We consider a one-dimensional network in which the nodes at Euclidean
distance l can have long range connections with a probabilty P(l)∼l−δ in addition to nearest neighbour connections. This system has been
shown to exhibit small world behaviour for δ<2 above which its
behaviour is like a regular lattice. From the study of the clustering
coefficients, we show that there is a transition to a random network at δ=1. The finite size scaling analysis of the clustering coefficients obtained
from numerical simulations indicate that a continuous phase transition occurs
at this point. Using these results, we find that the two transitions occurring
in this network can be detected in any dimension by the behaviour of a single
quantity, the average bond length. The phase transitions in all dimensions are
non-trivial in nature.Comment: 4 pages, revtex4, submitted to Physical Review