Two complementary representations of a scale-free network

Abstract

Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx k^{-\gamma }$, where $P(k)$ denotes the frequency of the nodes that are connected to $k$ other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied to a power-law distribution. Our results indicate that a power-law distribution as $P(k)\approx k^{-\gamma +1}$ is found for the transformed network together with a peak for low-degree nodes. In the present work we show a parametrization of this behaviour and discuss its application to real networks as metabolic networks, protein-protein interaction network and World Wide Web.

18 pages, 8 figures. Minor changes. One figure added

References in corpus (11)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Lethality and centrality in protein networks
• Assortative mixing in networks
• The large-scale organization of metabolic networks
• Mixing patterns in networks
• Classes of behavior of small-world networks
• Mean-field theory for scale-free random networks
• Topology of evolving networks: local events and universality
• Organization of Growing Random Networks
• Evolution of reference networks with aging

Cited by in corpus (5)

• Line Graphs of Weighted Networks for Overlapping Communities
• Clustering in random line graphs
• Line graphs as social networks
• Assortativity in random line graphs
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks