Degree Landscapes in Scale-Free Networks

Details Degree Landscapes in Scale-Free Networks Degree Landscapes in Scale-Free Networks

2005-12-08

arxiv.org/abs/physics/0512075v1

Phys. Rev. E 74, 036119 (2006)

Physics

Physics and Society

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.74.036119

We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes corresponds to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or, in molecular networks, to functional localization. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains.

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