On the concepts of complex networks to quantify the difficulty in finding the way out of labyrinths

Labyrinths have been a tradition and part of the imagination of the human kind for centuries, and were probably built either as a challenge to make it difficult for someone to find the way out, or for aesthetic purposes. They are conventionally classified according to the country they were built, to the style (Roman, classic and contemporary) or to the construction site. In this study, we show that labyrinths can be modeled as complex networks, whose metrics can be used to classify them in terms of their difficulty to find the way out. This is performed by calculating the absorption time, defined as the time it takes for a particle on an internal node to reach an output node through a random walk. The absorption time correlates well with the shortest paths and length of the networks, as expected, and has a very high correlation (Pearson coefficient of 0.97) with the betweenness, therefore allowing one to quantify the level of complexity of any labyrinth. It is shown that the conventional classification is inappropriate to distinguish between labyrinths, because some with very similar properties exist in different countries or were built in distinct time periods. A refined analysis in 77 famous labyrinths indicated that the majority were built for aesthetic purposes, with relatively small absorption times. Furthermore, with the expectation maximization algorithm, we could combine the complex network metrics to identify four clusters of labyrinths that differ in terms of density and shape.