Correlations and clustering in a scale-free network in Euclidean space

Empirical study shows that many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. Quite often they are modular in nature also, implying occurrences of several small tightly linked groups which are connected in a hierarchical manner among themselves. Recently, we have introduced a model of spatial scale-free network where nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link of the existing network. It has been already argued that the large scale behaviour of this network is like the Barabasi-Albert model. In the present paper we briefly review these results as well as present additional results on the study of non-trivial correlations present in this model which are found to have similar behaviours as in the real-world networks. Moreover. this model naturally possesses the hierarchical characteristics lacked by most of the models of the scale-free networks.