Abstract
In 1965 Christopher Alexander took the original step of analysing the city in graph theoretical terms and concluded that its historical or natural form is a semilattice and that urban planners of the future should adhere to this model. The idea was well received in architectural circles and has passed without serious challenge. In this paper, the value of such analysis is once again emphasized, although some of Alexander's arguments and his conclusions are refuted. Beginning with an exposition of the relationship between the graph theoretical concept of a tree, and the representation of a tree by a family of sets, we present a mathematical definition of a semilattice and discuss the ‘points’ and ‘lines’ of a graph in terms of a city, concluding that it is neither a tree nor a semilattice. This clears the ground for future graphical analysis. It seems that even general structural configurations, such as graphs or digraphs with certain specified properties, will fail to characterize a city, whose complexity, at this stage, may well continue to be understood more readily through negative rather than positive descriptions.
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