Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks - Moretti, Paolo; Hütt, Marc Thorsten (Proceedings of the National Academy of Sciences of the United States of America, 2020)
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.
CRIS-Team Scopus Importer:2020-08-14
Keywords: collective patterns; excitable media; networks