  Many real-world networks exhibit scale-free feature, have a small diameter
and a high clustering tendency. We have studied the properties of a growing
network, which has all these features, in which an incoming node is connected
to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a
probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the
network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto
k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0,
\beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which
the network is scale-free. Interestingly, we find scale-free behaviour even for
$\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class
is indicated from the behaviour of the degree distribution and the clustering
coefficients. The network has a small diameter in the entire scale-free region.
The clustering coefficients emulate the behaviour of most real networks for
increasing negative values of $\alpha$ on the phase boundary.
