Clustering in random line graphs

Abstract

We investigate the degree distribution $P(k)$ and the clustering coefficient $C$ of the line graphs constructed on the Erd\"os-R\'enyi networks, the exponential and the scale-free growing networks. We show that the character of the degree distribution in these graphs remains Poissonian, exponential and power law, respectively, i.e. the same as in the original networks. When the mean degree $<k>$ increases, the obtained clustering coefficient $C$ tends to 0.50 for the transformed Erd\"os-R\'enyi networks, to 0.53 for the transformed exponential networks and to 0.61 for the transformed scale-free networks. These results are close to theoretical values, obtained with the model assumption that the degree-degree correlations in the initial networks are negligible.