Graph Vision is a beautiful book, replete with diagrams, schemas and colour images from manuals and notebooks, which are as much a part of the book as the text. In some senses, the book is itself a notebook, with material presented so that the reader is almost encouraged to take notes, scribble, make calculations in the margins. Graph Vision is the story of a journey, the journey of graphs, across disciplines – from mathematics to architecture, from design to computer science – across continents – from Europe to the United States – and finally over the course of the years – from their birth on the bridges of Königsberg to their adulthood behind algorithms. Such a journey touches upon many different territories and challenges their borders; for these reasons, the book is an incredibly rich resource for readers who are interested not only in (the history and the philosophy of) architecture but more generally in (the history and the philosophy of) science.

The book is structured into five chapters. Chapter 1, ‘Graphs’, introduces readers to the book’s protagonists. If in the early twentieth-century graphs were derided as recreational mathematics, by the 1960s they were living a much more interesting life, in mathematics and outside it. The story in the book is in reality a ‘prehistory’ of what is called today ‘digital architecture’: contrary to a common view, according to which architects are confronted with the manipulation of abstract structures because they make digital architecture, the multifaceted narrative of the way architects turned toward structures through graphs is revealed as the very condition for the development of digital architecture. There were architects, and there were graphs, and both have been historical agents: graphs were not simply imposed from mathematics upon architects, but they embodied concepts, they were epistemic objects, allowing for the simultaneous treatment of data and shape. It is not that architects nowadays see and manipulate points and lines and webs and networks because of digital architecture; rather, it is the graph vision that has characterized architecture in the second half of the twentieth century that has also shaped digital architecture.

Without defining ‘graphs’ or ‘diagrams’ out of context, Vardouli follows their historical path and evaluates their role in the history of architecture, from the 1950s to today. The following three chapters focus on uses of graphs as images (Chapter 2), tools (Chapter 3) and infrastructure (Chapter 4). Graphs as images were introduced as new architectural drawings that were not drawings: the mathematical properties of the graphs evade metric specificities, and this is why a graph is to be considered a picture but not a shape, which is a seemingly paradoxical negation of the visual. The ‘structural revolution’, which at the time was spreading across disciplines, aspired also in architecture to theory, rigour and mathematical explanations. In this chapter, some readers will hear ‘echoes’: of the development of structuralism in philosophy of mathematics, and the dream of the new or modern mathematics reform in science education.

Graphs as tools generated new architectural drawings and automated design, thus moving from an epistemic to an operative level, from structure to process. Thanks to graphs, form was revealed for what it was thought to really be: the product not of creative artistic genius, but of rule-based, algorithmic processes. Several concrete and historical examples of graphs as tools are given in the chapter. Thanks to the mathematics that comes with graphs and makes it possible to relate them to other mathematical tools, graphs were mediators between the available data – in the meanwhile, ‘data’ were born too! – and algorithmically generated form.

Graphs have also had the role of infrastructure for participatory architecture. Would it be possible for non-specialists to design their own environments, according to their needs? The mathematical structure behind the patterns was embedded in an accessible form, like a ‘cookbook’: do-it-yourself architecture manuals were published to empower individual and collective design, and several machines were constructed; the challenge was to find an equilibrium between keeping control and guaranteeing freedom in architectural design. In the last chapter, entitled ‘Skeletons’, the author comes full circle. At the end of the journey, the reader has learned that today digital architecture is indeed ‘haunted’. Even though graphs were conceived as skeletal structures to work with, ‘once architecture has been stripped of its soft tissues’, they were no bare bones, but had ‘cultural and material flesh’ (p. 187). If graphs have been many things, have been presented in many different media, have taken different names, each of them was something in between an object and a concept. The book finally shows that ‘surfaces are profound’, and that there is a way in which one can be superficial ‘out of profundity’ (p. 191).

Graph Vision is a fascinating book, for architects, philosophers, mathematicians, computer scientists, historians: each of whom will find their own path through the story. I recommend forgetting about the extensive footnotes while reading the book not to break the flow of the story; however, notes contain important information for the curious reader who chooses to go deeper. The book is also an example of how history can be relevant today, as it touches upon subjects such as data-based science and generative methods and their complicated relationship with understanding, and participatory scientific enterprises. Moreover, the story is also a story about the role of institutions, business and ideals of democracy in architecture.

Before the last page of the book, my only criticism would have been that the reader at some point gets lost in the story, and paradoxically, given the spirit of the book, no schema – a graph? – summarizes at one glance the numerous people, centres, prizes and countries involved, and more importantly their relationships. However, the author explains why it is so when she writes in her conclusions that the ‘overwhelmingly male cast of characters’ – including her former PhD supervisor – are not to be considered the real protagonists of the book. At the centre of the book there are only the graphs and their queerness: graphs and the vision that comes with them have kept alive what they were designed to suppress: ‘visual ambiguities, serendipitous similitudes, the seductiveness of appearance’ (p. 191).