Abstract
Abstract Temporal evolution of the (multi-)fractality in the Madrid Metro subway (Spain) is explored by using it as a study case of a public transport network (PTN). By considering this subway as a graph network, a box-covering method for multifractal analysis of complex networks is employed for assessing the evolution of multifractal parameters along time from two perspectives. On the one hand, the development of the topological structure of the subway (unweighted network), and on the other, the influence of the travelling times in its multifractal properties (weighted network). Multifractal results are in agreement with the evolution of the system, which begins with the monofractal structure of a one-dimensional solely line, but increasing in complexity until 1980s-1990s. Nowadays, the system is slightly multifractal due to certain heterogeneity in node density distribution. Scaling behaviour in the current Madrid Metro subway is evaluated by means of the generation of synthetic networks, in which topology is kept but travelling times are reassigned. Additionally, multifractality is also evaluated by studying the effect of the commuter railway system and the deletion of the circular line in the network.
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