Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks
Moretti P, Hütt MT (2020)
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 117
Pages Range: 18332-18340
Journal Issue: 31
Abstract
In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of "link-usage asymmetry" are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.
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APA:
Moretti, P., & Hütt, M.T. (2020). Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks. Proceedings of the National Academy of Sciences of the United States of America, 117(31), 18332-18340. https://dx.doi.org/10.1073/pnas.1919785117
MLA:
Moretti, Paolo, and Marc Thorsten Hütt. "Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks." Proceedings of the National Academy of Sciences of the United States of America 117.31 (2020): 18332-18340.
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