双対的視点による複雑ネットワーク-のアプローチ(特集)

概要

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One slogan of science of complex networks is "functionality from network topology". In order to achieve this slogan, many characteristics such as degree distributions, average path length, clustering coefficients, network motifs etc have been introduced. However, these are all based on the "real view" on networks, that is, nodes are just points and an arc or an edge between two nodes indicates existence of some interaction between the two nodes and nothing more. In this paper we introduce "dual views" on networks in contrast to the "real view" in order to promote further achievement of the slogan. In a "dual view" we interpret objects as processes. This is an abstraction from real systems in which each component has its own process. There are infinitely many "dual views", however, we can show that there is a canonical "dual view" among all possible ones. We explain mathematical idea to formulate "dual views" and discuss its application to the study of complex networks.
2012-06-20