Degree landscapes in scale-free networks

We generalize the degree-organizational view of real-world networks with broad degree distributions in a landscape analog with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes correspond 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. To quantify the topology, we here measure the widths of the mountains and the separation between different 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.