Clustering properties of a generalised critical Euclidean network

Abstract

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 $k_i^{\beta }{\ell }^{\alpha }$. 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 Barabási-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.

4 pages REVTEX, 4 figures

References in corpus (1)

• Small-world properties of the Indian Railway network

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