the 2-connectivity in one-dimensional ad hoc networks

2-connectivity is the basic graph theoretical metric for fault tolerance to node failures,and it is an extremely desirable property in network design.For a one-dimensional finite ad hoc network formed by n nodes uniformly and independently distributed in a closed interval[0,z](z∈R+),we give a closed form expression for the probability that a connected one-dimensional finite ad hoc network becomes disconnected after removing a node.We also sketch a procedure of finding the exact formula for 2-connectivity in a one-dimensional ad hoc network.